diff --git a/lab_classes/dss/index.ipynb b/lab_classes/dss/index.ipynb index 7e81a76..f29b065 100644 --- a/lab_classes/dss/index.ipynb +++ b/lab_classes/dss/index.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:5f088aa09ece4c868c0227f55893d711723c04870addf87a331c9773fc5a1202" + "signature": "sha256:12b4ed68eb96de17bd8650a6012dc583c393ee6b237a9fb6d2eaf24e0ccb929d" }, "nbformat": 3, "nbformat_minor": 0, @@ -47,12 +47,18 @@ "* [Model Validation](./model validation.ipynb) Validation of model predictions is one of the most general and important concepts in machine learning, statistics and data science. Here we teach the general concepts and apply them to polynomial regression.\n", "* [Bayesian Regression](./Bayesian regression.ipynb) Bayesian averaging over models is one way of improving performance through reducing variance, but without increasing bias.\n", "\n", - "## Dimensionality Reduction and Classification\n", + "For the third day we will consider extensions of the fundamentals we've described. Different extensions are outlined below.\n", "\n", - "The third day focusses on dimensionality reduction and classification.\n", + "## Dimensionality Reduction\n", "\n", "* [Dimensionality reduction](./dimensionality reduction.ipynb) Unsupervised learning is an exploratory approach to understanding a data set. Here we consider dimensionality reduction as an approach to unsupervised learning.\n", + "\n", + "* [Non linear Dimensionality Reduction](./non linear dimensionality reduction.ipynb) TODO Non linear dimensionality reduction seeks to find a low dimensional space that is non linearly related to our observed data.\n", + "\n", + "## Classification and Generalized Linear Models\n", + "\n", "* [Probabilistic classification and naive Bayes](./probabilistic classification.ipynb) Classification of data is a mainstay of machine learning and data science. Here we consider the naive Bayes approach from the perspective of probabilistic modeling. \n", + "\n", "* [Logistic regression and Generalized Linear Models](./logistic regression.ipynb) Naive Bayes classifies the data by modeling the entire joint distribution of the the labels and inputs, this can be useful when there's missing data, but it requires a very rich class of models. Logistic regression models the conditional distribution of the label given the data. It also leads to a very general class of models know as 'generalized linear models'.\n" ] }, diff --git a/lab_classes/machine_learning/week9.ipynb b/lab_classes/machine_learning/week9.ipynb index a75cefa..8ee670a 100644 --- a/lab_classes/machine_learning/week9.ipynb +++ b/lab_classes/machine_learning/week9.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:e8a4041b578e09ca93ad1795a027f7cdfda80b63d4c00b2fc6df801e6399ebad" + "signature": "sha256:b89a62c5de2874c7cdc36948acc7176bd99db61b3ce247b1bf58cb5a713aacae" }, "nbformat": 3, "nbformat_minor": 0, @@ -28,7 +28,7 @@ "\n", "Mathematically we can use a trick to implement this same table. We can use the value $y$ as a mathematical switch and write that\n", "$$\n", - "P(y) = \\pi^y (1-pi)^(1-y)\n", + "P(y) = \\pi^y (1-\\pi)^{(1-y)}\n", "$$\n", "where our probability distribution is now written as a function of $y$. This probability distribution is known as the [Bernoulli distribution](http://en.wikipedia.org/wiki/Bernoulli_distribution). The Bernoulli distribution is a clever trick for mathematically switching between two probabilities if we were to write it as code it would be better described as\n", "```python\n", diff --git a/lab_classes/mlss/.ipynb_checkpoints/index-checkpoint.ipynb b/lab_classes/mlss/.ipynb_checkpoints/index-checkpoint.ipynb new file mode 100644 index 0000000..bdd79f7 --- /dev/null +++ b/lab_classes/mlss/.ipynb_checkpoints/index-checkpoint.ipynb @@ -0,0 +1,100 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:43e13b0d3446c3bca3497c75aa3b092226d220c8b4dcd5f679f4e662bfd988e9" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Machine Learning Summer School, Sydney\n", + "\n", + "### February 2015\n", + "\n", + "### Neil D. Lawrence\n", + "\n", + "## Introduction\n", + "\n", + "Welcome to the lab for the Gaussian process section at the Machine Learning Summer School in Sydney.\n", + "\n", + "This notebook provides you with the guide to your lab classes for Gaussian processes. The lab classes are intended to help get you familiar with modeling with Gaussian processes as\n", + "\n", + "The lab classes are based on our two software packages, `pods` which is used for access to datasets and `GPy` (release 21st November 2014) for Gaussian processes. You can install the GPy framework with\n", + "\n", + "```sh\n", + "pip install GPy\n", + "```\n", + "As well as the GPy software we use our `pods` software for ['open data science'](http://inverseprobability.com/2014/07/01/open-data-science/) for access to data sets and other resources.\n", + "\n", + "```sh\n", + "pip install -pre pods\n", + "```\n", + "\n", + "on some systems you may need to use ```pip install -pre pods``` to allow the prerelease to install.\n", + "\n", + "As well as these lab classes here are a range of tutorials on how to use `GPy`, many of which are written by members of the Sheffield research group. `GPy` is under active development and is released under a BSD license, you'd also be very welcome to contribute!\n", + "\n", + "\n", + "\n", + "## Review\n", + "\n", + "Before you start, if you aren't familiar with probabilistic processes, the following lab classes from the GPRS schools might be useful. The first session will allow you to become familiar with the Jupyter (the ipython notebook) and start to work with Gaussian processes.\n", + "\n", + "* [Welcome to `Jupyter`](./gprs/jupyter introduction.ipynb) A quick introduction to `Jupyter`, `python` and `numpy`. \n", + "* [Introduction to Probabilistic Regression](./gprs/probabilistic interpretations of regression.ipynb) A review of least squares, basis function modelling and the probabilistic interpretation of least squares.\n", + "* [Introduction to Bayesian Regression](./gprs/bayesian approach to regression.ipynb) Introducing priors over parameters and averaging over solutions.\n", + "\n", + "## Gaussian Processes\n", + "\n", + "The second day will focus on Gaussian process models and developing covariance functions. \n", + " \n", + "* [Introduction to Gaussian Processes](./gaussian process introduction.ipynb) We move from the Bayesian regression with polynomials to Gaussian process perspectives by looking at the priors over the function directly.\n", + "* [GPy: Introduction through Covariance Functions](./GPy introduction covariance functions.ipynb) `GPy` is a Python Gaussian process framework that implements many of the ideas we'll see in the course. In this session we introduce its covariance functions and sample from the associated Gaussian processes.\n", + "* [Gaussian Process Regression with GPy](./GPy gaussian process regression.ipynb) In this example we show how to do a simple regression model using Gaussian processes in GPy.\n", + "* [Optimizing Gaussian Processes](./GPy optimizing gaussian processes.ipynb) The parameters of the covariance function can be optimized. In this example we show how to optimize the parameters of the covariance function. (TODO HMC)\n", + "\n", + "# Advanced Topics\n", + "\n", + "Things we haven't had time to cover in the MLSS can be found below.\n", + "\n", + "### Structured Outputs with Gaussian Processes\n", + "\n", + "Gaussian processes for learning vector valued functions.\n", + "\n", + "* [Multiple Output GPs](./gprs/multiple outputs.ipynb)\n", + "* [TODO Differential Equations and Gaussian Processes](./gprs/GP differential equation.ipynb)\n", + "\n", + "\n", + "### Approximations\n", + "\n", + "These examples look at approximations for speeding up inference in Gaussian processes and/or making inference tractable.\n", + "\n", + "* [Low Rank Approximations for Gaussian Processes](./gprs/low rank approximations.ipynb)\n", + "* [Non Gaussian Likelihoods](./gprs/non gaussian likelihoods.ipynb)\n", + "* [Low Rank and Non Gaussian](./gprs/low rank and non gaussian.ipynb)\n", + "\n", + "### Dimensionality Reduction\n", + "\n", + "These examples look at dimensionality reduction with Gaussian processes.\n", + "\n", + "* [Dimensionality Reduction with Gaussian Processes](./gprs/dimensionality reduction with gaussian processes.ipynb) " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/lab_classes/mlss/GPy gaussian process regression.ipynb b/lab_classes/mlss/GPy gaussian process regression.ipynb new file mode 100644 index 0000000..f790bc1 --- /dev/null +++ b/lab_classes/mlss/GPy gaussian process regression.ipynb @@ -0,0 +1,306 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:4a95cc8ac4784d9884e9eca006446655b954da06402f08df15653d9139d722e2" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Gaussian Process Regression in GPy\n", + "\n", + "## Gaussian Process Winter School, Genova, Italy\n", + "\n", + "### 20th January 2014\n", + "\n", + "### Neil D. Lawrence and Nicolas Durrande\n", + "\n", + "In the introduction to `GPy` you saw how it was possible to build covariance functions with the GPy software. The covariance function contains the assumptions about the data in it. In the Gaussian process, the covariance funciton *encodes* the model. However, to make predictions, you need to combine the model with data. \n", + "\n", + "If the data we are given, $\\mathbf{y}$ is *real* valued, then the problem is known as a regression problem. If a Gaussian noise model is used, then this is known as Gaussian process regression.\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%matplotlib inline\n", + "import numpy as np\n", + "import pods\n", + "import pylab as plt\n", + "import GPy\n", + "from IPython.display import display" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stderr", + "text": [ + "/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/pytz/__init__.py:29: UserWarning: Module pods was already imported from /Users/neil/sods/ods/pods/__init__.pyc, but /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages is being added to sys.path\n", + " from pkg_resources import resource_stream\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will now combine the Gaussian process prior with some data to form a GP regression model with GPy. We will generate data from the function \n", + "$$\n", + "f(x) = \u2212 \\cos(\\pi x ) + \\sin(4\\pi x )\n", + "$$ \n", + "over $[0, 1]$, adding some noise to give $y(x) = f(x) + \\epsilon$, with the noise being Gaussian distributed, $\\epsilon \\sim \\mathcal{N}(0, 0.01)$. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "X = np.linspace(0.05,0.95,10)[:,None]\n", + "Y = -np.cos(np.pi*X) + np.sin(4*np.pi*X) + np.random.normal(loc=0.0, scale=0.1, size=(10,1)) \n", + "plt.figure()\n", + "plt.plot(X,Y,'kx',mew=1.5)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 6, + "text": [ + "[]" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A GP regression model based on an exponentiated quadratic covariance function can be defined by first defining a covariance function, " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "k = GPy.kern.RBF(input_dim=1, variance=1., lengthscale=0.2)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And then combining it with the data to form a Gaussian process model," + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "model = GPy.models.GPRegression(X,Y,k)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just as for the covariance function object, we can find out about the model using the command `display(m)`. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "display(model)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n", + "

\n", + "Model: GP regression
\n", + "Log-likelihood: -13.3414898005
\n", + "Number of Parameters: 3
\n", + "

\n", + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n", + "\n", + "\n", + "\n", + "
GP_regression.ValueConstraintPriorTied to
rbf.variance 1.0 +ve
rbf.lengthscale 0.2 +ve
Gaussian_noise.variance 1.0 +ve
" + ], + "metadata": {}, + "output_type": "display_data", + "text": [ + "" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that by default the model includes some observation noise\n", + "with variance 1. We can see the posterior mean prediction and visualize the marginal posterior variances using \n", + "```python\n", + "model.plot()\n", + "```" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "_ = model.plot()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The actual predictions of the model for a set of points `Xstar`\n", + "(an $m \\times p$ array) can be computed using \n", + "\n", + "```python\n", + "Ystar, Vstar, up95, lo95 = model.predict(Xstar)`\n", + "```\n", + "\n", + "### Exercise 1\n", + "\n", + "What do you think about this first fit? Does the prior given by the GP seem to be\n", + "appropriate?" + ] + }, + { + "cell_type": "raw", + "metadata": {}, + "source": [ + "# Exercise 1 answer" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exercise 2\n", + "\n", + "The parameters of the models can be modified using the parameter name, for example \n", + "```python\n", + "model.Gaussian_noise.variance = 0.001\n", + "```\n", + "Change the values of the parameters to obtain a better fit." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Exercise 2 answer here" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 12 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we saw when we introduced GPy and covariance functions, random sample paths from the conditional GP can be obtained using\n", + "```python\n", + "np.random.multivariate_normal(mu[:,0],C)\n", + "``` \n", + "Now you can sample paths from the *posterior* process by first obtaining the mean and covariance of the posterior, `mu` and `C`. These can be obtained from the `predict` method, \n", + "```python\n", + "mu, C, up95, lo95 = model.predict(Xp,full_cov=True)\n", + "```\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exercise 3\n", + "\n", + "Obtain 10 samples from the posterior sample and plot them alongside the data below." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Exercise 3" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 13 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/lab_classes/mlss/GPy introduction covariance functions.ipynb b/lab_classes/mlss/GPy introduction covariance functions.ipynb new file mode 100644 index 0000000..19fecef --- /dev/null +++ b/lab_classes/mlss/GPy introduction covariance functions.ipynb @@ -0,0 +1,845 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:81d15f4e5504b5e3a79a177c06233272245e10b15057208834e75123cc7f2775" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# GPy Introduction: Covariance Functions in GPy\n", + "## Gaussian Process Winter School, Genova, Italy\n", + "\n", + "### 20th January 2014\n", + "\n", + "### Neil D. Lawrence and Nicolas Durrande\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%matplotlib inline\n", + "from IPython.display import display\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import pods\n", + "import GPy" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stderr", + "text": [ + "/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/pytz/__init__.py:29: UserWarning: Module pods was already imported from /Users/neil/sods/ods/pods/__init__.pyc, but /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages is being added to sys.path\n", + " from pkg_resources import resource_stream\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Covariance Functions in GPy\n", + "\n", + "We've [introduced Gaussian processes](gaussian process introduction.ipynb) and built a simple class in python for fitting these models. In the last session we introduced Gaussian process models through constructing covariance functions in `numpy`. The `GPy` software is a BSD licensed software package for modeling with Gaussian processes in python. It is designed to make it easy for the user to construct models and interact with data. The software is BSD licensed to ensure that there are as few as possible constraints on its use. The `GPy` documentation is produced with Sphinx and is available [here](http://gpy.readthedocs.org/en/latest/).\n", + "\n", + "In the introduction to Gaussian processes we defined covariance functions (or kernels) as functions to which we passed objects in `GPy` covariance functions are objects.\n", + "\n", + "In `GPy` the covariance object is stored in `GPy.kern`. There are several covariance functions available. The exponentiated quadratic covariance is stored as `RBF` and can be created as follows." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "kern = GPy.kern.RBF(input_dim=1)\n", + "display(kern)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n", + "\n", + "\n", + "
rbf.ValueConstraintPriorTied to
variance 1.0 +ve
lengthscale 1.0 +ve
" + ], + "metadata": {}, + "output_type": "display_data", + "text": [ + "" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here it's been given the name 'rbf' by default and some default values have been given for the lengthscale and variance, we can also name the covariance and change the initial parameters as follows," + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "kern = GPy.kern.RBF(input_dim=1, name='signal', variance=4.0, lengthscale=2.0)\n", + "display(kern)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n", + "\n", + "\n", + "
signal.ValueConstraintPriorTied to
variance 4.0 +ve
lengthscale 2.0 +ve
" + ], + "metadata": {}, + "output_type": "display_data", + "text": [ + "" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plotting the Kernel\n", + "\n", + "The covariance function expresses the covariation between two points. the `.plot()` method can be applied to the kernel to discover how the covariation changes as a function as one of the inputs with the other fixed (i.e. it plots `k(x, z)` as a function of a one dimensional `x` whilst keeping `z` fixed. By default `z` is set to `0.0`." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "kern.plot()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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These parameters can be changed later in a couple of different ways firstly, we can simple set the field value of the parameters. If we want to change the lengthscale of the covariance to 3.5 we do so as follows." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "kern.lengthscale = 3.5\n", + "display(kern)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n", + "\n", + "\n", + "
signal.ValueConstraintPriorTied to
variance 4.0 +ve
lengthscale 3.5 +ve
" + ], + "metadata": {}, + "output_type": "display_data", + "text": [ + "" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can even change the naming of the parameters, let's imagine that this covariance function was operating over time instead of space, we might prefer the name `timescale` for the `lengthscale` parameter." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "kern.lengthscale.name = 'timescale'\n", + "display(kern)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n", + "\n", + "\n", + "
signal.ValueConstraintPriorTied to
variance 4.0 +ve
timescale 3.5 +ve
" + ], + "metadata": {}, + "output_type": "display_data", + "text": [ + "" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can set the time scale appropriately." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "kern.timescale = 10.\n", + "display(kern)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n", + "\n", + "\n", + "
signal.ValueConstraintPriorTied to
variance 4.0 +ve
timescale 10.0 +ve
" + ], + "metadata": {}, + "output_type": "display_data", + "text": [ + "" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Further Covariance Functions in GPy\n", + "\n", + "There are other types of basic covariance function in `GPy`. For example the `Linear` kernel,\n", + "$$\n", + "k(\\mathbf{x}, \\mathbf{z}) = \\alpha \\mathbf{x}^\\top \\mathbf{z}\n", + "$$\n", + "and the `Bias` kernel,\n", + "$$\n", + "k(\\mathbf{x}, \\mathbf{z}) = \\alpha\n", + "$$\n", + "where everything is equally correlated to each other. `Brownian` implements Brownian motion which has a covariance function of the form,\n", + "$$\n", + "k(t, t^\\prime) = \\alpha \\text{min}(t, t^\\prime).\n", + "$$\n", + "\n", + "Broadly speaking covariances fall into two classes, *stationary* covariance functions, for which the kernel can always be written in the form\n", + "$$\n", + "k(\\mathbf{x}, \\mathbf{z}) = f(r)\n", + "$$\n", + "where $f(\\cdot)$ is a function and $r$ is the distance between the vectors $\\mathbf{x}$ and $\\mathbf{z}$, i.e.,\n", + "$$\n", + "r = ||\\mathbf{x} - \\mathbf{z}||_2 = \\sqrt{\\left(\\mathbf{x} - \\mathbf{z}\\right)^\\top \\left(\\mathbf{x} - \\mathbf{z}\\right)}.\n", + "$$\n", + "This partitioning is reflected in the object hierarchy in GPy. There is a base object `Kern` and this is inherited by `Stationary` to form the stationary covariance functions (like `RBF` and `Matern32`).\n", + "\n", + "## Computing the Covariance Function\n", + "\n", + "When using `numpy` to construct covariances we defined a function, `kern_compute` which returned a covariance matrix given the name of the covariance function. In `GPy`, the base object `Kern` implements a method `K`. That allows us to compute the associated covariance. Visualizing the structure of this covariance matrix is often informative in understanding whether we have appropriately captured the nature of the relationship between our variables in our covariance function. In `GPy` the input data is assumed to be provided in a matrix with $n$ rows and $p$ columns where $n$ is the number of data points and $p$ is the number of features we are dealing with. We can compute the entries to the covariance matrix for a given set of inputs `X` as follows." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "data = pods.datasets.olympic_marathon_men()\n", + "# Load in the times of the olympics\n", + "X = data['X']\n", + "K=kern.K(X)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now to visualize this covariation between the time points we plot it as an image using the `imshow` command from matplotlib.\n", + "```python\n", + "plt.imshow(K, interpolation='None')\n", + "```\n", + "Setting the interpolation to `'None'` prevents the pixels being smoothed in the image. To better visualize the structure of the covariance we've also drawn white lines at the points where the First World War and the Second World War begin. At other points the Olympics are held every four years and the covariation is given by the computing the covariance function for two points which are four years apart, appropriately scaled by the time scale." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def visualize_olympics(K):\n", + " \"\"\"Helper function for visualizing a covariance computed on the Olympics training data.\"\"\"\n", + " fig, ax = plt.subplots(figsize=(8,8))\n", + " im = ax.imshow(K, interpolation='None')\n", + "\n", + " WWI_index = np.argwhere(X==1912)[0][0]\n", + " WWII_index = np.argwhere(X==1936)[0][0]\n", + "\n", + " ax.axhline(WWI_index+0.5,color='w')\n", + " ax.axvline(WWI_index+0.5,color='w')\n", + " ax.axhline(WWII_index+0.5,color='w')\n", + " ax.axvline(WWII_index+0.5,color='w')\n", + " plt.colorbar(im)\n", + " \n", + "visualize_olympics(kern.K(X))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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If we increase the timescale to 20 we obtain stronger dependencies between the wars." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "kern.timescale = 20\n", + "visualize_olympics(kern.K(X))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Covariance Matrices and Covariance Functions\n", + "\n", + "A Gaussian process specifieds that any finite set of realizations of the function will jointly have a Gaussian density. In other words, if we are interested in the joint distribution of function values at a set of particular points, realizations of those functions can be sampled according to a Gaussian density. The Gaussian process provides a prior over an infinite dimensional object: the function. For our purposes we can think of a function as being like an infinite dimensional vector. The mean of our Gaussian process is normally specified by a vector, but is now itself specified by a *mean function*. The covariance of the process, instead of being a matrix is also a *covariance function*. But to construct the infinite dimensional matrix we need to make it a function of two arguments, $k(\\mathbf{x}, \\mathbf{z})$. When we compute the covariance matrix using `k.K(X)` we are computing the values of that matrix for the different entries in $\\mathbf{X}$. `GPy` also allows us to compute the cross covariance between two input matrices, $\\mathbf{X}$ and $\\mathbf{Z}$.\n", + "\n", + "## Sampling from a Gaussian Process\n", + "\n", + "We cannot sample a full function from a process because it consists of infinite values, however, we can obtain a finite sample from a function as described by a Gaussian process and visualize these samples as functions. This is a useful exercise as it allows us to visualize the type of functions that fall within the support of our Gaussian process prior. Careful selection of the right covariance function can improve the performance of a Gaussian process based model in practice because the covariance function allows us to bring domain knowledge to bear on the problem. If the input domain is low dimensional, then we can at least ensure that we are encoding something reasonable in the covariance through visualizing samples from the Gaussian process. \n", + "\n", + "For a one dimensional function, if we select a vector of input values, represented by `X`, to be equally spaced, and ensure that the spacing is small relative to the lengthscale of our process, then we can visualize a sample from the function by sampling from the Gaussian (or a multivariate normal) with the `numpy` command\n", + "```python\n", + "F = np.random.multivariate_normal(mu, K, num_samps).T\n", + "```\n", + "where `mu` is the mean (which we will set to be the zero vector) and `K` is the covariance matrix computed at the points where we wish to visualize the function. The transpose at the end ensures that the the matrix `F` has `num_samps` columns and $n$ rows, where $n$ is the dimensionality of the *square* covariance matrix `K`. \n", + "\n", + "Below we build a simple helper function for sampling from a Gaussian process and visualizing the result. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def sample_covariance(kern, X, num_samps=10):\n", + " \"\"\"Sample a one dimensional function as if its from a Gaussian process with the given covariance function.\"\"\"\n", + " from IPython.display import HTML\n", + " display(HTML('

Samples from a Gaussian Process with ' + kern.name + ' Covariance

'))\n", + " display(kern)\n", + " K = kern.K(X) \n", + "\n", + " # Generate samples paths from a Gaussian with zero mean and covariance K\n", + " F = np.random.multivariate_normal(np.zeros(X.shape[0]), K, num_samps).T\n", + "\n", + " fig, ax = plt.subplots(figsize=(8,8))\n", + " ax.plot(X,F)\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 12 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We are now in a position to define a vector of inputs, a covariance function, and then to visualize the samples from the process." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# create an input vector\n", + "X = np.linspace(-2, 2, 200)[:, None]\n", + "\n", + "# create a covariance to visualize\n", + "kern = GPy.kern.RBF(input_dim=1)\n", + "\n", + "# perform the samples.\n", + "sample_covariance(kern, X)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "

Samples from a Gaussian Process with rbf Covariance

" + ], + "metadata": {}, + "output_type": "display_data", + "text": [ + "" + ] + }, + { + "html": [ + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n", + "\n", + "\n", + "
rbf.ValueConstraintPriorTied to
variance 1.0 +ve
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gFxwsQMLyBLhPcUevT3uhdXfj5sE7ckRUfH18gG7d5Lh8eSEMhlIMGrTv+mxb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bAAAg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\ne0cSHDybI0cetdoxbaXDCVkpt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Samples from a Gaussian Process with poly Covariance

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poly.ValueConstraintPriorTied to
variance 1.0 +ve
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pa+P/4uK4KS6OMDt1PMnOhkcfhY8+gssu00/7GjjQLk8lhN0pm6LskTLKHisj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\nn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+ "text": [ + "" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Combining Covariance Functions\n", + "\n", + "Covariance functions can be combined in various ways to make new covariance functions. \n", + "\n", + "### Adding Covariance Functions\n", + "\n", + "Perhaps simplest thing you can do to combine covariance functions is to add them. The sum of two Gaussian random variables is also Gaussian distributed, with a covariance equal to the sum of the covariances of the original variables (similarly for the mean). This implies that if we add two functions drawn from Gaussian processes together, then the result is another function drawn from a Gaussian process, and the covariance function is the sum of the two covariance functions of the original process.\n", + "$$\n", + "k(\\mathbf{x}, \\mathbf{z}) = k_1(\\mathbf{x}, \\mathbf{z}) + k_2(\\mathbf{x}, \\mathbf{z}).\n", + "$$\n", + "Here the domains of the two processes don't even need to be the same, so one of the covariance functions could perhaps depend on time and the other on space,\n", + "$$\n", + "k\\left(\\left[\\mathbf{x}\\quad t\\right], \\left[\\mathbf{z}\\quad t^\\prime\\right]\\right) = k_1(\\mathbf{x}, \\mathbf{z}) + k_2(t, t^\\prime).\n", + "$$\n", + "\n", + "In `GPy` the addition operator is overloaded so that it is easy to construct new covariance functions by adding other covariance functions together." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "k1 = GPy.kern.RBF(1, variance=4.0, lengthscale=10., name='long term trend')\n", + "k2 = GPy.kern.RBF(1, variance=1.0, lengthscale=2., name='short term trend')\n", + "kern = k1 + k2\n", + "kern.name = 'signal'\n", + "kern.long_term_trend.lengthscale.name = 'timescale'\n", + "kern.short_term_trend.lengthscale.name = 'timescale'\n", + "display(kern)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
signal.ValueConstraintPriorTied to
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" + ], + "metadata": {}, + "output_type": "display_data", + "text": [ + "" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Multiplying Covariance Functions\n", + "\n", + "An alternative is to multiply covariance functions together. This also leads to a valid covariance function (i.e. the kernel is within the space of Mercer kernels), although the interpretation isn't as straightforward as the additive covariance. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "k1 = GPy.kern.Linear(1)\n", + "k2 = GPy.kern.RBF(1)\n", + "kern = k1*k2\n", + "display(kern)\n", + "fig, ax = plt.subplots(figsize=(8,8))\n", + "im = ax.imshow(kern.K(X), interpolation='None')\n", + "plt.colorbar(im)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n", + "\n", + "\n", + "\n", + "
mul.ValueConstraintPriorTied to
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dmFwNqzSnhG0JlEu/AocEWUrX7tu44/gW5OR5nMa0rXemsdK+1MdKZNQYmnGX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+ "text": [ + "" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exercise 3\n", + "\n", + "Now try a range of different covariance functions and values and plot the corresponding sample paths for each using the same approach given above." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Try plotting sample paths here" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exercise 4\n", + "\n", + "Can you tell the covariance structures that have been used for generating the\n", + "sample paths shown in the figures below?\n", + "
\n", + "
\n", + "\n", + "\n", + "
\n", + "\"Figure\"Figure\"Figure
\"Figure\"Figure\"Figure
\n", + "
\n" + ] + }, + { + "cell_type": "raw", + "metadata": {}, + "source": [ + "# Exercise 4 answer" + ] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/lab_classes/mlss/GPy optimizing gaussian processes.ipynb b/lab_classes/mlss/GPy optimizing gaussian processes.ipynb new file mode 100644 index 0000000..dfeaae2 --- /dev/null +++ b/lab_classes/mlss/GPy optimizing gaussian processes.ipynb @@ -0,0 +1,1263 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:e536d3195e4f11c355f3ffa9515f59741de6135d0301c7d95ce8436884cac106" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Introduction to GPy: Gaussian Process Regression in GPy\n", + "\n", + "## Gaussian Process Winter School, Genova, Italy\n", + "\n", + "### 20th January 2014\n", + "\n", + "### Neil D. Lawrence and Nicolas Durrande\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%matplotlib inline\n", + "import numpy as np\n", + "import pods\n", + "import pylab as plt\n", + "import GPy\n", + "from IPython.display import display" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stderr", + "text": [ + "/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/pytz/__init__.py:29: UserWarning: Module pods was already imported from /Users/neil/sods/ods/pods/__init__.pyc, but /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages is being added to sys.path\n", + " from pkg_resources import resource_stream\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Covariance Function Parameter Estimation\n", + "\n", + "In this session we are going to optimize the parameters of the Gaussian process using gradient based optimization approaches. These maximize the likelihood function: which is defined as the probability of the model given the parameters, $p(\\mathbf{y}|\\mathbf{X}, \\boldsymbol{\\theta})$. \n", + "\n", + "First we'll load in the olympic marathon data." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "data = pods.datasets.olympic_marathon_men()\n", + "x = data['X']\n", + "y = data['Y']" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then we'll construct a Gaussian process model with an exponentiated quadratic covariance function." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "k = GPy.kern.RBF(1)\n", + "model = GPy.models.GPRegression(x, y, k)\n", + "display(model)\n", + "model.plot()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n", + "

\n", + "Model: GP regression
\n", + "Log-likelihood: -118.821194703
\n", + "Number of Parameters: 3
\n", + "Updates: True
\n", + "

\n", + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n", + "\n", + "\n", + "\n", + "
GP_regression.ValueConstraintPriorTied to
rbf.variance 1.0 +ve
rbf.lengthscale 1.0 +ve
Gaussian_noise.variance 1.0 +ve
" + ], + "metadata": {}, + "output_type": "display_data", + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 3, + "text": [ + "{'dataplot': [],\n", + " 'gpplot': [[],\n", + " [],\n", + " [],\n", + " []]}" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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dPWir8+t5xzxetwN9sVEUigru/5HVwgGAj376JgBqJLhh/TOGHgWlFK+/sh4f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\nF4tY53xzxcFjmtFs1FFmc7BDTlZCjO9egqQfuBNkfS0GAYn94Ag7DjG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+ "text": [ + "" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Rather sensibly, we've given the model an initial plot, and we can clearly see that the inital length scale is too low. This makes sense, our prior says that the length scale is 1 year, which means that athletic performance varies across very short time scales. This is perhaps unlikely, let's choose a larger lengthscale and try again.\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "model.rbf.lengthscale = 10.\n", + "model.plot()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 4, + "text": [ + "{'dataplot': [],\n", + " 'gpplot': [[],\n", + " [],\n", + " [],\n", + " []]}" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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9aJuSt2h7+7w8t+kAAB+5OT5LrwohzptRksu/fuFW/vG+60hPdbHvcD1/969P\n8s6+k2aHFnNTMmk/t2k/fQM+Fs0uYk5FvtnhCCFGQSnF2mWV/OQbH2b5glI8fT6+9dMXefz5nTFd\n7stsUy5p9/X7+NNr+wD4yAeWmRyNEGKsMtKS+cZnb+Ke21diUYrHntvBT367heAlhhBONlMuab+w\n5SC9fV7mVuYzf2aB2eEIIcbBYlHcfeNSvvbpG3DYrbz0RjUPPfJyxMaWx7MplbQHvH7+sGEPEGpl\nx/OEDCHEyFYtLudfv3ArKclOtu89yTf+4zn6BoYvKZDoplTSfumNarp6Bqgqm8aSOcVmhyOEiIC5\nlQU8/KXbycl0U13byL/89MVJ3eKeUNJWSk1XSm1SSh1USh1QSn0+UoFFms8f4JlXQ63sD3/gMmll\nCzGJlBZm8dAXbyMrPZn9R87y0CMv4w8EzQ4rKiba0vYD/0drPQ9YBfxvpdSciYcVea++WUN7Vx8V\n03NYsaDU7HCEEBFWkJvOv37hVtJSXOw8cJrvPfraiIW6EtGEkrbWulFrvSe83QscAuJjwcch/IEg\nT728G4AP37RUWtlCTFIlhVl86/O3kOxysPXdYzzyu62TbjhgxPq0lVJlwBLg7UgdM1I2vX2Elo5e\nSgoyWb24wuxwhBBRVFmSyzc/9wHsNivPv36Q5zbtNzukiIrINHalVArwFPCFcIv7Aj/5/vmFOpev\nvoIVq6+MxGlHJRg0BldY/9BNSyd1vQIhRMi8ygL+/p6r+O4vNvDz379FQW46y+O8W/SdbW+wY9vW\n0DfDfDiYcMEopZQd+DPwotb6hxd53tSCURu3H+b7v9pI4bR0/vOBj0z54upCTCWPPbeDx5/fSZLT\nzr99+Q7KixOj/PJwBaMmOnpEAb8Aqi+WsM0WDBr87sVdAHzoxqWSsIWYYv7ylmWsW15Jv9fPv/z0\nxTEt6ByvJprFLgc+BlyllNod/oqbwtRbdtZS39RFQW4aV62sMjscIUSMKaX4wsevYmbpNJrbe/je\nLzck/IiSiY4e2aq1tmitF2utl4S/XopUcBMRDBo88cJOAD5802UxWStQCBF/HHYb93/6etLcLnYd\nPMMTz+8yO6QJmbSZTFrZQohzpmWl8qVPXYtS8MQLO9l54JTZIY3bpEzaZray+71+Dh1vouZEM7Un\nWzh8spmDxxppaOmZdONFhUgkS+dO569uXYHW8O+PvkZja7fZIY3LpFy5xoxWdltnH02tXUxLT+ID\nK8tJdtmDD/h+AAAa1klEQVQHnzO05nh9B4dPt+LxBigvzibZ5YhJXEKI8z5041IOn2hix/5TPPTI\ny3z3y3fgsCdWGpx0Le1AMMjjz8eula215tDxJqw6wF3rZ7FuaekFCRvAohSVxVncvKaSO9dW0d3t\n4WBtA4FAYt8QESLRWCyKf/jkNeTnpHHsdCs/e+INs0Mas0mXtF95s4azzV0UTktn/cqZUT1X0DDY\nd/gs6xYWcfnC6aOaHm+1WrjmsjJuWT2DE2daqG/qimqMQogLpSQ7B+twv/JmDa++VWN2SGMyqZL2\ngNfP438OtbI/fttKbFZr1M51LmHfdmUluZnuMb8+2WXn9rVVFGQ6OVjbmPDDkIRIJBXTc/jsR9cC\n8J+Pb+F4XavJEY3epEraf3ptHx3dfcwsncblS6NXY0Rrzf7DZ/ng2ircE+ybXjAjjxuWl3LoaAM9\nnsQf+C9EorhuzWyuv3w2Pn+Qh/7rFTz9XrNDGpVJk7S7evt5+pVQvexPfnBVVCv5Vdc2ccOKsvf1\nXY9XeoqLD10zh+5uD3WN5k35F2Kq+fSHr6S8OJuGli5+9OtNCTHCa9Ik7SdffJe+AR9L505n4ayi\nqJ3ndGMnCyqyyckYe5fIcJRSXL+igvwMFzXHmyN6bCHExTkdNu7/mxtIdjl4a/eJwUW/49mkSNqN\nrd08//oBAD5xx6qonafX48Wqg8wpy4naORbNzGPN/AJ2H6qbtCtvCBFPCqel8/f3XAXAL5/ZTnVt\ng8kRDW9SJO2f//5NAgGDq1ZWUTE9egn1RH0b1y4vj9rxzynITuHu9bM4cqKJjq6+qJ9PiKluzZIK\n7rh2EUHD4OGfv0pnd/xedwmftHfsP8X2vSdJctqj2so+dqaN1fMKscRo1Runw8bdV83G5/VyqqEj\nJucUYiq7546VzK3Mp63Tw7/H8VJlCZ20ff4AjzwZKhr+0VuWkR3hfubz5wlixaA0Pz0qx78UpRRX\nX1ZGaa6b/UcaMOL0j0iIycBmtfKV+64nIzWJPTV1g8OH401CJ+1nXt1LQ0s3JQWZ/MXVC6J2nsMn\nmrguBt0ilzKvPJdbVldw6FgjLR0e0+IQYrLLznDzpU9di0UpnnhhV1wWlkrYpN3U2s2T4QUOPvOR\nK6M2kaazu5+Saak47NGbqDMaKckO7r5qNk6LpvqYTMYRIloWzy7mr25dDsD3fvkaTXFWWCohk7bW\nmp8+vgWfP8jaZZVRHeJX39TJ6vnRO/5YKKVYPb+I65aVcuxUC6fqpa9biGi4+8alLJtfQo/Hy7/8\n54v0DfjMDmlQQibtl96oZtfBM6QkO/nUXWuidp6m9l5ml2RGdaLOeGSkuLhjbRVzSzM4cqKJY2fa\npOUtRARZLIov3XstxXkZnKxv598fjZ8VbxIuaTe0dPGLp98C4G//cm3Ubj4CtLf3srAyL2rHn6iy\nggzuWFvFqjl5nKlvo7q2kRP17QSD8fHHJUQiS0l28o2/vYmUZCfv7DvFr//4ttkhAQlWTztoGPzg\nVxsZ8AZYu6yStcsqo3auhpYe5pRlRe34kTQt083NayrRWnO2tYfqk214fQECBgQNTXBwaq4i9Jlh\n6Pc69KgCVOh5TWg16HP7JSc7yc1IIclli7tPHUJEU1FeBl/79A1840d/5ulX9lCUl8H1l88xNaaE\nStp/eHUv1ccayUp389mPXhnVc3V2e7h2aXFUzxFpSimKctMoyk274HHD0BhaM7SsglKh/S3hfy/G\n0Jpg0KC1s4/TjV3Ud/jwBQy8AYOUJCdFeelYLJLExeS2cFYRn/nIFfzkt1v48WOvk56axMqFZabF\nkzBJ+9DxRn7z7DsAfOHj60l1u6J2rrbOPioK0kbeMUFYLAoLY0+uFqWw2KwU5KRSkJM6+LjWmjPN\n3Rw6GVqJx2F3UFYUf33/QkTKTWvn0dLey5MvvcvD/98rfOvztzB/ZqEpsSREn3Zndx/feeQVAkGD\n265eyGXzSqJ6vqa2bpZU5Uf1HIlMKUVJXjo3rJzBB9fOYkllNifPtHLgaAO9CVLeUoix+uvbVnDj\nlXPx+YN86ycvcvyMOTW4476l7fcH+fYjL9PW6WFuZT6fvDN6U9UBevu8FGYmSatxDM51yQSCBtv2\n11Fd305+bjpZ6clmhzasQNCgt99HX78fT98AvoAx2KdvAVxOOyluJ6nJTux2K1bpCprSlFJ89qNX\n0uMZ4M13j/PP//Fn/vXvb6WsKDu2cUS7fqxSSh84Pb4a0Vprvv+rjWx6+wjZGW5+cP+dZKVHb7QI\nwIGjDdy1vgqrJSE+hMQlrTW7jzRyvKGbzHQ3+UO6VsyKx9Pv40xDJxYLOO0WbBYLDpuF9BQn2enJ\nZKa6cDntg0k7EAjS2++no7uPtq5++v1BAgGDgNYYQU3A0ASCoWsnIy2JnAy36ROwRGz4/UG+9Z8v\nsrv6DKluJ9/6/C3MLJ0W0XNoQ7OgLBOt9ftaCnGbtLXW/OoP23n6lT24nDb+7Ut3RLWCH4RqjLS0\ndHD9yhlRPc9UUn2ihUOn20lOclJSkBmz8waCBmcaO/H5/LjsVvIyk5hfMQ2nI3IfLrXWeP0GZ1u7\nOdPYTb8vMJjMg0FNEI1FKXIy3WSnJ2ORhsCk4fMHeOiRV9ix/xTJLgcPfO4DzK0siNjxEzJp/+6F\nXfzPs+9gtVj4+mdvZPmC0ihEd6GDtQ38xeWVuCJ4YYuQY/Ud7DvWgtVmo6I4KyrdTz5/kBP1bSit\nSU22s2jGtHGt3xkpgaBBvzfAqaZuGlt78AWNUEI3QkldAxYF2ZkpZKS6sFktk6Jb7txoJcPQeP0B\n+gf8GIYGDVqBy2Ej2eXAZrMMO3op3gWCQb736Gu8sesYToeNr9x3HSsiNKokoZK21prf/nknjz+/\nE6Xgy5+6LqrjsYee91RdKzevif65prLGtl521DTi8QYoL8oiJdk5oeMN+PycONOOzQqpSXZWzCkk\n1T2xY8bKuaR+pqmLls4+/AEDf9DA0KGLNqhDcxMMAww0FsBA4bBZSXLZSU5ykOyyY7dZzw2zn3AC\n1OGhoTocn9cXoNczQE+fj2DwfJ+/1aJCo4ssDCZeqwJlsWCzKmwWsFksJLvsuJMcWCwKq0VhaPD0\n++jxePEFjNAbmaEJBAx8fgN3spPivHSs1sT4VBI0DP7f/2xmw7bDKAV/fdtK7r5hycT/HxIlaQcN\ng5///i2e27Qfi1J84Z6ruGbVrKjGd86J+g4uq8y+YGibiJ5A0GD7wXpau0I3AIvzM0hzO0f8Yw8G\nDc629NDT24/TbiHd7WD5nMKIrdcZr861XgNBgwFvgC6Pl26Pl+7eAfxBg6ARSrhBDecG5BsaFBqD\nUKJVDN0IObcZGm8fGrdvUQqrBaxK4U52kJWaREZaEklOG9Zw8o1G69jQmobWHg6eaKV3wI/Dbqes\nKDqfyiJJa82TL77L/4SHJK9dVsnnP74el2P8f5MJkbT7Bnx89xcb2LH/FDarhS/dey1XXBa7vuUj\nJ5u548qZMTufOM/nD7L/WBPNnf0Ewjf5guGP0wAWS6hlZ7NacNmtzJyeSfG0tJgtSCHM0dDWy66a\nRvr9BlWludhs8d36fnvvCf7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+ "text": [ + "" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That seems better, now we can think about optimization. First though we have to consider the fact that some of the parameters are constrained (for example lengthscales and variances can only be positive). `GPy` allows the user to specify such constraints when constructing the model.\n", + "\n", + "### Parameter Constraints\n", + "\n", + "As we have seen during the lectures, the parameters values can be estimated by maximizing the likelihood of the observations. Since we don\u2019t want one of the variance to become negative during the optimization, we can constrain all parameters to be positive before running the optimisation." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "model.constrain_positive('.*') # Constrains all parameters matching .* to be positive, i.e. everything" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "WARNING: reconstraining parameters GP_regression\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The warnings are because the parameters are already constrained by default, the software is warning us that they are being reconstrained.\n", + "\n", + "Now we can optimize the model using the \n", + "```\n", + "model.optimize()\n", + "``` method." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "model.optimize()\n", + "model.plot()\n", + "display(model)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n", + "

\n", + "Model: GP regression
\n", + "Log-likelihood: -6.94713791215
\n", + "Number of Parameters: 3
\n", + "Updates: True
\n", + "

\n", + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n", + "\n", + "\n", + "\n", + "
GP_regression.ValueConstraintPriorTied to
rbf.variance 25.3995048241 +ve
rbf.lengthscale 152.045313 +ve
Gaussian_noise.variance0.048506484546 +ve
" + ], + "metadata": {}, + "output_type": "display_data", + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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ereC51z+hoqYZgNm5qdx18zLm5qV5Nc6JYGhNeVUzvVYrESEWFkxPISVeJtQS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\nKv2OJ4GOlOBHuv5kKMF39Vh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+ "text": [ + "" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The parameters obtained after optimisation can be compared with the values selected by hand above. As previously, you can modify the kernel used for building the model to investigate its influence on the model.\n", + "\n", + "By adding covariance functions together we can try and decompose the observation in to a longer lengthscale process and a shorter lengthscale process. Below we consider a GP that is initialised with a long lengthscale exponentiated quadratic, and a Matern $\\frac{5}{2}$ covariance to take account of shorter lengthscale effects. We also add a bias term to allow for an overall average." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Exercise 5 a) answer \n", + "kern = GPy.kern.RBF(1, lengthscale=80) + GPy.kern.Matern52(1, lengthscale=10) + GPy.kern.Bias(1)\n", + "model = GPy.models.GPRegression(x, y, kern)\n", + "model.optimize()\n", + "model.plot()# Exercise 5 d) answer\n", + "model.log_likelihood()\n", + "display(model)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n", + "

\n", + "Model: GP regression
\n", + "Log-likelihood: -5.99078279431
\n", + "Number of Parameters: 6
\n", + "Updates: True
\n", + "

\n", + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
GP_regression.ValueConstraintPriorTied to
add.rbf.variance 2.58425103654 +ve
add.rbf.lengthscale 102.447254296 +ve
add.Mat52.variance 0.0204066240251 +ve
add.Mat52.lengthscale 6.52778209539 +ve
add.bias.variance 17.5408872485 +ve
Gaussian_noise.variance0.0368133074589 +ve
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hEmy3khxUy6cv/4S7vvp1/vnffgrQndCfeXH9gLX98cRlGJwurCImzMaq+Rmy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\n82V1FBRVkl9URWllAwdOXOD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+ "text": [ + "" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exercise 2\n", + "\n", + "Now model Model the data with a product of an exponentiated quadratic covariance function and a linear covariance function. Fit the covariance function parameters. Why are the variance parameters of the linear part so small? How could this be fixed?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Exercise 2 answer" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "DRAFT\n", + "===\n", + "\n", + "## Gene Expression Example\n", + "\n", + "We now look at a real data example where there are multiple modes to the solution. In [Kalaitzis and Lawrence](http://www.biomedcentral.com/1471-2105/12/180) the objective was to understand when a temporal gene expression was either *noise* or had some underlying signal. To determine this Gaussian process models were fitted with and without a temporal kernel, and the likelihoods were compared. In the thousands of genes they considered, there were some where the posterior error surface for the lengthscale and the signal/noise ratio was multi modal. We will consider one of those genes. The example can also be rerun as\n", + "```python\n", + "GPy.examples.regression.multiple_optima()\n", + "```\n", + "The first thing to do is write a helper function for computint the likelihoods add different signal/noise ratios and different lengthscales. This is to allow us to visualize the error surface. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def contour_objective(x, y, log_length_scales, log_SNRs, kernel_call=GPy.kern.RBF):\n", + " '''Helper function to contour an objective function in a set up where there \n", + " is a kernel for signal corrupted by noise.'''\n", + " lls = []\n", + " num_data=y.shape[0]\n", + " kernel = kernel_call(1, variance=1., lengthscale=1.)\n", + " model = GPy.models.GPRegression(x, y, kernel=kernel)\n", + " y = y - y.mean()\n", + " for log_SNR in log_SNRs:\n", + " SNR = 10.**log_SNR\n", + " length_scale_lls = []\n", + " for log_length_scale in log_length_scales:\n", + " model['.*lengthscale'] = 10.**log_length_scale\n", + " model.kern['.*variance'] = SNR\n", + " Kinv = GPy.util.linalg.pdinv(model.kern.K(x)+np.eye(num_data))[0]\n", + " total_var = 1./num_data*np.dot(np.dot(y.T, Kinv), y)\n", + " noise_var = total_var\n", + " signal_var = SNR*total_var \n", + " model.kern['.*variance'] = signal_var\n", + " model.Gaussian_noise = noise_var\n", + " length_scale_lls.append(model.log_likelihood())\n", + " print SNR, 10.**log_length_scale\n", + " display(model)\n", + " lls.append(length_scale_lls)\n", + " \n", + " return np.array(lls)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 9 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we load in the data and compute the likelihood values." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "data = pods.datasets.della_gatta_TRP63_gene_expression(gene_number=937)\n", + "x = data['X']\n", + "y = data['Y']\n", + "y = y - y.mean()\n", + "kern = GPy.kern.RBF(input_dim=1)\n", + "model = GPy.models.GPRegression(x, y, kern)\n", + "resolution = 2\n", + "log_lengthscales = np.linspace(1, 3.5, resolution)\n", + "log_SNRs = np.linspace(-2.5, 1., resolution)\n", + "lls = contour_objective(x, y, log_lengthscales, log_SNRs)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.00316227766017 10.0\n" + ] + }, + { + "html": [ + "\n", + "\n", + "

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Gaussian_noise.variance 1.0 +ve
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Vy76iVAHdAqxw95vNbDCwjbtvVrib2SvAT9x9rpkNBdq6+6AGtiu6KiAIvXmO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\nQESkTCkBiIiUKSUAEZEypQQgIlKm/j97/HKURg95ZwAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Sampling with Hamiltonian Monte Carlo" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "model.kern.lengthscale=30.\n", + "model.kern.variance=0.5\n", + "model.Gaussian_noise=0.01\n", + "model.kern.lengthscale.set_prior(GPy.priors.InverseGamma.from_EV(30.,100.))\n", + "model.kern.variance.set_prior(GPy.priors.InverseGamma.from_EV(0.5, 1.)) #Gamma.from_EV(1.,10.))\n", + "model.Gaussian_noise.set_prior(GPy.priors.InverseGamma.from_EV(0.01,1.))\n", + "_ = model.plot()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "WARNING: reconstraining parameters GP_regression.rbf.lengthscale\n", + "WARNING: reconstraining parameters GP_regression.rbf.lengthscale\n", + "WARNING: reconstraining parameters GP_regression.rbf.variance\n", + "WARNING: reconstraining parameters GP_regression.rbf.variance\n", + "WARNING: reconstraining parameters GP_regression.Gaussian_noise\n", + "WARNING: reconstraining parameters GP_regression.Gaussian_noise\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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HXBMnH/3eN/n9E4/z+G+fZcM11/LWO8W8uD+f2sb3c1JcVCgbVi5hZWYiq7KSiJ3i/2lL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\nH4/y3N6z+FnNfO9Lt7I6e26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vtEcEvodkeDJ4dsmz2BPspLhTKKsr48YFN3Lf58bkpbpgneV3tifYrVwukdIW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\n2symeMqEU6ztbTNDDmV+su9PuP3I2zv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+ "text": [ + "" + ] + } + ], + "prompt_number": 52 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "labels = ['kern variance', 'kern lengthscale','noise variance']\n", + "samples = s[300:] # cut out the burn-in period\n", + "from scipy import stats\n", + "xmin = samples.min()\n", + "xmax = samples.max()\n", + "xs = np.linspace(xmin,xmax,100)\n", + "for i in xrange(samples.shape[1]-1):\n", + " kernel = stats.gaussian_kde(samples[:,i])\n", + " plt.plot(xs,kernel(xs),label=labels[i])\n", + "_ = plt.legend()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 53 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "fig = plt.figure(figsize=(14,4))\n", + "ax = fig.add_subplot(131)\n", + "_=ax.plot(samples[:,0],samples[:,1],'.')\n", + "ax.set_xlabel(labels[0]); ax.set_ylabel(labels[1])\n", + "ax = fig.add_subplot(132)\n", + "_=ax.plot(samples[:,1],samples[:,2],'.')\n", + "ax.set_xlabel(labels[1]); ax.set_ylabel(labels[2])\n", + "ax = fig.add_subplot(133)\n", + "_=ax.plot(samples[:,0],samples[:,2],'.')\n", + "ax.set_xlabel(labels[0]); ax.set_ylabel(labels[2])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 46, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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eDyH6g8LS4TKIm2I/BWw1s/cDe4B3NdvwpZemfj/8cLjttjA/OamIkBCtMjkZ+j/kTS0t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\nIGY2H/h74Hfd/Wdmdug3d3cz86ztNm/efGh+fHy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+ "text": [ + "" + ] + } + ], + "prompt_number": 46 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## More Advanced: Uncertainty Propagation\n", + "\n", + "Let $x$ be a random variable defined over the real numbers, $\\Re$, and $f(\\cdot)$ be a function mapping between the real numbers $\\Re \\rightarrow \\Re$. Uncertainty\n", + "propagation is the study of the distribution of the random variable $f ( x )$.\n", + "\n", + "We will see in this section the advantage of using a model when only a few observations of $f$ are available. We consider here the 2-dimensional Branin test function\n", + "defined over [\u22125, 10] \u00d7 [0, 15] and a set of 25 observations as seen in Figure 3." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Definition of the Branin test function\n", + "def branin(X):\n", + " y = (X[:,1]-5.1/(4*np.pi**2)*X[:,0]**2+5*X[:,0]/np.pi-6)**2\n", + " y += 10*(1-1/(8*np.pi))*np.cos(X[:,0])+10\n", + " return(y)\n", + "\n", + "# Training set defined as a 5*5 grid:\n", + "xg1 = np.linspace(-5,10,5)\n", + "xg2 = np.linspace(0,15,5)\n", + "X = np.zeros((xg1.size * xg2.size,2))\n", + "for i,x1 in enumerate(xg1):\n", + " for j,x2 in enumerate(xg2):\n", + " X[i+xg1.size*j,:] = [x1,x2]\n", + "\n", + "Y = branin(X)[:,None]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 35 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We assume here that we are interested in the distribution of $f (U )$ where $U$ is a\n", + "random variable with uniform distribution over the input space of $f$. We will focus on\n", + "the computation of two quantities: $E[ f (U )]$ and $P( f (U ) > 200)$.\n", + "\n", + "## Computation of $E[f(U)]$\n", + "\n", + "The expectation of $f (U )$ is given by $\\int_x f ( x )\\text{d}x$. A basic approach to approximate this\n", + "integral is to compute the mean of the 25 observations: `np.mean(Y)`. Since the points\n", + "are distributed on a grid, this can be seen as the approximation of the integral by a\n", + "rough Riemann sum. The result can be compared with the actual mean of the Branin\n", + "function which is 54.31.\n", + "\n", + "Alternatively, we can fit a GP model and compute the integral of the best predictor\n", + "by Monte Carlo sampling:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Fit a GP\n", + "# Create an exponentiated quadratic plus bias covariance function\n", + "kg = GPy.kern.RBF(input_dim=2, ARD=True)\n", + "kb = GPy.kern.Bias(input_dim=2)\n", + "k = kg + kb\n", + "\n", + "# Build a GP model\n", + "model = GPy.models.GPRegression(X,Y,k)\n", + "\n", + "# fix the noise variance to something low\n", + "model.Gaussian_noise.variance = 1e-5\n", + "model.Gaussian_noise.variance.constrain_fixed()\n", + "display(model)\n", + "\n", + "# optimize the model\n", + "model.optimize()\n", + "\n", + "# Plot the resulting approximation to Brainin\n", + "# Here you get a two-d plot becaue the function is two dimensional.\n", + "model.plot()\n", + "display(model.add.rbf.lengthscale)\n", + "\n", + "# Compute the mean of model prediction on 1e5 Monte Carlo samples\n", + "Xp = np.random.uniform(size=(1e5,2))\n", + "Xp[:,0] = Xp[:,0]*15-5\n", + "Xp[:,1] = Xp[:,1]*15\n", + "Yp = model.predict(Xp)[0]\n", + "np.mean(Yp)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "WARNING: reconstraining parameters GP_regression.Gaussian_noise.variance\n" + ] + }, + { + "html": [ + "\n", + "\n", + "

\n", + "Model: GP regression
\n", + "Log-likelihood: -74285.8774977
\n", + "Number of Parameters: 5
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dmsGBKVJI5akPIcZFZZ+8QFCADPnL0MuMyAzXJsJliaLIepFLusPA5VKb2ORC\nudT7aVsAjjWBVuHQaDe8e8r27DkvziFBD0/vl8JeC2tCYDaeBA1GeHMVfP0MBNsRETRnI7SpDQVs\nyOv+exl0ecFym23btDRpYr/PzyMMNkCJAlLzolElqP0mbD/u7hn9dwj0l7KsQf5S5S8l3d0zkjQs\nAfsHwoYL0P4PiHfTvPw18E5pONFUhpJV3Aazrkp/qhd1uaWF5nugTh6YWQ18s2mxph2AArmgkx3R\nSELAtNUw2AZNIZ0Olq+BTs9bbrdjh46mTe2PIfUYgw3Skf9pL/jlTencn7Q45+p45DT8/eQ+whMF\nZARJgoc8/hcOgU2vQdl8UHc6HL3pvrkUDIAZ1aT/9JerssLNihjvPaoWV9KlrnmHgjA5UqowZoc7\nafDJFpjS1r4wwK3H5NiNK1tvu3ErRJaHIlZyCnbs0NK4cQ5eYd9Pm7qw71uYv1U+piemuntG/w18\nfOSXZZ1y0HKk52Sm+vnA5LZS9rLVbzDLjRV1AOrlhZ0N4LPy8MEZaLzHtaXJ/gscSoSme2SG6tjy\nzomL/2A9dK0CVeyUXZ22CgbZaOQXLYfO7S23iY42kpwsqFjRfke8RxpsgCcKwo6voXAY1HkLjl50\n94z+G2g0MHkgtK0Dzd6D6Fh3z+geParJlPaJO6H3YtdVsskKRZF6y0eawKAS0OuI3JiMSnLfnB4H\nhICpl+DZ/TKJaZiTtG1WnYX1F2C8jZVkMrkWK5X5XrEhmsRgkOp8L1p1h2hp1MjfoVh2jzXYAAF+\n8MMbMPZlaD0Klu5294z+GygKfPYq9G4Njd6FU1fcPaN7VCog/domAfWmu64ogjl8FJkZeboptImA\nZ/dBj8Nwwk0qgDmZBD10OgSzr8HuBvCSk6QK4tKg/1KY1QFC7cz3mLxE6obktUEkbNsuWQbsieKW\n223Z4tiGI3i4wc7k5RYy/GzITzB+vtdn6Cre6yJDLluMlIlOnkIuf5j9IrzTCJrOhNmH3T0jCPCB\noSXhXHOoEgIt98KLB2X2pBfr7EuAWjugWKB0N9mismcrQ1dBl8r2F85ITIWZ62CYlYiPTBavgBfb\nWW9na/3GLBFCqHLIrp1LdKwQ9d4SousXQqSmO717L2ZYvV+I/F2FWLrb3TN5lKM3hag4RYjei4VI\n0bp7NvdINQgx+V8him0U4um9Qmy9I4TJ5O5ZeR4mk/ycItYLseiG8/tfeFyI8pOFSHXg3vjqLyFe\nnmBbW6N+8CjJAAAgAElEQVRRiCKVhDh91nK76GiDCAu7JoxG8zfDXduZpV3NESvsTIqEw5av5CZU\n0/ekf8mL+jxbRz7hDJwKv3pYBc+qBaWLxGByfxTJ/QT7wFul4Hwz+Wjf96iMeFgR4w0HzORKOnQ8\nBPOuw56G8KKFRBNHiEmBISulzIE9MdcgNY+mLIMRnWxrv+8g5A2FClaytbdulXKqGgdDXnKUwQaZ\n6DHnXXipCdR/Gw5fcPeM/hvUqwDbJsDnf8G43z3LLZU7AOa8CB80kVEk3+3xnPkF+EDf4nCqKQx5\nAsaeg3JbYOK/srr3f5FUA4w5K8Miq4fAjiehdLD16+xBCBi0HHrXgAYl7L/+z61QqThUt9GNsngF\ndLTRHWJrObAsMbf0zu6BCi6Rh1m0Q4iIbkJsOar6UF7ucuOOEHXfEqLnBCEydO6ezaOcixWi3jQh\n2swR4mayu2eTNXvjhegVJUTetUL0PSLE4UR3z8g1GE1CzL0m3UTdDwlxJU29seZGCVFlqhAZevuv\nNZmEqDJIiLUHbW9ftrYQB6Osty1X7oaIirLsn8FdLhG9yrogLzaC+e9Dl8/h7x3qjuVFUigfbPkS\n0rTw9Idwx8PC2MqGw45+shhCzZ9g9Vl3z+hR6uWF2dXhTDO5snz+gBTin3NNanM/juxNgIa7pRLi\ngprwR00oHqTOWNFJMHyN3JgOcEBzZN0hGSn1VE3b2p88LQWfalaz3O7GDSOxsUaqVrVQgsYKqhrs\ntnMhMUPNEaBlDVj7Gbw1Hb5bqu5YXiTBgbBwFNSvAA2Gw7lod8/oQfx8YHxr+LOz1CIZtkpqpXga\nBQJgVFm42BzeLgkLb0KxTfDSIfjnJmTkcCE0IWBnHHQ7LCNmBpeAvQ2hoY1ypo6O2X8pvF4Xalmp\nCGOOrxfBOy/anqyzZBV0eM56+61btTRt6rj/GlQ22BXyQ+Nf4YrKoU01y8DOr+GnVTBihvuEgv5L\naDQwoa+8sZu8BztOuHtGj9KsFEQNhuhkqDMdDl1394yyxlcDnQrD8jrwb3NonR++uwRFNkGfo7Ah\nVm6q5hQS9fDDJai2Hfocg7p55NPEq8Wyn15ujZ8PwM0U2wvqPsyRf+HkVesFdu9nySro0NZ6u8wN\nR0tMnHjacifmfCXZPQBhMgnx9Q4hin8txOnbtvmDssOdJCEaDBdi0FQZZuPFNWSG/c3e4O6ZZI3J\nJH2aEV8KMW6TEDqDu2dkG9fShZh0QYja24UIWydEl4NCzLgiz3siUYlCDDwqffNdDgqxKda1oYy7\nLsvfcXZsTa+vhfhige3tr14TIl9pIXQ27OdERt4QBw5Y9l+XK7fCog/bJQUMZh2CURtg9StQQ+VC\nq0lp0GY0VCsFP7zuGeWv/gucuCyLIXRuDJ+/6hkVbB7mWiL0XQJx6TCnE0RGuHtGtnM9A9bFwprb\nsD4WigbCsxHwTH6onxdyZ0Mf2lFSDbA9HjbdkU8Bt3QwsDj0Kw6FXVxB6kayDOuc/jw8V8GxPq7f\ngSqDZUWZMFsrqM+EXftg7jTL7WJjjZQpc5O4uCL4mKlplpKip0CBpaSnd3F/xZm/T8hKIku6S9lM\nNUlKg2dHQ3Wv0XYpsYlSZTE0GH4fASFODtVyBkLA9APw0UYY1QSGNch594dRwP4EWBsLa2/DkWQo\nHgg1Q6FWHvlvzVDnV4BPM0pRpo13YGMsHEqS1edb5Zd64U/mzb78qSPoDNBiFjxbDkY3d7yfD2dL\n2zF1sO3XPNsZ+vaELh0st1uyJJ1p01JYs8b8KmH37liGDj3EwYPPuN9gA6w5B68sgt87216l2FEy\njXa1kvDjGznvjzKnotNLCYHdp2D5WChppzKaq7gQJwWkNArM7Ahl8rl7Ro6jN8HpFDicJI3ooUSI\nSoa8vjISo3AAFAmQ/xYOlP9G3DXmJgECMN19bRKQbITL6XAxDS6ly+NiGiQaoHLuewa6cRjkcsPK\n/mEGL5d+60VdHf87T82Akr1h9zdQ1sbNyqQkKFYFok9AiJUV+TvvJBAermHUqFCzbaZNO8/+/XHM\nnFnfMww2wI7L8OJ8+KkddLJBXzY7JKVBu4+hdGGYOcxrtF2FEDB1GXzxFyz4AJpWdfeMssZogsm7\n4YvtMLIJvPWkZ9S1dAYmIQ1tdAbc0MKNDLiuvfc6Vg8K8tAoMvpAo8gjWCNLpJUMkkepu68LBai/\naWgvvx6ESTth7wD7hZ3u58cVsP4w/DPa9mvmLoC/lsDyP623rVcvhkmT8loUfRo8+ACRkaG89VYF\nswbbLYkzh64LUfArIea7IOElJV2IpiOEGPidV8vB1aw9KBObpq1090wscy5WiOYzhKjzkxBHVNCz\n8KIOe65kf5NRCCH0BiHK9hViq5326LmuQsz7y3q7lBSjyJXrmkhPt2yAGjZcLzZvjvE8LZGahWFd\nLxi2Gv44qu5YuQJhxViZwv7OL56Tsvxf4OlasGMiTF4Kr//gGUV+s6JsuKxqM6COTG0fvVFWb/fi\nucSkQOcFsmBzhfzZ62veJigabt+TYHwCbN8N7Z+13nbfPh3VqvkRGGj+8UQIwfHjSVStmsdiX25z\nElQrBOtfhXfXwpwodccKCYY1n8LmozBmrrpjeXmQ8sVgzzdw5RY8/ZHcmPREFAX614Ejr8PxWzJL\ncpcH6YB7uYfeCF0WQJ9a0L5iNvsywCd/Shlhe1iyElo1s+67Blm/sXFjyzvAV66kkTu3L+HhluO0\n3erVrVIQNvaGkevVL/sUFgLrxsOinfDFAnXH8vIgeXLB0jHwZAWo97ZnVw8qEgqLu8lyZJ0XwKBl\nshagF8/AYIReiyEsCD5unv3+5myE0oWgmZ37LH8tgZds1MneuVNLo0aWDfGxY4lWV9fgAWp9kRHy\ncXT0Jpir8ko7Ig9s+Bx+Xet5MqGPOz4+8MVrML4XtBoJC7a6e0bmURToXBlODpFhapWmwsxD3gxa\nd2M0QZ8l8gt0QZfsBxHo9PDZfBj3sn3XxcXL2Ot2z1hvazIJ9uzR0bCh5RX2sWMJVKmSAww2SB/U\nul7w3joZr60mRcJh9Sfw0VxYc0Ddsbw8SvfmsH48jJwN7/4qV0yeSt4g+L6dTPiavh+azIAjHqK3\n/V/DZJJyqVcSZS5HoOP6Sf9nzkYoVwQa2RmttnQVtG4GuW0oG3bypIGICB8iIiyHH504kZRzDDbI\nWn2rX4E3VsDSU+qOVb4YLBoFr3wNe62k7ntxPjXKwP7JcOySVPzzlOrs5qhVBHb3h9414anZUkwq\nSWVRMy/3EEKW+Tp5C1a8bH8xgqzQ6WH8Avi4h/3X/r0MOtvoDtm9W0uDBtYnfOJEIpUrm4/RzsRj\nDDbItPWVPaH/MlnlWE0aVYZZb8MLn3pWkdn/CuGhsGocPFkR6rwJBzxQBvV+NBq5KXliCCTrIPKu\nm8TodZOoihDwzhrYHw2rXpHFKpyBo6vrhETYsQfaPW1b+927dVYNttFo4syZZCIjc5jBBqhTFJb1\ngN7/wEaVq8m0qw8T+siMyGhvuTGX4+MDn/eGbwdAmzEwY627Z2SdiFwwo4PcmJx5CGr9pP59+l/m\no42w+SKs7QV5nKRPkp3V9bLV0KKJbdEhALt2WTfYFy+mUqBAALlzW/fzeJzBBniyOPzdFbr/DYdv\nqDtWr1YwsC10/AyS02DSQmjwJrQaAX9uUndsd3MnAUZMhDpdoONQ2HHQPfN4sZEsP/b1Yug7GdK1\n6oxz+gb0ngG1x0G/WXDhluN91S8O2/vCmOYwYBm0/x3OeNiX/qZr0H4V1FkIo/ZAokqfq1p8vhWW\nnIJ1r8qoEGv8th2afw6NPoWp68xvEs/dBGUL27+6BlkKrNPztrWNjzcRHW2kShXLhvjUqSQqVbLu\nvwaVU9NNJmGzCHhWLD4JQ1fKCiKlVBY97/4V7DsNFx8S4/92MAx7Ub2x3YVeD7U6w/Fz9875+sLG\nmdC0jnvmlJwG/b+DM9dg0YdSUsBZXIqFmmMh4b4QvYgQODIOCufNXt9aA0zdA1/tgB7VZLhZPjcL\nX62+DO1WyRT1TOoWgD2dPC+9/GEMRhmAsPIsbH5Nhlpa49MlMGbxg+debwU/vPrgOb0BKgyAOe9A\nYzsNdkoKFK0Ml49CXhvs67p1GYwfn8TWrQUstpsw4RQxMRlMmiRL3CiKYjY1XdUV9odns5dZ+GIl\nGNUUnp0Dt1OdN6+HURQY2wMuxvDIJ/Ll/McznGvZ5geNNYDBABNnumc+IBOc/nwfXnsKnhwOy/Y4\nr+8fNz1orAFuJ8Ov27Lfd4AvvNsYTg6VhQYqfAefbYFkN65ovzz8oLEG2H8LNlx1z3xsJT4d2s6T\nyUu7+9tmrLV6mJRFmO4vW+D2QyXsft8MJQvYb6wBVm+ABnVtM9YAe/fqqF/f+obj6dPJVKxow38U\nlQ328hj47Hz2+nijvoyJbTcPUlWsMn07ETAgP5H7vtti4tV7RHcnF6/Zd95VKAq8+YJMtBnyE7w/\n0zmhfxfNuCsuOdGNEZELfmgHO/vB6VgoMxm+3AYpbrh/LpqptXkx2bXzsIeTt6DedKhSAFb1tP0p\nJS4VErNIbtIbITr+3s8G413ftZ1x15ksXgEv2lAZPRNbDfapU0meYbA31Id512FKNjPbPmsFlQtA\n5/nqFfatUeaufrMRuC9ksnY5yKVSsVB3Ys7t4S53yMM0iISD30kNmFYjpbh8dmha3sx5B8XuLVE+\nP8zrDFv7QNRNKDsFvt3l2rqSTc24k8yddzcrz0DzWfBRM/imjX2qiYXyQPlCj56PCIHI+6RSF2yD\nwmH2ZzWCLLK7egO8YEMpMJDaIPv26ahXz7LBFkJw+nQSFSvatoupqsEuGADr6sHEi7AgG/X0FAV+\nbi99b4OWqyPgFBIMkwff9e+ZAF/IHQRTXnf+WJ5AvWowqOuD50oXh48GuWc+WRGRRyY5ta4Btd+E\nDYcd76tfU2hc7sFzT1WG7vWzN0dLREbA/JdkUtiWS1BuCvy0D9JdYLg/rQ/Fcj14bkQNiPQw3W8h\nYOIOuXG7rAe8amOl8vtRFPi+FwTdZxt9fWDqKxBwd79Pq5c6Qo6urjdtg6qVoKBld/T/uXrViEYD\nxYpZ/uaJjdWiKAr589sWr+gSPeyjSdB6H8yvAS2zoayVopXfwu0rwJgWTproQ5y7Bot3wJK9Un9k\nxdjHW0d712HYtBdKFIYuz0CQi0s72cqmKOj5NfR/FsZ0d6wEmdEEy6PgeDTULAFtqrr2d7vvGny2\nFfZeg9frwRv1IH8u69c5Sooe/joPN1Lh6eJQ18OKSSSky4SYE7dgaQ8obqNv2BzX4+GvvXIfoVNd\nKHVfcZeJf8P2E7DsY8f6Hvg2lC8D7wyxrf2iRWnMmpXGihWWDd7Onbd5550o9ux56v/nLG06uqyA\nwZY78NJhueKuYZu7JktiUqDBLzC6GbxWywkTNYNWLx/FW1aHT15RbxwvtnMzDnpMkK9/fw8Ke9hq\n0VZO3YZvdkkZhu5VYXhDKfH6X0EI+POYVOp8vgJ88yzkcnI5s/uJiYfKg2H3JChX1P7rTSYoUgl2\nrIKypW27ZvjwBCIiNIwcadnYzZr1L5s332LOnCf/f85tUSL30zwcfqwMz+2X5YYcpWBumcI+cgOs\nPWe9vaME+MnQstkb4O8d6o3jxXYK5ZM6JM2qShfJepUVHtUiMgJ+eQFODYV8QXIB0mm+rMb0uOu1\nn42F1r9JN8jibjC9vbrGGmDMPHi1lWPGGmDvAYgIt91YA+zYYV2hD+Ds2RTKl7cxCwdcX3Fm6kUh\nym8R4rblau9W2XHJOdUmrHHgrBD5uwpx4bq643ixj01RQhTpKcTIWbJiSE4mRSvEd7uFqDBFiMjv\nhPh2pxB3Ut09K+eSoRdi7CYhwr+Q/z9X/c6O/CtEge5CxCc73scH44QY9ant7dPSTCIo6JpITTVa\nbdup0w4xf/7lB87hSRVnhpSEjgWh/QFZhdlRGj0BX7SWGWYJ6U6b3iPULgcjX5KP4p5aMeW/SIvq\ncHgqHLoAzd6TBRJyKrn8YeiTcsU97Xk4cB1KT4aef8O2Szl71S0ErD8P1X+USodRg2FYQ9fUzhRC\nVpka3R3y2qCsZ47la+B5G6RUMzl8WEelSr4EB1s3rxcupFCmjO2Tc8t22ucVoEwwdD8sNwgcpW9t\neKYsdF+orkznsA4QlhvG/q7eGF7sp0BeKSD1wpNQdxgs3e3uGWUPRYGmJWVI4IVhUKeIjIqKnCoT\ncU7cyjnGO00nC+TW+FFuLH71FCzuDsWyubFoD6sPwNVYGNjG8T5OnYH4RKhX2/Zr9uzR8eST1v08\nQgjnGmxFUWYqihKjKMqx+87lUxRlvaIoZxVFWacoit2JvRoFZlSTK+whJ7J3E056Vhr9d1QUDtJo\n4LfhMGs9bD6i3jhe7Eejgfe6yESbYT/DGz88HolO4cFyJXpiCMx4AW6nQZu5Movy/XWw56pnZuBe\nTpDze+IbKZP89TPyyeGFSNfOw2CUeusT+4Kfr+P9/LkIunawL5rIVoN9+7YWX18NYWG2O/GtTWMW\n8HCZyQ+A9UKI8sDGuz/bjb8GFtWCvYkw4V9HepD4+cDCrrDuvBSZV4uCYVKOtdckiPPgbLH/Kk9W\nhKjvIS4F6g2D45fcPSPnoCjS/TelLVweDn92AT8N9F0CxSdJrZ1lpyHOjWXM0vUyAKDzfKleqDfC\nngGwvCc8VZZs6Qk5yi9rZBRRu3qO9yEEzP8Huney7zpbMxzl6tq+uE6rYX2KopQElgshqt79+TTQ\nTAgRoyhKIWCLEOKRUpgPh/WZIzoD6u+SESTtsxEneu4ONPoV/ukmb3C1GP4zXLgJS0a750b0Yhkh\n4Lf18N5MWVh18HOP7+/p9G0pkLb5IuyNhifyQOMnoMndI7txzeYwmuDQDdhwQR77oqFGIXipiizy\nEOIkzWpHSUqD8v1l0lXNMo73E3UMXuwFFw7Zfg/FxBiJjLzJnTtFUKxc9Oefl1myJJoFCxo+cD5b\ncdhZGOx4IUTY3dcKEJf580PX2WSwAfYlwHMHYFM9qJqNGO1VZ6H/Utg/0DbRGEfQ6aHxCHi5ObzV\nQZ0xvGSfs9eg+wQonh9+fQvyu9B36g4MRpkGv/3yvSPYDyrmh9L5oEwYlMknj9JhthUCSNPBtSS4\nmnjv38M35RdE0RBoXQZal5Z+d3cb6fv5aDZcuQ1z3s1eP6M+lW6nL+1ItlmxIp3vvkth3boIq20/\n//wkiYl6vvqq+gPnLRnsbHh3ZOyJoijZ3gaplxcmR0L7g7CvIUQ4+MtvW15mkHWaD1v6SBU1Z+Pv\nBws+gPpvQ8NKUNeMRoUX91K+mEyUGDUbagyRcpota7h7Vurh6yOLf9QpCm83lE8a5+Pkk+eFOPg3\nHrZdlq8vJkCgrzz8NODvI12Lfhr5r94oDXSqHoqFQvFQuVlYPBQ6RsL3z0FhO0KHXUl0LPy0SkYQ\nZQchZGX0v+xUr9y/X0fdurb5pC9dSqVWLft0ox0xaTGKohQSQtxUFKUwYDagauzYsf9/3bx5c5o3\nb26205eLwskU6HAINtaDQAfDfkY1lY9rQ1bK5AQ1KFUIfnoDun0Jh6ZCHhXTi704jr8ffN0Pnq4F\nr0yCbk1h/KsQqHKihiegKFAuXB4PYzJBXDpojdI4602gu++1r0Ya6vzBOcudJITceB7UFkrYqPlh\njqhjsr+a1ey7bv9+PQMG2GYQLl5M5cUXi7Flyxa2bNli0zWOuEQmAHeEEF8pivIBkFcI8cjGo6Io\nYq/OQD0/2y2vScj09RAfmFnN8ZslWStlGt9vIn1qajH4e5nCPvNt9cbw4hxiE2HAVDh/Hf54D6qU\ndPeMvDibhdtlVuPhqdn/UnbEHSKEoFChGxw4UIDixa2vhcuXX8nSpU0eqeVoySViLVvxT+A6oAOu\nAq8B+YANwFlgHdJgZ5npWPRWqrhksJ7tcz8peiGqbxPim3/tuuwRjt0UIv8XQhyPyV4/lkhOE6LU\na0Ks3KfeGF6ch8kkxMy1MnN18j9CGO27Nb14MLGJQhTqIcSuk9nvy2QSonxdIfYdtO+6a9cMIiIi\nWphMJhvGMInAwIUiJUX/yHs4mukohOguhCgihPAXQhQXQswSQsQJIVoLIcoLIZ4WQiSYu35EsB/t\nEzJIfLj0hQVy+cLSOjLUb91tmy97hCoFYcLTMtRIrcofuYNgxlswcCokpKgzhhfnoSjw2tOw51uY\nv00WX86uzrYXz2DYdOjWTOqoZ5eTpyE9HerY+XR+6JCOWrX8rEaHgJRVDQ72IVcu+7zSqmY6vhns\nSxM/H7olajHYkR3zRBAsqAmvHIFz2SgN9lotGd702j/qZYi1qA7t68PbP6vTvxfnU6YwbJ8IjSpB\nzaFeca+czqr9sOsUfNbLOf0tWi4ry9jrkj10SE/t2rb5Yq5cSaNECfsLf6pqsBVFYXKIPwrwdrJ9\n9b2a5oNx5eCFg5CcDQ2Pqc/BlUSYtNPxPqzxVR/YelzeOF5yBr4+Usx+2Rj4aI4swuxNiMp5JKXB\noO/hlzchl5O03BevgE7t7b/u0CEdNWtarpCeydWraRQv7mEGG8BXUfgzTwAbdUZm2llqY9AT0CAv\n9D/m+Ao5wFdmQk7cKdN51SB3EPw8VG5CJrkx48yL/dSvKDepCoVBtddhzQF3z8iLPXwwC56p5byQ\nzYuX4fpNaOhAhmRUlJ4aNWxbYUdHp1OsmP21B10i/pRHo7A4byCjknXstbMo4/eV4UwqfH/Z8fGf\nyCt1d7svlFWZ1aB1TXi2jtc1khMJCoBvB8Dcd+VqbdBUSFFRAdKLc9h+HJbtkXohzmLpKmj/rP0V\njeLjTcTFmShd2rYLo6PTKVLEQw02QEVfDT+HBvBSgpabRttVa4J84O+a8Ol52BVvvb05OkTK6hb9\nlqrnz57UD7YclTeRl5xHi+pw5AfQGaD6G7DjhLtn5MUcGTroNwWmDs6edOrDLFkFHZ6z/7qjR/VU\nreqHRmOb4/v69XSKFvVggw3QPtCXvkG+dE7UorXDapbJBbOqyRjtGxmOjz/xGbgUDz/sc7wPS+QO\ngtnvyFXaLbOxM148mTy5ZFz9twPgpS+kdkxqNu45L+rw6Z9QtSR0bGi1qc3E3oHDR6FVU/uvPXpU\nT/XqtvmvIQessDP5KJcfhTQKb9q5CflcARhQHLpFOa6hHeALC16CcZvhWIxjfVijcWV4uQW8NV2d\n/r24hvZPwrEf4VaiXG1vPWb9Gi+uIeqCVOObOti5/a5aD62aQZD9dvT/K2xbuX49ncKFc4DB1igK\ns0ID2KUz8kuafZuQH5WFIA18dNbx8cuGw1dPw8t/g1alCjLjXob9Z71RIzmd8FCYN0Kutl+eAEN/\n8vq23U18MnT+HKYMdH4RZnsry9zPiRN6qlSx3WDHxGRQqJD9YS1uqTgTolFYlDeQ0Sn2bUJqFJhb\nHf64DiuysUJ+rSaUzQejNjjehyWCA2HaEHj9B+8f+OPA8/Xlajs5Haq94S1i4S5MJuj5tdS47t7c\nuX3rdLB+C7R9yv5rhRCcOKGncmXbkmD0ehOJiXrCw+3Pn3eLwQYof98mZIzRdn92RADMrwl9j8El\nB0PoFEUKQy08ASvPONaHNVrXhObVYPRcdfr34lrCQmTVoamDZBGLwd9DYjaSurzYz2fzZdisM6NC\nMtm+GyqWg4IOiEZdu2YkOFghPNy2CJHbt7Xkzx+Aj4/95tdtBhvkJuRrQb50S8ywKxOyYRi8X1pu\nQuoc9GeHB8PvnaDvUrie5Fgf1pjUD/7cCgey4cLx4lk8V0+utg1GqDwIFu3IOXUWczKr98P01fDX\nyOyV/DLHirXw3NOOXXv8uJ7KlW13h9y8mU7Bgo5l+bjVYAOMyeVHgKLwcYp9/uy3S0HBABidDWPY\npCQMrAN9lqjzRxceChP6wOAfwKhikWAvriVvbvjlLZj/AXw0Fzp+KnWYvajDpRjo/S3Mf9/5fmuQ\nf/sr1jlusE+fNlCpku0GOzZWR4SDov+qGuyjWM/11SgKc/MEMC/DwGo7dgEVBWZWhXnRsCEbfywf\nNZPJNGqF+r3SUko9zlinTv9e3EfjyrKOZI3SskjCjys8szBuTiZDB53HwwddoEkVdcY4clwuqOzV\nvs7k9GkDFSrYvuyPjZUuEUdQ1WC/xzlisR6+F6FRmJcngL5JOq7akVQTEQCzq8OrR+CWg4p8fj4w\nr7MM9TuVDXVAcygKfD9Y6lXEZCPxx4tnEuAHY3vC1gnw+2ZoMgJOXnH3rB4f3pouC4YMU7Ec38Kl\n0OUFx/X3T5/WU7Gi7Qb7zh2tQxuOoLLB7kgBRnAOPdaNcBN/H4YF+9ItUYvODv9E6/zQuxj0PCIL\nIDhCuXAY31qG+ulUCPWrXhr6PA1vTnN+3148g0olpALgyy2g2XswYoZXVya7zN4g499nDFOv8o0Q\n0mB3dkDsKZMzZwxUrGi7SyRz09ERVDXY/SlKKL58i21LjhHBfhTQKLyfYl9SzbhykG6UGtqO0r+2\nLCz62VbH+7DExz3g8AVYvled/r24H40GXm8nNyXvJEHkQPhjs3dT0hF2nYR3f4VFH0Ko/aJ2NnP8\nlAzps1f7OpPERBMpKYIiRWw3pbdvaylQwAMNtgaFTynDNuLZgHWleEVRmBkawLIMI0sybF/q+mrg\n9xrwzUXY72BKuKLAzy/AtANw+IZjfVgiKAB+GgJDfvTGZj/uFMon09sXjoQJi6DVSDjldZPYzN7T\n0OFTmbRU+Ql1x1qyEjo+5/gK/vx5A2XL+tpUtCCTuDgd4eEeaLABQvHlK8rxORe5inVRhjCNwh95\nAxicrOWSHf7sEkHwY2XoEeW4fnbhEPj6GVnwQA3XSKsa0LQKjP3d+X178TwaVoIDU6BDA2j6Hrw/\n0/tlbY0DZ6H9JzLm/Zna6o/3z0rHxJ4yuXBBGmx7iIvTkS+fB/qwM6lMbgZQjPc4i9YGf3Z9Px9G\nBO6TtnQAACAASURBVPvTw05/dufC0CwfvJkNlbVXqsuK0Wq5Rib1hzkbpR6Cl8cfXx948wU4+iNE\n34GKA2DGWm+YZ1YcvgDPjZXFCNrWVX+8y1fhajQ0qu94H5krbHvweIMN0JWCFCeQr7lkU/u3g33J\nryh8aKc/e0ol2JUA86/bP8fEDBi8BnbFwPjt0H852LHIt4kCeeHzV2UdSHeHgJ39FzoMhDzVoMqz\nMG+Je+ejNht3Q6OXIbQuNOsFOw+5buzC+eQj/t8fys20am/IZBA1+WU9RA6FvD2hy0S4dEvd8bLD\nsYvQZgz8+LoU3rIXvR4+nAxFm0OBxvDmeEi1sum7dJXUDvHNRiLO+fMGypSxTzw7Lk5HWJiDZd3N\nVefN7iG7fpBkoRfPi0NirYi1WlVYCCFijSZR4laqWJdhsKl9JgcShCiwXojodLsuE61/F4Lxd49P\nhGCMEMPX29eHLRiNQtQfJsSsdc7v21ZSUoUo8qQQlHrwWLTafXNSkyOnhfCvJgSR946gmkKcvej6\nuZhMQizdLUT5fkI885EQxy85f4zfNglBxwePUv9j77zDmyrfP3yfJE26W0qhLXvL3iBLQBzgxPET\nXF8Vla0MBRFERUEU3AxBURQHDlwoKipIQWSPInuXVUYX3U1Hnt8fB5Q252Q1aQFzX9e5tGe875uU\nPnnzjM8zRMRa4P25ysqeYyJx94l8Hu/5GENfKPm7pYnIHSMcP3PtbSLf/uj5nCIiPXuekWXL3DM0\nlSp9K6mp+brX8bRrurcJxcQ0GvEyhzmCc2deZYMahHwk00qKGzl77SJgaC1Vb8RVj8qeFFiWeMEJ\nI6DArHWey7nqYTCoamPPfAxZFZT69c1SSNIQ0Jp1mWqfvPsVFJQqps3Lh/nflv9aFOVf+dY+7aDn\nOBg+G5IzvDfHzJ/tzx0+DT9t9t4c3uDQSbh2gvqt8+4eno2Rkwsffmd//rtlcPyU9jOZmbBuM1zX\n07M5z5OYWESdOq5v0UWEzMxCwsJcTwO8kHIvTW9CCEOpwVPsJ98Ff/Y1FiN3B5oYlGk9v3N3iWca\nQLIV3nOxj2Oq1udHgJrys+Kwy9O6zJWNoVdLePkr74/tCqk6RTwpaeW7jvIiVSd7KKUCG02YA9SC\nkD3vqS2pGg9SexR6w3Cn6hQZp1xEjYY374de42F8P3jIA5W88+TkQb5G4ZwIpOm8l7/HQ9eOEFqG\nbjVFRUJSUjE1a7ruEsnPL8ZkUggI8Mz0VoiWyF3EUIcgl/3Zk0MDOFosvJvneupGgAE+bqVqZ+/L\ndn5/h2pQtXS+pwLNq8GQHyDHPVe6S7wyAN5bCod1dgG+5Martc/fpHP+Uucmnd3bTR50F/E2lcNh\nxhC1GXBmLlwxUC28KUtl7E0aGRZGA/TxMN/Ym4jAjMWqz3r6w2ruelmoWhnaa5St164GzRtqP7Pk\nV7jZQ+3r8yQlFVOlihGz2fWUvszMIsLDPdtdQwUZbAWF56jHRjJZinMhEIuisDDCwvPZBexwwz/R\nNAwmNVCrIAudPGY2wie3QvgF6ZF1IuDru6BrLd9oZ1ePhlF94cn3vT+2M66oB69NKBlwuaoDTBhW\n/mspD+69Ce6/peS5wf2g7zUVsx4talWFd4arGSX5BdB0iLrjTvNgV/zi3dChwb8/m00wayDUjPbe\nej0hI0fVBvl4Oax9A/p56QPzg8lQ7QJp1KgI+OQV1f1YGpsNflnuudjTeTwJOGZnFxEaWoYop55z\nu6wHGkHH0uyULLlaNsoJcc1pPz+3QFql5EiezebS/SJqgKf3epEX9rl2f5ZV5JvdIr8cECksVs+l\n5IjETBNZf8zlaV0mzypS/2GRJeu9P7YrnDgl8sWPIms2V8z85c32fSKf/ySy51BFr8Q5x5JFBs0Q\nqdxfZMJHIseT3R9j1U6RL1eLnE73/vrcJeGgSINHRIbNEsn3QfDTahVZEi/y3e8iObn6923ZJtKo\nQ9nn++CDbHnggVS3nvn773Rp1uxnh/fgIOjoU4O9XY47fQEL5IQ8JDukUJwbYZvNJnel58noTP0I\nqxbH89SskY1l+Ef7SYJIq9kiBe4lrLjEb5tF6jwkkuNmVouf/wYHkkQenyNS6S6Re14RWbe7olfk\nPh/8KhLdX+SzPyp6JSIvvyny+Liyj/P882fl2WfPuvXM+vUp0r79rw7vcWSwfeoSeY94zuI4DeJ+\n4rBg4ANOOB1PURTmhlv4Jr+YX92QYq0eqOZn/2+bqjniCfe1hKoh8NZaz553xHVtoXNjtRO0Hz+l\nqR+n+rgPfwgdGsE906HTaPhiJRT6qC+ptzh8Su2H+do3qqLhvRdBjOTXP6B3r7KPc+RIMbVru+fe\nyMsrJijIc5eITw321TTmHf7A5iAb5LzeyCJOk+CCfnaUQeGjCAuPZhaQ7Eaq393VoHU4PO1hSzBF\ngbm3wLTVcMgHmRRvDFQ1s3cken9sP5cHESEw+nbYP0/Vh373F6g7QC1531YG4TNfcPAkDHgD2o+E\nujGw4S1V0bCiyc6GTQnQs2vZx1INtns+bNVgu/fMhfjUYPelDQYUfiDB4X1VMDORukzkANk43zJc\nbTZyb6CJ4W6m+s1uBotOwp8eGtx6UfB0N3h0sferFGOjVEW/EXP96m5+HGM0wm1dYMUr8MuLanPq\nW1+AlsNg+iI4XoHdb46chkffgitHQ+2qcPADmPIghAZV3JouZNVaaN8aQkLKPtbx48XUqOGe8S0o\nsGE2e252fazWZ2AQPVnOLvbjuM15T6K4kgimuZjq90JoALuLbHxpdd3HEWWGWc3gkb89d42M7qKm\n+M3zQQHC4BvVHNzvfeB28XN50qIuvDxAdZfMHAr7k1TDfc14mP8bHPNBUw4tDp1Ui3/ajoCYSrBv\nntrYIbIMec6+4I9V0Ouqso8jouZgV6/unsEuKhICAjwX9/Z5Wl8UITxEN+bwB7lOus+MoTY7yeYX\nF1L9AhWFDyMsjM6yctINwY87YlXXyAv7XX6kBEYDfHg7TFwOR71cdGEywluD1TS/fB/kffu5fDEY\noEcLtddk0qcw9Cb4eSO0fVx1mzz4Ory/FPYd9843uNRM+Ho1DJkJDR6Bzk9CcKBaBPTSgxAVVvY5\nfMEff3rHYGdlqW9iWJh7JrSoyIbJ5LnZVdxxKbg1sKLIhWN/xGpyKWAoV6Og/wmzhxyGsptPaE4N\nnHcWfi67gIRCG4sjLS5r0p62Qss/4af20D7SpUfsmLoSVibC0ge83w3jjinQviFM6O/dcf389xCB\nPcdg1Q74c6f634Ii6HSFmvddvTJUizr333NHaCBk5cHZbDibo+ZOnz137EiE5dvgQJLa0/La1qps\ncPPa2jnPFxOpaVC3NaQcALOH2kvn2bOnkFtvTWXfvli3nlu48AhLliSxcGFn3XsURUFENK2KDxrG\na3MPnZjEd6xmP1fRSPe+xoTwCNV5hgN8QDNMDow7wMSQALqk5fN+XhEDg12rIIqxwBtNYMDfsKkr\nWDyIAYztBl/vgo8T4EEvV4+99gh0GAUPXav+Afnx4ymKAk1qqcfgG9VzR07Dhn2q3GtSKvx9GJLS\n1P8/kQq5VtVoR4ZCZMi549z/149TdXA6NlJL6y8lVq2BLh3LbqwBTp4sJi7O/U+ooiIbRqPnO7xy\nM9gWTAylF9P4mcbEUoVw3XvvJZY/SWcBSTxCdYfjmhWFBREWeqXlcY3ZSD0Xv27cWw0WnYLJB2DK\nFW69FEBt3juvL9z0Kdx8BVT2YhujenHwyPXw7CdqPzs/frxJ7Rj10MNmu/h3y56weh1cpb+xdYvk\nZBtVq3qe7eEp5fprqUVlbqYVc4mn2Emq3wvU5zNOspccp+M2MxkYF2Lm4UwrxS66eBQF5jaHecdg\nk4e+6HbVoH9zGPebZ887YkJ/WLLh4kvX8nP5czkaa4BlK+Hqbt4ZKyXFRnS0+2+UwaCUKYZQ7r+a\n3rTAgonFbHV4XywWnqA2EzlAgQuqfiODVefJW7muVxLEWtSCmgf/BjeSTUowuRcsPQB/Jnr2vB6R\nofDcPTDyXX+anx8/ZSXppNpdpqOX2o6lpnpmsBUFbG7Uj5Sm3A22AYVB9GQFu9mLY5m6m4imNkG8\ng3ONVKOiMD/CwrQc9wSi+sdB4xCY5GHWSHggvHUDDPnR+30gB9+oqrctjPfuuH78/Nf4bYWqfV2W\n7jIX4ukOWw0oej5vhXz5iSSYh7mKd1lBnoNUPwWFZ6jLT6S4VAVZ12hgSqiZRzKsFLnhGpnTHD48\nDls91CG+synUjoS313n2vB4mo6re9tR81XD78ePHM36PL3uzggtJS7NRqZL75tNkUigqQ0cUnxrs\n4+gr/7ehNs2pwWc4rhKpRABPU5fnOUgezv0WA4NMhBvgbTdcI1UtMK0xDNzuWXcZRYGZN6ll697O\nze7UGHq3hRcXendcP37+K4jAitVwtRfyr8+TmWkjIsJ982k2GygouEgN9o98Sr6DVmD30ok9nGSz\nk+rGa4iiGSG8zVGncyqKwrthqmtkvxvW94HqEBEAMxwvRZf6UTC6Mwz90fs+55cfUhu37nb+8v34\n8VOK/QfVb6v16nhvzMxMITzc/fQ8i8WI1XqRGux6NOY3vkbQtmCBBDCInnzEajKd9Hh8mrrEk846\nnG9h65kMTAgxMyjTis0N18i7zWHqQUj00P0wtiscy4Qvtnv2vB4xlWDi3X6dET9+PGHFaujZzbsF\nbpmZNsLD3TefFovh4jXYvejLGU6wE33hjUbEchWNmM+fuoYdIBwTk6jHJA6R5YJA1OPBJgqA99xo\nK9YgBJ6sC0N3emYYzSZ4vy+MXgqpXvY5D78FTqXDd2u8O64fP5c78auhRxfvjpmZKYSFuf8JEBho\nxOppSho+NtgBmLmZ+/mDxWSi36DudtqRTBZrOehwvE5E0p1KvMYRp3MbFYX3wtW2Ykfd0BoZUw+O\n5cFXJ11+pAQda0C/ZvD07549r4fJCG8OUgOQ1kLn9/vx40dlzQbo1sm7Y+blCUFB7hvskBAj2dme\np5N5bLAVRUlUFOVvRVG2KoqyQe++WGrQnu78xOeITj51AEYG0oOFrCPdSaHMKGqxmUz+dPABcJ5m\nJgOjQwIY6IYMa4AB3m8Bo3ZDiocCTJOvgZ/3wRov+5yvbQONa8DsH707rh8/lytJJyE7Bxo1cH6v\nO1itgsXivsEOCwsgK6sCDDYgQE8RaSMiHR3d2IleFFLAFv7SvacO0fSiCR84cY0EY+Q56vESh11y\njYwJDuCsDd53wzXSqRLcHQejdrn8SAkiAuGNPmpudqHn3340efURePkrVS3Njx8/jlm3CTq1975A\nm+cG20RWludfkcvqEnFpxQaM3My9rOZXUjmje9+ttCGLPFaw2+F4HYlw2TViOldQMzG7gCNuuEam\nNIK1Z2GJYxlvXfo1h7hQeNvL2tZNasFdV/nbifnx4wprN0LnDt4fNz9fCAy89HbYyxRF2aQoykBn\nN0dRlW704ScW6rYMM2FgMFfzNZs4g+Mt5ChqsYlM/nIha6SZycCokACGZha47BoJMcG85jBsJ3jy\n/ioKzL4ZXlkNJ7y8G37hfvh0hapt7MePH302boUrvVSOfiGFhRDggVqhxaKa3Px8z756l8VgdxWR\nNsANwHBFUZympbelCwGYWc8fuvdUI5JbaM08VmJz4hqZSF1e4hC5LhTUjAkOIMlm43M33qhe0dCr\nMjy/z+VHStCgMgxuD095WRyqSgSM+z+/zogfP44QgYTt0LqFb8b3xM2iKAqVK5tJTbV6NKfHlfUi\ncvLcf5MVRfkO6Aj8eeE9kyZN+uf/e/bsSc+ePbmRe1jAG9SjCTE60qm9ac4mElnGTq6nue4aOhNJ\nO8KZxTGeoo7D9QYoCu+GW7j9rJXeFiOVDa692681gWar4P7q0DbCpUdKMKE7NJkJqxKhu+MlusXI\nvvDRMjXN7w4vNBT14+dyI/EohIZAleiKXklJKle2kJpaQPXqqiZzfHw88fHxrj0sIm4fQDAQdu7/\nQ4C/gOtL3SN6/C0b5H2ZJoVSqHtPkqTLUFkgp+Ss7j0iIulSINfKJtkiGQ7vO8/IjHx56Gy+S/ee\n58NjIu3+FCmyufXYP3y5XaTlLJGCIs+e1yP+b5GaD4hk5Xp3XD9+Lge+/VHkpv6+GRuOic3mmUHo\n0WO5/PHHKQdjI6Jjez11icQAfyqKkgCsB5aIiN0X/wK01ZSa055KRPMnP+tOEEckt9LGqWskkgDG\nU5dJHHJJa2RyqJn4gmKWuZG8/mB1CDXBbOcxTk3uagYxofCWlwOQPVpAzxZ+nRE/frRI2A6t9L+g\nlxlP3ZGVK1tI8TBn2CODLSKHRaT1uaO5iLysdd923tJM0VNQ6EM/drCJEw50RK6nOQL84SRrpBdR\nNCaEd3EehQszKMwMN/NYlpV8N5sdTD4AJ/NdesTu+Tm3qOJQR7wsDjX9YZj/uz8A6cdPaXbvg2aN\nfTN2QAAUeZjsERsbyKlTjqU49PBppWM2x0jSCTAGE8p13MFPfE6hjsSqAYWHuYrv2EwK2Q7nGkcd\nfiSFnU7uA7jZYqK5ycDLOa7nQzYOhUdrwJg9Lj9SgvPiUI8t8W6gMDZKDUA+Mc97Y/rxczmw9wBc\n4eWCmfNYLAr5+Z79IVerFkRSkgc7P3xssFszjl3MIY9kzeuNaU1V4ljNUt0xqlOJ62nGAlY7LKiJ\nIoAnqc0LHKLQhQ41M8LMzM0t5O9C13OzJzaA1WmwPMXlR0owpiscSIPvHX9hcJuRfWHfCfh5o3fH\n9ePnUsVmg/2HoGE934wfGKhgtXpmsC/aHXYEDanD7fzNa7rG9jrudOoauYlWpJHDXzhuC3MDlYnF\nzHySnK6tmtHAS6FmBma63uwgxASzm8GQHZDnQRqlxQRzb4ERP0OWZ1k9mpgDVJ2R0e9BgV9nxI8f\njidBZASE6/f6LhOBgZ7vsGNjAzl92jMD4POOM/W5myJyOMoSzeshhHEdd/Azn1OkU2puOqc18jnr\nOYu+DN75DjVfcIpDTuRaAR4JMhGmwCw3mh3cHKOm900+4PIjJehRF66tDy+s8Ox5PW7qCPXjYJZf\nZ8SPHw74cHcNEBSkkJvrucFOSroId9jqBEZaMpZ9fEQe2nXeV9CKKGJYg77EXR2iuZrGTl0jMVgY\nTA2mcMhhdgmoSexzwi1MzXFP0e+tJmq39Z3Ou5Zp8sp1sCABdmt7ijzm9UdVnZEUD1ud+fFzuXDs\nBNSq4bvxIyIUMjI8M9i1agVz7Jhn+svl0tMxjNrU5U6286Zu1sj13EkCazjNCd1x+tKWk2SwgUMO\n57uLGKzY+EHHd34hDU0GRgYH8NgFZevpNiHbQWfjuEB4oaHqGvGkAXJMKDzTHUb+7N0AZJNa0L87\nvOBmml9yOlg9VCa81CguhjPJqo/zv0C+FZLTKnoV5UdWNmRkqi6RGtV8N0+lSgbOnvXsH1F0tIW8\nvGKys933X5ZbE9569MPKWY7zq+b1MCLoyc38zOcU6+RTB2DkUbrzKWvJQj/KakThWeoxg6Ok4fxN\nGRsSwOFiG3Nzi7g2pYCoU+rxQHqhruEeXAsKBeZ7mE43/EpVY8TbAchJ98EXK2GXC9Kuf26FFndD\n1eshpjdMes+7a7nYmP8Z1GwFMU2hTlv4/NuKXpHvsNlg3JtQpQdU7Qlt+8HGHRW9Kt9xNgP6PwqV\nGqjHuwsgPMx380VGem6wFUU5t8t23y1SbgbbgImWjGEP88hHO82iBR0JJZy1LNMdpwExdKYBn+K4\n9UpjQriJKrzhgqKf+ZxrZFR2AcvPNcgsBD7JszEyU9u/bTzXUmzCXjjjQfwgwKg27n1iKeR5MVAY\nHQHP3QvDZjvevaeehRtHwY5zPSMysuGFefDeZWrEVq2BR0bByXNeuWMn4P6hsHlbxa7LV7zxMUz/\nELLPffPeugf6DP3358uNgaPhq8XqNygROHYcPl3ku/kiIw2kp3v+Na1WrWCOHHGs/a9FuRlsgAga\nUItbHBbU9KYfm/mTZPRbvtxJew5whr855nC+odRgK1msdUHRL0RRKLQpKErJX8JnuTYKdCxfq3C4\nvxqM3+t0eE161YP21WH6as+e12PYTZCVB5/qa2zx9R/af7wfaseGL3k++sL+nM0Gn3xV/mspDz5c\nbH8uLQN+8HKw+2IgIxO+0yia3rUPDh72zZxVqhg4c8Zzg123bgiHDjmvGSlNuRpsgIbcRx6nOaGz\niw4nkh7cyC98qSvDasHEg3RlAX9hddDEIBgjE6jLFA47LVsvFBAxgCJwwYdJETjM6p7UEH5JhnXO\nG+Bo8lpvmLkeDqR69rwWRiPMfQzGzoc0ncBooc7bdrmmBfpfr0qB51LMFy3Fxeqhha9+v3FxRk6e\n9Lw7ScOGYezff5EZbCsJGhMG0Iqn2M27uq6RVnTCRACbWKU7dktqUp+qfM8Wh2voSiRtCGO2k914\n+wCF+kYFEQOKoZjzRrtvoIFABzqK4QEwrTE8thOKPQgg1o6Ep7vB0B+9G4Ds0Aju6AITPtK+fntP\nCNDQaux/nffWcDHR/zad833Ldx3lRf/e9ueCA+GWHuW/Fl8TVQmu62l/vmljaNLIN3PGxRm8YLDd\nTzPzqcFOYwSiERyMoCG1uNmBa8TADfRjLctId5DpcS+dWMVejuE4DP4ktVlKKjsclK0bFIVvowJo\nZDj3lihCT7PCnAjnCrT3V4MgI3zg+DNBl5Gd4UwOfL7ds+f1mPogLF4H6zXK6atXhc9fgiqV1J+N\nRhhwCzxxr3fXcLFw8/XwwjgIClJ/DgmGVydBj8tUmnbiILjnBjj/zzk2Gha9DpUjK3ZdvmL+22or\nMOCfL8hf+FCuQd1he+4SadgwlH37PMgL1pPxK+sByBkZIOkyWVNCsFgKZKUMlOOyTFdmcJ38IQtl\ntthEX8bwD9klk+R7KZZi3XtERH6WZLlLtkmhg7FERGw2m3yVWyjRp7PllBt6qgkZIlV/F0m2uvxI\nCdYeFYmdJpLuZanUT5aLtHlMpEhH2jXfKrJpl0hSsnfnvVhJSxfZlCCSkVnRKykfjp8S2bxTpKCg\noldSPuzZL7Jhi0hgnG/nSUwslBo1kjx+Pj+/SCyWr8Rqtf/DxAfyqi4RxStk8zkF2IfiDQTQkifY\nzVysOkHBDnQnn1x2sEl3jh40xojCcieKfn2oTBQBfM4ph/cpisJdQSYGBAUwJtv19I9W4XBPNRjr\nYZpep5pwyxXwnINAoSfcdzUEW1RFPy0sZmjXBOIuMpF3X1EpEtq18m3K18VE9Rho29SzdlaXIlc0\nUCsczT5+vdWrG0lOLvZYT8RiMVKnTojbu2yfGmwjVanEC6QyCtFQ5IukMdW4ht3M1VmckT70I54f\nydVxZ6iKft2dKvopKIynDvM5wSmcG+LnQwNYU2Djdzd0syc3guWpEO9hAPHl6+DLHZCgnyDjNooC\nM4fCs59AuoeVmX78XEoUFYHJ415armEyKdSsaeLwYc+juM2bR7B9u3tlyT7PEgnmToxUI5OZmtcb\n8SBp7OAMGzSvx1GLJrRhBfoiGdWIpDfNnZat1yaI/sTwqgu52SGKqps9PMtKnovRwDATzGwGg3eA\nG3b+HyoHw5RrYPgS71bitakPt3WCSZ95b0w/fi5WysNgAzRoYOTAAc8NdosWF6HBVlCI4lWy+IAC\nDbeFiSBaMJodvE2RjmDTVdzAEfaRiH433JtoRSrZrOWgw/UMoDr7yeVPnOfh3Wgx0cZkYIobJaR9\nY6BpKLzseBm6PNIWimyq1og3mfIAfL4SdiR6d1w/fi42iovLx2DXr2/i4MHLbIcNYKIaETxNGk8g\nGvnQVWhHFC3ZxwLN5y0Ecj3/x1IW6TY7MGHkEbrzOevIceDysGBgAnWYRiL5LuhmvxlmZl5eIXuL\nXN/yzmgKs47AQfcLmTAYYPbNMGEZZHimca7J+QrIEXP9ndb9XN4YDPp52d7kiisC2L3bc4PdunUl\ntm51r4Cj3ApnQrkfBTPZfKR5vSlDSGI5GTq76AY0I46arNbRIgGoT1XaUYevdNwr5+lEJE0IYb4D\noanzVDMamBBiZkSW9R9xKGfUDIKx9WDELs+MY/vqcFMjeDHe/WcdMeRGSM2ChV4e14+fi4mQYMgt\nhxL8Fi1MbN/ueWVOvXoh5OUVc/Kk65oi5WawFQxE8RoZvEaRhqE0E0FjBvE3r2PTqV68ltvZzgZO\nOejdeBcd2MpR9utIuZ5nLHVYxGmXdLOHB5s4WSx844ZjenRdOJgLP55x+ZESTL0WPk6APV6UYDUZ\n4f2R8OT7kOyXYPVzmRIcDDm5vv8m2bx5ADt2FLq8kSuNoii0bx/Fxo2uyymWa2l6AA0JYyBpPKUZ\nHKzOtViI4hDaAg8hhNGTW86VrWsbzxAs3MOVfMRqih24PKpidlk3O0BRmBluYUxWATku/nLMBpjV\nDEbt8qw7TdVzEqyP/eT9Csj7eqrdafz4uRwxmdTD6sWuTlpERxsxmxVOnfI8Q6BDh4vJYBfZa3yG\n8xjFnCCXb+yuKSg0ZxSH+JpsnVLyFnQgkCA2Oihb70R9wgniNxzrSd5FDEUIi13Qze5hNnKV2cBL\nbgQgr42G9hHwiocByMeuhNRc+Oxvz57X48X/wZrdsFQ/vd2Pn0uakGBVG9vXNGliYudOz90iHTtG\nsWHDxWKwU4bYbQ8VzETxBulMohj7hOVgYmjI/U4U/e5iHcvJ1Mn0UFB4gC78SAJp6Ef+jChMoC6z\nOEa6C7rZ00PNvJ9XyD43ApCvN4HZRyDRA5+ayQjv3gpjf4V0zzoKaRISCO8Mg2HvQK4XA5t+/Fws\nxFaF0x66I92hdWszCQmeG+wuXaJZty6VIhdtim8NdvEJyP7U7rSFtoRwB+k8p/lYHfpSTJ5us4Mo\nqtCWbizje92p44ikF01YyDqHS2xMCH2ozNs4V/yPOxeAHO5mAHJUXXjCwwrIjjXgjqbwtH73N1G9\neAAAIABJREFUNI/o0x46NoIpGrKjfvxc6lSLgxNeLEDTo23bALZs8bxdU3S0hRo1gti2zbkENPja\nYEfPh7QxUGwfAIxgHFbWk4d9LbaCkRaMZg/v65atd+YakkniILt0p7+FNiSSzDYXdLPXkkECzksB\nHws2kWaDz/Jdd0yPqQvbs+CnMgQgl+yFNS50kXGHNwfBvKWw03kdkR8/lxTVy8lgt2tnZvPmsmm4\ndu9ehVWrXMsu8K3BtrSDsAGQ+rjGxCFE8RppPIVNw20RQUNqcB27mKM5tIkArudOfuMb3dxsVTe7\nGwtYjdWByyMUE09Qi5c4RKGT3GyTojAn3My47ALSXGzoGGiEd5rB8J2Q40HaZkQgvNEHBv8AhV7M\nL42Lghfuh8Ez/zs9Dv38Nygvg92kiYljx4rJzPT8D+jiMdgAkc+DNQFy7UvLg+iJhU5k8Krmow15\ngHR2kKKjeV2XxlSjtsOWYi2oQUNi+J6tDpd5PZWJxsyXTtIBAToGGLndYmRitutfha6rAl0iYcoB\nlx8pQb/mEBcGs9Z79rweg29Qxe4/0n8L/fi55KhbCw4m+n4ek0mhdesANm703C3Ss2dVVq5MdsmP\n7XuDbQiC6LmQ8hjY7MO2lXieHL6igJ1210wE0Yzh7GAmxTq76F7cylbWkOLA0N5zTjf7uAPdbAWF\np6jDB5wgRWeuC5kcamaxtZiNbmx5X28C7x+HXR6IMCmK2gNy6io46UURJ6MR5jwG4z+C1EzvjevH\nT0XSoils1/eWepWrrjLz55+e5xDGxQVRo0aQS+l95ZOHHdQLgnpCun2Q0UgVIhlPGmMRDXdEDF0I\noQaH0O6oGUYkXbmeX1mk+TxAJMHcTlsW8JdDcai6BNGXKsxwIQBZyaAwNTSAxzILKHYxABkXCM81\nUF0jnuRWXxGtao2M+839Zx3RtgH07w5Pf+jdcf34qSiaNYbd+8qnRL17dwt//un5DhugT584fv3V\nsfQzlGfhTNTrkP0ZWDfbXQrhPsBANvYZJQDNGM5hviGXJM3rbelGEYX8zUbd6XvRhAKKWM1+h8sc\nSA3Wk+lSAPJ/gSYsCryf57pjelhtyCiChdovxSkTe8CKw7Day4HCyf+DpZvhDy+LTvnxUxGEhamp\nfQcO+X6url0tbNhQQEGB5xVuvXvHsnSpc6d7+RlsYzRETYOUQSAlP/bUsvXpZPAKxdinUgQTS336\ns523NXfIBgz0oR8rWUKOjqE1YOAhuvEVG8jWaFt2nhCMjKYWUznsNABpUBRmhVl4PruAFBcDkEYF\n5jaHsXsgw4PgcqhFbdw7fAkUeXH3EBEC7z0OD78FWeWgw+DHj69p2Qy2Oa6d8wqRkQbq1zexebPn\nu+xu3aLZtSuTlBTHrpXy7Zoe+iAYwiBzlt0lM00J4R7SeV7z0brciZV0ThKveT2G6jSjPfEs0Z2+\nLlVoT12+wX6XfyG9XexOA9AywED/QBPPuRGA7BgJN1WFFxxv9nXp1xyiguAd/S8UHnFDB+jVCp6a\n791x/fipCLpdCavWls9c119v4ddfPa9Cs1iMXHddLEuWOP7q7VuDfSa+5M+KApXnwtnJmmXrETyJ\nlU2audkGTLRgFLuYS6FOZ5lu9CaRvRxzoIl9J+3YyGESdTq2w7/daT4kyaXuNJNCzXxvLWarGwHI\nlxrBJ0meByDn3KKq+R3zsojTGwNhyQZY7neN+LnE6dUd/tBXsPAqN9wQyM8/l61s+Pbbq/Ptt/rC\nduBrg71lIBSXqqk2N4bwkZAy3C7yZiCYKKbr5mZXoikxdGEP72tOZyGQa7iN3/iGYh1xqFACuZP2\nfMIar3WnqWRQeCEkgJFZBS5XQFa1wMT6MNJDCdbGVWDElTDsR++KQ0WGqq6RR/yuET+XOK2aw6kz\nkFQO+dhdu1rYt6+I06c991PefHM14uMdV9f51mBHtoFdL2icHwdFhyHHPvMjiKux0IEMXtMcsjGP\ncJq1pOtUOF5BK0IJZ5MDcageNKKIYtbgOCnane40DweZsAosyHcvAHnSCt85T/3W5Omr4FA6LLLP\niCwTN3SAa1rD2A+8O64fP+WJ0Qg9u8GK1b6fy2xWuOaawDK5RSIjzdx/f22H9/jWYLeeAYnz4Wwp\nuTnFDNHzIG002Oy/01fiRXL4UjM3O4BQmjKEHbytKbGqoHAdd7KO5WTplLUbMPAAXfmC9U670zxN\nHaaTiNVJANKoKLwTbmZCdiGpLgYgAwxqd5ondntWAWk2wby+MOoXOOtFcShQXSM/bYR4LysF+vFT\nnvTuBUv0e554lZtvDmTx4rK5Rd55p73D67412IGx0GwybBkMUsrgBXaG4JshfaLdY0aqnGspNk4z\ntzqOngQQzhF+0Jw2iiq0prPDxr3nu9MscpAKCNCFSBoRzCc4/17VLsDI/1mMTHAjANkrGq6qBJM8\nDEB2qQW3XAHPLPfseT0iQmD2MBg4A/J8rCvsx4+vuPMW+GUZZJeD1OpttwWxbFk+WVm+03nwfZZI\n3YGAAofn2V+r9DLkfA1We2HmUO4DisjhS7trCgrNeIwDfIpVx13RmWs5ziGOOghA3kUHNpPIQY1U\nwgt5ktp8xklOuhCAfDHUzE/WYtYVuFcBueAEJHhYafjKdfDtLtjgOF7hNrd2grb14YWF3h3Xj5/y\nIroydL0SFv/i+7kqVTJw1VUWfvjBd5rFvjfYigHavQs7n4X8Us5aYxRUmg4pg0FK+gQUjEQxjbNM\noVijpDyM2tSgD7vRbp1ixkIv+vK7gwBkCBbu5koW8Bc2By6PagRyN7G84UIAMtKgMD3UzLCsAorc\nCEC+fAUM3g7FHgQQKwXBq71VcShv5mYDzBgC83+DLR5qoPjxU9Hcdxcs/Lp85urfP4gvv/RdtL58\n8rAjWkDtAbDtCftrofeDIRwy37G7ZKYVwdzKWV7SHLYh95NKAmls17z+bwBype7SutCAIAJY5kCm\nFeBBqrGLHNbhPI/unkAjlQ3wjhsVkANqgMUAcz2sYLyvpZqb7W1xqJhKMP1htaDGWjYVST9+KoRb\n+8Bf68unoUHfvkGsXGklLc03bpHyK5xp+hyk/gVnSuVYKwpUfudcbra9nziS8eTxG1YNtT0TQTRh\nEDuYqRuAvJ47WccfTrrTdGUxW8l00JA3EANjqM2rJDqtgFQUhRlhFl7KLuC0i1tmgwJzmsOkA3Da\nA5+xosA7t8CUVZDkZRGnB6+F+rEw3q814ucSJDQU+t8Oc8qhICw83MCNNwby2We+2WWXn8E2hUCr\nt2DrcLCVCsqZm0DYw5D2lN1jBsKJZCLpPI1oGOU4emImgiM63WcqnetOs9xBd5rqVKIbDfmKDQ5f\nQk8qEYOZL1yQYG1iMvBAkMmtAGSzMHioOozb4/IjJbgiGga3hye9HBVXFJg3Er7+y98H0s+lyeih\nMOdDyPNyNpUWgwaFMG9ejsfd1B3hW4OdUSoKVq0vhNSHvRo51pHPQn485MXbXQrhLhTMZPOJ3TW1\nce8I9vMZeTrNdDvRi9MkcQj9Pl230ZbtHHcYgFRQGEcd5nOC0y4EIJ8NMfNrQTHr3aiAfK4hLEuF\n1a735SzBM91h7TH4zcs+56gw+PhJ1TVy2nlauh8/FxWNG0HHtvCZtuinV+nZ00JenrB+fdkU/LTw\nrcH+sVSnGUWBNrNg/xuQXSp7wxAKld+G1KEgJY2hgoFKTCOD6ZriUKHUpDa36nanCcDMddzBb3xL\nkU7nmSDM9KMjH/MXNicVkP1crIAMNyi8HBrAiMwCbC5+2oaZ4PXGqgSrG71+/yHYDHNvgUE/QLaX\n0/F6toQB18FDb/g71Pi59Bj8EMz/zPfzKIrCwIHqLtvb+NZgJ++CXaVcESF14IqnYesw+5rq4Nsh\noCFk2O/A/xWHmqQ5VQPuIZMDJOvkVdenCVWJYz0rdJfbhQaYMLKKvY5eFQ9TnX3ksEanMOdC7g80\nYVbgQzcqIPvFQbRZ7bbuCX0awtV1YbwPushMug/Ss2G2vsaWHz8XJX2ugaPHIUE7R8Gr/O9/wXz7\nbR7Z2V7e2YiIRwfQB9gD7AfGaVwXObBcZHotkfwsKUFxgcivzUWOfil2FBwWSawsUnDI7lKxZMtx\naSN5str+ORE5JWtlhTwgRWLVvJ4uqfKmTJCzkqp5XUTkoJyRobJA9kuS7j0iIqskTW6VrWKVYof3\niYhsKiiSuDM5klpsc3rveXZmikT/LnIq3+VHSpCaIxI3XWR1ouP7cq0ifx0QOaL/ltix77hIdH+R\n3Uc9W1tFciZFZPUGkdT0il5J+XDomMiarSL52n8Slx3bdols/lvEpvOnNv1tkXseLZ+19O2bLO+9\nl+X8xlKoZlnH7updcHQARuAAUAcIABKAJlLaYIuIfHW/yC9j7VeVvFpkSXWRggz7a+lTRU7epPmu\n58gSOSHdxKZjlDfIRNkvn+m+GX/KL/KdfKh57bCclnHysTwoc+RBmSMvySJJl2zdsUbKHnlfjute\nv5DHMvJlcIZ71vfJXSIPJLj1SAm+3iHS+G2RvALt6ws3iEQ+IcJQEWWYyL3zRayFro39zhKR9iNE\nCly8/2JgwjQRc30RaooENhCZMqOiV+Q7cvNEbn9chCbqEd1F5PtlFb0q35F4TKTNDervlpoijXqI\n7Nhjf19Ghkjl+iIHD/t+TT//nCvt2p1y+zlHBttTl0hH4ICIJIpIIfAF0Ffzzhtegy0fwalS30Oi\nu0JMH7WgpjQRT0LRQchdbHcpiBsxUYMsnYKZZgzjEF+Tp5PJcSW9SOIoiaU6z9iwMYelpJCJkWJs\nGDjAGT51kMM9ltp86mIF5JRQM0usxaxxowJyUkOIT4Xl+kqwDrmzGTSpAlM0XsLRNHhgwb8aJCKw\ncCO87qIbZciNUDkcptoXol6UfP8rTJ0FBefiQPlWmPgqLC8HYaCK4MV34LsLfpcp6XD3GEj2MJh9\nsTNgDGy9oFnBvkPQb5j9feHhqi/79dm+X9P11weSnGwrU2OD0nhqsKsDxy74+fi5c/aExsC1k2Hx\nEPtIVYtpcOwLSC/VFV0xQ+XZkDoSbCUd9woKlZhKJrMp4oTddMHEUYfb2MVczeUEYOYabmMZ35bI\n3U7kDKnnutUogJFiijGSQCKFaPufq5+rgHzdhQBkhEHhtTAzQ7OsFLoYgAw1wexmMHgH5HlYwTj7\nZnhvM2wr1Yvh+23aQc1FjpvL/4OiwPxR8M5PsHGfZ2srTxb9pH3+65/Ldx3lxSKN1M58KyyJL/el\n+JzUdFixxv78rv2wS+Pf5ohB8Pk3cMpDlUxXMRoVHn00hHff9V7w0VOD7ZLFmTRpknr8lET8njRI\n+LjkDZbK0HwqbH3MXhwqqBcEdoWzU+3GDaAuoTzEWV7UnLc+/clgPyls0bzeiBaEEMYW/rpgTFOJ\newz/FMcYUVB0X+NDVGMPOax3oQKyv8VIrEFhdq7rAcibY6BNOLzkYZpeXBhMvRYGLYbiC97ioADt\n+wNN2ue1qFZZFYjq/wqkebGTuy8ICtQ+H2gp33WUF3qvV+/8pUyACUw6/261Xm9MVXj4PnjW3rR4\nnYEDQ1i0KJfkZP0dV3x8/L+2ctIkxwPq+UocHUAnYOkFP4+nVOCR8z7s8xzbKDI1RiQ3reR5W7HI\nso4ihz+yd+YUHj8XgNxvd6lYcs4FINdo+oFOyp8SL49IsRRpXk+Wk/KWPCNZ8q8PfbJ8JY/IrH+O\nATJbHpEPJEvyNMc4z3JJlTslQQrFeVBxT2GxVDmdLSeKnAcrz3MiTw1A7sx0+ZESFBeLdJsnMmvd\nv+dSs0UizvmvLzw++Mv98Ue9K3Ljc+o8FyurN4gotf71cVJTxFhHZOuOil6Zb3hzwb/+6/NHla4i\n2TkVvTLfcPfwkr9baopc3V///rMZIrGNRTaXIUbkKgMHpslzz511+X584MPeBDRUFKWOoihmoD/o\naJ2ep0Z7aHIbLHuu5HnFoOZm73gaCkqlyZmqQ8RYSB1lN5yBYCJ5nnQmIBouixi6YqGSrgRrNLG0\n5EpWXHB9ODfQktooKARgpCdN6EJDpz0gr6YSlQlgkQsVkFeYDAwMCmCsGxWQ1QLh+QYwZAe4KLVd\nAoMB3r0VJq2AE+fK1qNCYOlj0K6W+nPlEHi5Lzzcxf3xpz8Mmbkw5Qv3ny0vunaAT96C2jXUn+vX\nhq/egdbNKnZdvmLk/+C5oRAZrv7cqRX8+h6EBFfsunzFe6/A/+4As1ltXHB7H/jSgZ86IhxefBpG\njvduxyYtnnwylDlzcsjJ8UKKn54ld3YANwB7UbNFxmtcF0k6WPKjIydF5KWqIie22n+sbBoosnWk\n/XlbvsixRiI5P9pfEpucktskU+ZrflJlSqL8JndIvqRpXrdKvsyWSXJESu7g86VACs7tzLMkTx6T\nT+SwJGuOcZ4DkiNXy0ZJFZ2UjAvIttmkzpkc+cOqvfvXosgm0n61yAdlSKWbuEzkjs/tz2fkirix\n4dckKVWk2v0iP28o2zi+xmZTd1d6aV+XG4WFIhnuZ5ZdsuTlieTkunZvUZFI6+4iX3zj2zWJiNx2\nW7LMnOnaLwJvp/W5cgAiE2+w/8vYME9kTif778/5ySI/VBE5+7f9K8j5ReRofZFie9eEVXbKMWki\nRZKi+eJ3ybuyVV7RfXN2S4LMk5elSMd1IiKyQnbLC/K92Jy4PF6Vw/KcHHB4z3m+zSuUZsk5UuCG\n5dhyVqTK7yLJHubU5hWINHpLZJGP3ACrtotUvUck0f1MJj9+KoSVf4nUaCaS7rrHwiPWrMmX2rWT\nJD/f+d+7I4Pt20rH00fgr+9Knmv3sJpisLlUw0BLNDR9EbZoVUD2AXNzyHjVbgq1AvIOzjJFcwnO\nJVhbEkoEW9DP7+rOFRRhY62DZggAQ6jBOjLYinO5vNssRmoYDW4FINtEwN1xMN5xIaYugQGw4A54\n7Cc47YMOHFc1hydvh7unQaEHLc/8+ClvuneBW2+AEU/7dp7OnS00bRpQ9nJ1PUte1gMQ2RYvcn9N\nkdxSXwWSEkReqiKSfabkeVuRyLIO2gHIgkQHFZAZclxaSr5ofx8/IX/IShnoIAB5St6SZyRb9KN6\ne+WkjJDPJM+Jy+NXSZH/kwQpcKECcndhsVQ9nS2nilzfZZ8tEIlbJrJW28vjEhN+F7n1M9+4BYqL\n1QDkmPe9P7YfP74gO1ukQTuRn37z7TxbtlglNvaEZGc7tg1U2A67ZQ9o2RM+K5V+F9cKWt0Hv5b6\nWFOM0HYObB8HBaUy/ANqqwU1qSPsplElWJ8jzakEq14AMoYWdCAefYGMRsTSmFiWkKB7D8B1RBHt\nogRrY5OBB4MCGO9GADIiAKY3hmE7PetOA/BcT0hMhwWOX4pHGAyw4An4chX86OVmCn78+IKQEJj5\nCoyaAFYf9i9t08ZM9+4WZswow9dbPUte1oPzaX1pp0T6VRE5vL3kx0hehsgr1UUSNXRBtgwX2TzY\n/rzNKnLsCpHsxfaX/glAam/tnAUg8yVPZsrzclwOa14XEUmVLBkiC+S0aJTTX0Ci5EpP2SinxHkp\nemaxTWqdyZF4NwKQNptIj7UiM/SX6pSEkyLRL4sc8ZGmxuodfn+2n0uLW+4ReeUt386xd2+BREef\nkNRU/V02FRZ0PM/iWSJje9p/B9/2ucjM1iLFpYyVNV3khxiRtE32ryb3d5GjdUWK7UPBVtl9LgCp\nndGxU+ZKgryqeU1E5G/ZIB/JG2Jz4M5YLFvkdVmqe/08s+SojJN9Tu8TUQOQTZNzJN8NH8XuLJHK\nv4kkuhgR12JKvMj1H/kuY+L1b0RaDRfJvExzf/1cXhw8LBLdQGSXhgaJNxkyJE1Gj9bfKTky2OXT\nceamwZCdDqu+Knm+RX8IjICNpXRBzJHnKiAf16iAvBbMbXQkWBufC0C+rLmMhtxHMhs4qyOf2px2\nAOxwkHd9Ay05TQZbnJSjP0w1tpHFJhcDkPWNBl7Pcb1pYuNQeKKumptdOkbrKk91g+Rc+NDFcnR3\nGX07dGwE90zzfnNgP368Tb06MOUZeGAYFPqwf+nzz4ezYEEux465H5kvH4NtNMGwWTBvDORd4L9R\nFLh5Jix/HnJKKRzVeQikGI7Yd5kh6nXIfAsK7Y1mBGPJ41cK2GZ3LYBQrmAAO5mNaFTXKxi4lttZ\nyU9Y0W5VH4CRB+jKp6zBqqMxAhCEkSeozXQSKXJSya8oCjPDzbyVW8hBN7oWjK0HJ/Ph0ySXHylB\ngBE+vB3G/fZvQY03URS1dN1aCE/M8/74fvx4m0EPQnQUTH3Dd3PExhoZNCiEyZPd13PwrcG+cOvX\nvBu06AFflCrgj20BLe+B3yeWPP9PBeR4KCyl0xFQB8JHQNoYuykNRBDJeNKYoGmUa9AboYgTLNdc\ncnXqUJuGrOE33ZfVjOrUpyo/OglAXksUkZj42oUAZG2jgadCAhieVXDepeSUAAN80BLG7IYzHgZL\nWsXC8I4w5AffVHwFmGDRBFi2FWY6roX146fCURR4/214Zz5s8tE3T4CxY8P49ts89u93cyuv5ysp\n6wGILF5U0jmTckLkrsoix0v5dnPTRabGihzfbO/Q2fiISMJo+/PFuSJH64jkLre7ZJNiOSnXS7Ys\nsn9ORNJkpyyT/lIo2g7gLMmQt+QZSRb9iFmqZMsw+VhOiuOMe3cqIAtsNmmVkiNf5LknMv3UbpG7\nt7j1SAmshSItZ4l84kNdhUMnRWLvvfgrIf34ERH5/GuRRh3UqlhfMWVKhvzf/9kX/FFhQceWNUWy\nSuVgfzVdvwJybhf783mnRRZHi2Tstn/F2V+LHGshYrM3cPmyQY5LKynWaUCwRabKbvlA85qIyAaJ\nl4Uy22F14xJJkNfkF93r55kmh2WyHHR6n4jIKmuR1DqTI5ludKfJKRKpt0LklzNOb9Vl0wmRKq+I\nHPVhxdfqHSJV7hbZdcR3c/jx4y2GPqlmjvhK1Cwnp1hq106SP/4oWcHtyGD71iXSpQe8UaoC8baR\ncDoR1pTq9dhuABRZIeHTkucDq0Lj8fD3E/bjB98BxsqQZe8gtdABC53JZKbm0powkKMsIYfjmtfb\n0Y1cstmr4Qs/T2+ac5pMEjiqew+oFZArSWcHzvMvrzIbudpsZIobAchgI7zTDIbtgFwPg3vtqsHI\nTvDANyVlWL1J12aqUNStL178cqx+/Lw1FdLPwmT7AmuvEBxs4PXXIxgx4ixFRS76I/UseVkPQOTU\nSZFG0SJ7d5X8aEn4Q+R/tUTySu1+j6wVeTlOJK/UNq/YKrL0CpET9vnXkp8gklhVpMj+q0WhnJBj\n0lgKdHKrD8gXsl7G6+6ij8gBmS2TxOogn3qbHJUx8sU/YlF6LJEzcrdsc0mC9VSRTaqezpadhe59\ntN+zRXWPeEpRsUj390WmrvR8DFd44j2Ra8ZfWu3F/Pw3OXlKpHpTkWXxvhnfZrPJNdeckRkz/vVE\nUGE77JhYePJZGPdYyYhWq6uhaVf4/KWS99fqBI1uVLNGLsRghtYzYdsoKM4rec3SCkL7QfozdtOb\nqEY4w0jH/hpAXe4gj1OcRqNdBVCL+tSgHmv4XfcltqQm1ajEUh2tkvPcSDRhmPiKUw7vA4gxKjwb\namZEptXlACTAm03hw+OwzcOMD6MBPv0/eHMtrD/m/H5Pmf6wqmvy8Jv2TYj8+LmYiI2BD2bAgMfU\n3ba3URSFGTMiefHFTM6cceHrsZ4lL+vB+cKZwkKR7i1Fvv+q5EdLSpJ2ADI7WdUZOVWqMlJEZM3/\nieycZH++KF3kSIxIvn2hjU2sckI6S65oCwUky2ZZLvdJkc4uOlPOylvyjKSJvoP4lGTIUFkgaQ4a\n9oqIHDpXAXlGp4HwhRTabNImJVcW5rq3DX3viMiVf4m44QK3Y9EOkfpvimR52LHdFXLyRLqPFRk6\n678jdern0mXk0yI33+07f/aYMelyzz2ql4AKr3RcHS/SqpZITqmSt6+mi0y80X71a2aKzOtp/5ec\nc0RkcZRI9mH7ZzLniZzorHawKUWuLJcTcqXYdIzyJpkk++QTzWsiImtlmSzSKXk/z5eyXubKCof3\niIi8LUdkvIsVkGusRVL9TI6kuWF9i20i3daIvH3Y5Uc0efAbkYHfl20MZ2TkiLR7XORpbTlzP34u\nGgoKRLrdIDJJX6m5TOTkFEuDBifl++9zL4JKx649oH1nmDGt5PnbRkLSAVhfqkNqxyGQmwo7FpU8\nH1wLGoyCv5+0nyP0YZBCyP7U7lIQvQigEZk6jXmbMJjDfKPbab09PUjhFIfZo/sSb6E1u0hiv5Oc\n64FUZytZbHShB2Rns5HbLEaeynJdHMqgwAct4MX9cKAMSo4zboTfD8IP+i+5zIQHw9LJ8MN6eOUr\n5/f78VNRBATAog/h/U9giUaD47ISHGzggw8qMWxYuuMb9Sx5WQ9K93Q8flSkYWWRxFLyqBt/ERnQ\nQMRaavd7KF5kWk0Rayk3Q1GeyM91RU79bv8xlbdO5EicSLF98mShHJZj0lgK5YTmJ9xe+Ug2y4ua\n10RE9sl2ec9Jo4O1ckAmyNdS5ERadbmkyu0uSrBmnBOHWuGGOJSIyJuH1J12WVwjqw6LxE4TOeXj\njiXHk0XqDhB5Z4lv5/Hjp6ysWS9SpaHIPtf6lLjN4sUVuMPO3b373x+q14Qho+G5Urvj9n2gVlP4\n7s2S5+v2gNpdYeUrJc8bA6HVm5DwONhKpb4FXglBvSHdvpu6iTqE8qDDTutn2UOqTvViA5oRTqTD\nRgdXUo8wAvmdnbr3gNoDsjoWFroQgAw3KMwIMzMk00q+GwHIEXVAAWYkuvyIHVfVgQFt4NHvfdv3\nrno0LHsJXvoCFq7w3Tx+/JSVzh1h8gToe59vgpC33hrk+AY9S17WA5Dt11wjtgv90Hl5Im3qiMSX\n2h2f2K8GIFOSSp5PPyoyOUokLbHkeZtNZOV1Ivvetv+IKjx5rtGBvZ+4WLLluLR20Ohk6yr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+ "text": [ + "" + ] + } + ], + "prompt_number": 36 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exercise 6\n", + "\n", + "a) Has the approximation of the mean been improved by using the GP model?" + ] + }, + { + "cell_type": "raw", + "metadata": {}, + "source": [ + "# Exercise 6 a) answer " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "b) One particular feature of GPs we have not use for now is their prediction variance. Can you use it to define some confidence intervals around the previous result?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Exercise 6 b) answer" + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Computation of $P( f (U ) > 200)$\n", + "\n", + "In various cases it is interesting to look at the probability that $f$ is greater than a given\n", + "threshold. For example, assume that $f$ is the response of a physical model representing\n", + "the maximum constraint in a structure depending on some parameters of the system\n", + "such as Young\u2019s modulus of the material (say $Y$) and the force applied on the structure\n", + "(say $F$). If the later are uncertain, the probability of failure of the structure is given by\n", + "$P( f (Y, F ) > \\text{f_max} )$ where $f_\\text{max}$ is the maximum acceptable constraint.\n", + "\n", + "### Exercise 7\n", + "\n", + "a) As previously, use the 25 observations to compute a rough estimate of the probability that $f (U ) > 200$." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Exercise 7 a) answer" + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "b) Compute the probability that the best predictor is greater than the threshold." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Exercise 7 b) answer" + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "c) Compute some confidence intervals for the previous result" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Exercise 7 c) answer" + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These two values can be compared with the actual value {$P( f (U ) > 200) = 1.23\\times 10^{\u22122}$ .\n", + "\n", + "We now assume that we have an extra budget of 10 evaluations of f and we want to\n", + "use these new evaluations to improve the accuracy of the previous result.\n", + "\n", + "### Exercise 8\n", + "\n", + "a) Given the previous GP model, where is it interesting to add the new observations if we want to improve the accuracy of the estimator and reduce its variance?" + ] + }, + { + "cell_type": "raw", + "metadata": {}, + "source": [ + "# Exercise 8 a) answer" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "b) Can you think about (and implement!) a procedure that updates sequentially the model with new points in order to improve the estimation of $P( f (U ) > 200)$?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Exercise 8 b) answer" + ], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/lab_classes/mlss/gaussian process introduction.ipynb b/lab_classes/mlss/gaussian process introduction.ipynb new file mode 100644 index 0000000..4d8ffb6 --- /dev/null +++ b/lab_classes/mlss/gaussian process introduction.ipynb @@ -0,0 +1,1023 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:d132a55f4fd06bd9bcfd3fce4e6a16df11818a010d327f7ad0a80eff9c24a96d" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Inroduction to Gaussian Processes\n", + "\n", + "## Gaussian Process Road Show, Genoa, Italy\n", + "### 19th or 20th January 2015\n", + "### Neil D. Lawrence\n", + "\n", + "When we form a Gaussian process we assume data is *jointly Gaussian* with a particular mean and covariance,\n", + "$$\n", + "\\mathbf{y}|\\mathbf{X} \\sim \\mathcal{N}(\\mathbf{m}(\\mathbf{X}), \\mathbf{K}(\\mathbf{X})),\n", + "$$\n", + "where the conditioning is on the inputs $\\mathbf{X}$ which are used for computing the mean and covariance. For this reason they are known as mean and covariance functions.\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%matplotlib inline\n", + "import numpy as np\n", + "import scipy as sp\n", + "import matplotlib.pyplot as plt\n", + "import pods" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 86 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Marginal Likelihood\n", + "\n", + "To understand the Gaussian process we're going to build on our understanding of the marginal likelihood for Bayesian regression. In the session on [Bayesian regression](./week7.ipynb) we sampled directly from the weight vector, $\\mathbf{w}$ and applied it to the basis matrix $\\boldsymbol{\\Phi}$ to obtain a sample from the prior and a sample from the posterior. It is often helpful to think of modeling techniques as *generative* models. To give some thought as to what the process for obtaining data from the model is. From the perspective of Gaussian processes, we want to start by thinking of basis function models, where the parameters are sampled from a prior, but move to thinking about sampling from the marginal likelihood directly.\n", + "\n", + "## Sampling from the Prior\n", + "\n", + "The first thing we'll do is to set up the parameters of the model, these include the parameters of the prior, the parameters of the basis functions and the noise level. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# set prior variance on w\n", + "alpha = 4.\n", + "# set the order of the polynomial basis set\n", + "degree = 5\n", + "# set the noise variance\n", + "sigma2 = 0.01" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 87 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we have the variance, we can sample from the prior distribution to see what form we are imposing on the functions *a priori*. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's now compute a range of values to make predictions at, spanning the *new* space of inputs," + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def polynomial(x, degree, loc, scale):\n", + " degrees = np.arange(degree+1)\n", + " return ((x-loc)/scale)**degrees" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 88 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "now let's build the basis matrices. First we load in the data\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "data = pods.datasets.olympic_marathon_men()\n", + "x = data['X']\n", + "y = data['Y']" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 89 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "scale = np.max(x) - np.min(x)\n", + "loc = np.min(x) + 0.5*scale\n", + "\n", + "num_data = x.shape[0]\n", + "num_pred_data = 100 # how many points to use for plotting predictions\n", + "x_pred = np.linspace(1880, 2030, num_pred_data)[:, None] # input locations for predictions\n", + "Phi_pred = polynomial(x_pred, degree=degree, loc=loc, scale=scale)\n", + "Phi = polynomial(x, degree=degree, loc=loc, scale=scale)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 90 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Weight Space View\n", + "\n", + "To generate typical functional predictions from the model, we need a set of model parameters. We assume that the parameters are drawn independently from a Gaussian density,\n", + "$$\n", + "\\mathbf{w} \\sim \\mathcal{N}(\\mathbf{0}, \\alpha\\mathbf{I}),\n", + "$$\n", + "then we can combine this with the definition of our prediction function $f(\\mathbf{x})$,\n", + "$$\n", + "f(\\mathbf{x}) = \\mathbf{w}^\\top \\boldsymbol{\\phi}(\\mathbf{x}).\n", + "$$\n", + "We can now sample from the prior density to obtain a vector $\\mathbf{w}$ using the function `np.random.normal` and combine these parameters with our basis to create some samples of what $f(\\mathbf{x})$ looks like," + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "num_samples = 10\n", + "K = degree+1\n", + "for i in xrange(num_samples):\n", + " z_vec = np.random.normal(size=(K, 1))\n", + " w_sample = z_vec*np.sqrt(alpha)\n", + " f_sample = np.dot(Phi_pred,w_sample)\n", + " plt.plot(x_pred, f_sample)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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AicFAidFIhkazKPJfhaNhJgITjPvHmQxMMhmYxBlwUm4tZ0Pxhll9Lyn0Esnl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\naWnJSSoh7InJSz3Nv+12w+uvw4svwiu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+ "text": [ + "" + ] + } + ], + "prompt_number": 91 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Function Space View\n", + "\n", + "The process we have used to generate the samples is a two stage process. To obtain each function, we first generated a sample from the prior,\n", + "$$\n", + "\\mathbf{w} \\sim \\mathcal{N}(\\mathbf{0}, \\alpha \\mathbf{I})\n", + "$$\n", + "then if we compose our basis matrix, $\\boldsymbol{\\Phi}$ from the basis functions associated with each row then we get,\n", + "$$\n", + "\\mathbf{\\Phi} = \\begin{bmatrix}\\boldsymbol{\\phi}(\\mathbf{x}_1) \\\\ \\vdots \\\\ \\boldsymbol{\\phi}(\\mathbf{x}_n)\\end{bmatrix}\n", + "$$\n", + "then we can write down the vector of function values, as evaluated at\n", + "$$\n", + "\\mathbf{f} = \\begin{bmatrix} f_1 \\\\ \\vdots \\\\ f_n\\end{bmatrix}\n", + "$$\n", + "in the form\n", + "$$\n", + "\\mathbf{f} = \\boldsymbol{\\Phi} \\mathbf{w}.\n", + "$$\n", + "\n", + "Now we can use standard properties of multivariate Gaussians to write down the probability density that is implied over $\\mathbf{f}$. In particular we know that if $\\mathbf{w}$ is sampled from a multivariate normal (or multivariate Gaussian) with covariance $\\alpha \\mathbf{I}$ and zero mean, then assuming that $\\boldsymbol{\\Phi}$ is a deterministic matrix (i.e. it is not sampled from a probability density) then the vector $\\mathbf{f}$ will also be distributed according to a zero mean multivariate normal as follows,\n", + "$$\n", + "\\mathbf{f} \\sim \\mathcal{N}(\\mathbf{0},\\alpha \\boldsymbol{\\Phi} \\boldsymbol{\\Phi}^\\top).\n", + "$$\n", + "\n", + "The question now is, what happens if we sample $\\mathbf{f}$ directly from this density, rather than first sampling $\\mathbf{w}$ and then multiplying by $\\boldsymbol{\\Phi}$. Let's try this. First of all we define the covariance as\n", + "$$\n", + "\\mathbf{K} = \\alpha \\boldsymbol{\\Phi}\\boldsymbol{\\Phi}^\\top.\n", + "$$" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "K = alpha*np.dot(Phi_pred, Phi_pred.T)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 92 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can use the `np.random.multivariate_normal` command for sampling from a multivariate normal with covariance given by $\\mathbf{K}$ and zero mean," + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "for i in np.arange(10):\n", + " f_sample = np.random.multivariate_normal(mean=np.zeros(x_pred.size), cov=K)\n", + " plt.plot(x_pred.flatten(), f_sample.flatten())" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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5H2aY/2GG46gDGWsyYLzZCNPNJqRVpH3Ad8FJKhij6Je33iLbu5ei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\nCmeXKhCk0yXOlUNKCP2Q3483LBa8brHgTYsFOSo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+ "text": [ + "" + ] + } + ], + "prompt_number": 93 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The samples appear very similar to those which we obtained indirectly. That is no surprise because they are effectively drawn from the same mutivariate normal density. However, when sampling $\\mathbf{f}$ directly we created the covariance for $\\mathbf{f}$. We can visualise the form of this covaraince in an image in python with a colorbar to show scale." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "fig, ax = plt.subplots(figsize=(8,8))\n", + "im = ax.imshow(K, interpolation='none')\n", + "fig.colorbar(im)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 94, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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M7BuSHpT0qthgTIQAgKK4+02SnhN8+lDQ59LU8fIvjWqyNNokJaLJziqpO8s02ZGl7RJr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\nFmtNpKZaDFzaqWSriO31dfy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+ "text": [ + "" + ] + } + ], + "prompt_number": 94 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This image is the covariance expressed between different points on the function. In regression we normally also add independent Gaussian noise to obtain our observations $\\mathbf{y}$,\n", + "$$\n", + "\\mathbf{y} = \\mathbf{f} + \\boldsymbol{\\epsilon}\n", + "$$\n", + "where the noise is sampled from an independent Gaussian distribution with variance $\\sigma^2$,\n", + "$$\n", + "\\epsilon \\sim \\mathcal{N}(\\mathbf{0}, \\sigma^2 \\mathbf{I}).\n", + "$$\n", + "we can use properties of Gaussian variables, i.e. the fact that sum of two Gaussian variables is also Gaussian, and that it's covariance is given by the sum of the two covariances, whilst the mean is given by the sum of the means, to write down the marginal likelihood,\n", + "$$\n", + "\\mathbf{y} \\sim \\mathcal{N}(\\mathbf{0}, \\alpha \\boldsymbol{\\Phi}\\boldsymbol{\\Phi}^\\top + \\sigma^2\\mathbf{I}).\n", + "$$\n", + "Sampling directly from this density gives us the noise corrupted functions," + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "K = alpha*np.dot(Phi_pred, Phi_pred.T) + sigma2*np.eye(x_pred.size)\n", + "for i in xrange(10):\n", + " y_sample = np.random.multivariate_normal(mean=np.zeros(x_pred.size), cov=K)\n", + " plt.plot(x_pred.flatten(), y_sample.flatten())" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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dkXYvrWi7LF2GwC8D8bjRY9g2tYXne54ImB0AOx07BC8JVpltVCWKHEWVmf7e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7OoOqoj52xyqqP+53JwjUkR8Zk0Xgr8Ko0nA3+IiGPATkl/BSYALwOjao4fxcnlnl4TEZuA2wAk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\nAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 95 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where the effect of our noise term is to roughen the sampled functions, we can also increase the variance of the noise to see a different effect," + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sigma2 = 1.\n", + "K = alpha*np.dot(Phi_pred, Phi_pred.T) + sigma2*np.eye(x_pred.size)\n", + "for i in xrange(10):\n", + " y_sample = np.random.multivariate_normal(mean=np.zeros(x_pred.size), cov=K)\n", + " plt.plot(x_pred.flatten(), y_sample.flatten())" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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k5lo+36G3P45EfPGNru12O6tXr8ZqHUAQtAiCGo0mj+7uTqqrqzn33HPZt28f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\nZfw6gPAL2GCDDTZcDAYO2CYIBCIrIJQ2aLVa7c7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gV0ZQfSzEL9+tDDBULOL/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\n0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j+E2WwDVcVRLGI/cIBXpNN8fGGB+2ae5pboVR3pMGJ1U8HCoWIRnXmVrG6SMf8YlAw0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\nVmv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11k0NRR9e18zWobxiC6z1ryWbz17wRUoDi0UojlyuNtGr8C+3/Quvvepd4kqXG8YD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\n0SiaCS4KjwcpmeT2TWc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+ "text": [ + "" + ] + } + ], + "prompt_number": 96 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Function Space Reflection\n", + "\n", + "How do you include the noise term when sampling in the weight space point of view?\n", + "\n", + "## Gaussian Process\n", + "\n", + "In our [session on Bayesian regression](./bayesian approach to regression.ipynb) we sampled from the prior over parameters. Through the properties of multivariate Gaussian densities this prior over parameters implies a particular density for our data observations, $\\mathbf{y}$. In this session we sampled directly from this distribution for our data, avoiding the intermediate weight-space representation. This is the approach taken by *Gaussian processes*. In a Gaussian process you specify the *covariance function* directly, rather than *implicitly* through a basis matrix and a prior over parameters. Gaussian processes have the advantage that they can be *nonparametric*, which in simple terms means that they can have *infinite* basis functions. In the lectures we introduced the *exponentiated quadratic* covariance, also known as the RBF or the Gaussian or the squared exponential covariance function. This covariance function is specified by\n", + "$$\n", + "k(\\mathbf{x}, \\mathbf{x}^\\prime) = \\alpha \\exp\\left( -\\frac{\\left\\Vert \\mathbf{x}-\\mathbf{x}^\\prime\\right\\Vert^2}{2\\ell^2}\\right).\n", + "$$\n", + "where $\\left\\Vert\\mathbf{x} - \\mathbf{x}^\\prime\\right\\Vert^2$ is the squared distance between the two input vectors \n", + "$$\n", + "\\left\\Vert\\mathbf{x} - \\mathbf{x}^\\prime\\right\\Vert^2 = (\\mathbf{x} - \\mathbf{x}^\\prime)^\\top (\\mathbf{x} - \\mathbf{x}^\\prime) \n", + "$$\n", + "Let's build a covariance matrix based on this function. First we define the form of the covariance function," + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def exponentiated_quadratic(x, x_prime, variance, lengthscale):\n", + " squared_distance = ((x-x_prime)**2).sum()\n", + " return variance*np.exp((-0.5*squared_distance)/lengthscale**2)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 97 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use this to compute *directly* the covariance for $\\mathbf{f}$ at the points given by `x_pred`. Let's define a new function `K()` which does this," + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def compute_kernel(X, X2, kernel, **kwargs):\n", + " K = np.zeros((X.shape[0], X2.shape[0]))\n", + " for i in np.arange(X.shape[0]):\n", + " for j in np.arange(X2.shape[0]):\n", + " K[i, j] = kernel(X[i, :], X2[j, :], **kwargs)\n", + " \n", + " return K" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 98 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can image the resulting covariance," + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "K = compute_kernel(x_pred, x_pred, exponentiated_quadratic, variance=1., lengthscale=10.)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 99 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To visualise the covariance between the points we can use the `imshow` function in matplotlib." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "fig, ax = plt.subplots(figsize=(8,8))\n", + "im = ax.imshow(K, interpolation='none')\n", + "fig.colorbar(im)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 100, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 100 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we can sample functions from the marginal likelihood." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "for i in xrange(10):\n", + " y_sample = np.random.multivariate_normal(mean=np.zeros(x_pred.size), cov=K)\n", + " plt.plot(x_pred.flatten(), y_sample.flatten())" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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U/MmTxh23sJC1CIyIYDXn9SE3N5c6duxI4eHh1Ebfi3QhlRL5+LDMrrg4opYtWZaWoUkA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\nZ2uP18aN2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+ "text": [ + "" + ] + } + ], + "prompt_number": 101 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exercise: Moving Parameters\n", + "\n", + "Have a play with the parameters for this covariance function (the lengthscale and the variance) and see what effects the parameters have on the types of functions you observe." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 101 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Gaussian Process\n", + "\n", + "The Gaussian process perspective takes the marginal likelihood of the data to be a joint Gaussian density with a covariance given by $\\mathbf{K}$. So the model likelihood is of the form,\n", + "$$\n", + "p(\\mathbf{y}|\\mathbf{X}) = \\frac{1}{(2\\pi)^{\\frac{n}{2}}|\\mathbf{K}|^{\\frac{1}{2}}} \\exp\\left(-\\frac{1}{2}\\mathbf{y}^\\top \\left(\\mathbf{K}+\\sigma^2 \\mathbf{I}\\right)^{-1}\\mathbf{y}\\right)\n", + "$$\n", + "where the input data, $\\mathbf{X}$, influences the density through the covariance matrix, $\\mathbf{K}$ whose elements are computed through the covariance function, $k(\\mathbf{x}, \\mathbf{x}^\\prime)$.\n", + "\n", + "This means that the negative log likelihood (the objective function) is given by,\n", + "$$\n", + "E(\\boldsymbol{\\theta}) = \\frac{1}{2} \\log |\\mathbf{K}| + \\frac{1}{2} \\mathbf{y}^\\top \\left(\\mathbf{K} + \\sigma^2\\mathbf{I}\\right)^{-1}\\mathbf{y}\n", + "$$\n", + "where the *parameters* of the model are also embedded in the covariance function, they include the parameters of the kernel (such as lengthscale and variance), and the noise variance, $\\sigma^2$.\n", + "\n", + "Let's create a class in python for storing these variables." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "class GP():\n", + " def __init__(self, X, y, sigma2, kernel, **kwargs):\n", + " self.K = compute_kernel(X, X, kernel, **kwargs)\n", + " self.X = X\n", + " self.y = y\n", + " self.sigma2 = sigma2\n", + " self.kernel = kernel\n", + " self.kernel_args = kwargs\n", + " self.update_inverse()\n", + " \n", + " def update_inverse(self):\n", + " # Preompute the inverse covariance and some quantities of interest\n", + " ## NOTE: This is not the correct *numerical* way to compute this! It is for ease of use.\n", + " self.Kinv = np.linalg.inv(self.K+self.sigma2*np.eye(self.K.shape[0]))\n", + " # the log determinant of the covariance matrix.\n", + " self.logdetK = np.linalg.det(self.K+self.sigma2*np.eye(self.K.shape[0]))\n", + " # The matrix inner product of the inverse covariance\n", + " self.Kinvy = np.dot(self.Kinv, self.y)\n", + " self.yKinvy = (self.y*self.Kinvy).sum()\n", + "\n", + " \n", + " def log_likelihood(self):\n", + " # use the pre-computes to return the likelihood\n", + " return -0.5*(self.K.shape[0]*np.log(2*np.pi) + self.logdetK + self.yKinvy)\n", + " \n", + " def objective(self):\n", + " # use the pre-computes to return the objective function \n", + " return -self.log_likelihood()" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 102 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Making Predictions\n", + "\n", + "We now have a probability density that represents functions. How do we make predictions with this density? The density is known as a process because it is *consistent*. By consistency, here, we mean that the model makes predictions for $\\mathbf{f}$ that are unaffected by future values of $\\mathbf{f}^*$ that are currently unobserved (such as test points). If we think of $\\mathbf{f}^*$ as test points, we can still write down a joint probability density over the training observations, $\\mathbf{f}$ and the test observations, $\\mathbf{f}^*$. This joint probability density will be Gaussian, with a covariance matrix given by our covariance function, $k(\\mathbf{x}_i, \\mathbf{x}_j)$. \n", + "$$\n", + "\\begin{bmatrix}\\mathbf{f} \\\\ \\mathbf{f}^*\\end{bmatrix} \\sim \\mathcal{N}\\left(\\mathbf{0}, \\begin{bmatrix} \\mathbf{K} & \\mathbf{K}_\\ast \\\\ \\mathbf{K}_\\ast^\\top & \\mathbf{K}_{\\ast,\\ast}\\end{bmatrix}\\right)\n", + "$$\n", + "where here $\\mathbf{K}$ is the covariance computed between all the training points, $\\mathbf{K}_\\ast$ is the covariance matrix computed between the training points and the test points and $\\mathbf{K}_{\\ast,\\ast}$ is the covariance matrix computed betwen all the tests points and themselves. To be clear, let's compute these now for our example, using `x` and `y` for the training data (although `y` doesn't enter the covariance) and `x_pred` as the test locations." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# set covariance function parameters\n", + "variance = 16.0\n", + "lengthscale = 32\n", + "# set noise variance\n", + "sigma2 = 0.05\n", + "\n", + "K = compute_kernel(x, x, exponentiated_quadratic, variance=variance, lengthscale=lengthscale)\n", + "K_star = compute_kernel(x, x_pred, exponentiated_quadratic, variance=variance, lengthscale=lengthscale)\n", + "K_starstar = compute_kernel(x_pred, x_pred, exponentiated_quadratic, variance=variance, lengthscale=lengthscale)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 103 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we use this structure to visualise the covariance between test data and training data. This structure is how information is passed between trest and training data. Unlike the maximum likelihood formalisms we've been considering so far, the structure expresses *correlation* between our different data points. However, we now have a *joint density* between some variables of interest. In particular we have the joint density over $p(\\mathbf{f}, \\mathbf{f}^*)$. The joint density is *Gaussian* and *zero mean*. It is specified entirely by the *covariance matrix*, $\\mathbf{K}$. That covariance matrix is, in turn, defined by a covariance function. Now we will visualise the form of that covariance in the form of the matrix,\n", + "$$\n", + "\\begin{bmatrix} \\mathbf{K} & \\mathbf{K}_\\ast \\\\ \\mathbf{K}_\\ast^\\top & \\mathbf{K}_{\\ast,\\ast}\\end{bmatrix}\n", + "$$" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "fig, ax = plt.subplots(figsize=(8,8))\n", + "im = ax.imshow(np.vstack([np.hstack([K, K_star]), np.hstack([K_star.T, K_starstar])]), interpolation='none')\n", + "# Add lines for separating training and test data\n", + "ax.axvline(x.shape[0]-1, color='w')\n", + "ax.axhline(x.shape[0]-1, color='w')\n", + "fig.colorbar(im)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 104, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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QZKpuF0IIISqNmd1jZk0z+ybN/Qcze8zMvmFmnzKzQveQFkQhhBDlcUUJ/9Zz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\nXYGkJM0iKvz+nHNfBPDPbdOx9/NWAPc75y44544hKUF06yC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+ "text": [ + "" + ] + } + ], + "prompt_number": 104 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are four blocks to this color plot. The upper left block is the covariance of the training data with itself, $\\mathbf{K}$. We see some structure here due to the missing data from the first and second world wars. Alongside this covariance (to the right and below) we see the cross covariance between the training and the test data ($\\mathbf{K}_*$ and $\\mathbf{K}_*^\\top$). This is giving us the covariation between our training and our test data. Finally the lower right block The banded structure we now observe is because some of the training points are near to some of the test points. This is how we obtain 'communication' between our training data and our test data. If there is no structure in $\\mathbf{K}_*$ then our belief about the test data simply matches our prior.\n", + "\n", + "## Conditional Density\n", + "\n", + "Just as in naive Bayes, we first defined the joint density (although there it was over both the labels and the inputs, $p(\\mathbf{y}, \\mathbf{X})$ and now we need to define *conditional* distributions that answer particular questions of interest. In particular we might be interested in finding out the values of the function for the prediction function at the test data given those at the training data, $p(\\mathbf{f}_*|\\mathbf{f})$. Or if we include noise in the training observations then we are interested in the conditional density for the prediction function at the test locations given the training observations, $p(\\mathbf{f}^*|\\mathbf{y})$. \n", + "\n", + "As ever all the various questions we could ask about this density can be answered using the *sum rule* and the *product rule*. For the multivariate normal density the mathematics involved is that of *linear algebra*, with a particular emphasis on the *partitioned inverse* or [*block matrix inverse*](http://en.wikipedia.org/wiki/Invertible_matrix#Blockwise_inversion), but they are beyond the scope of this course, so you don't need to worry about remembering them or rederiving them. We are simply writing them here because it is this *conditional* density that is necessary for making predictions.\n", + "\n", + "The conditional density is also a multivariate normal,\n", + "$$\n", + "\\mathbf{f}^* | \\mathbf{y} \\sim \\mathcal{N}(\\boldsymbol{\\mu}_f,\\mathbf{C}_f)\n", + "$$\n", + "with a mean given by\n", + "$$\n", + "\\boldsymbol{\\mu}_f = \\mathbf{K}_*^\\top \\left[\\mathbf{K} + \\sigma^2 \\mathbf{I}\\right]^{-1} \\mathbf{y}\n", + "$$\n", + "and a covariance given by \n", + "$$\n", + "\\mathbf{C}_f = \\mathbf{K}_{*,*} - \\mathbf{K}_*^\\top \\left[\\mathbf{K} + \\sigma^2 \\mathbf{I}\\right]^{-1} \\mathbf{K}_\\ast.\n", + "$$\n", + "Let's compute what those posterior predictions are for the olympic marathon data." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def posterior_f(self, X_test):\n", + " K_star = compute_kernel(self.X, X_test, self.kernel, **self.kernel_args)\n", + " A = np.dot(self.Kinv, K_star)\n", + " mu_f = np.dot(A.T, y)\n", + " C_f = K_starstar - np.dot(A.T, K_star)\n", + " return mu_f, C_f\n", + "\n", + "# attach the new method to class GP():\n", + "GP.posterior_f = posterior_f" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 105 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "model = GP(x, y, sigma2, exponentiated_quadratic, variance=variance, lengthscale=lengthscale)\n", + "mu_f, C_f = model.posterior_f(x_pred)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 106 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where for convenience we've defined\n", + "\n", + "$$\\mathbf{A} = \\left[\\mathbf{K} + \\sigma^2\\mathbf{I}\\right]^{-1}\\mathbf{K}_*.$$ \n", + "\n", + "We can visualize the covariance of the *conditional*," + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "fig, ax = plt.subplots(figsize=(8,8))\n", + "im = ax.imshow(C_f, interpolation='none')\n", + "fig.colorbar(im)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 107, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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CAKxSgqkJzTwAACiQYJoPAOhcgqlJT5p51NHGKbQVR+pzl3XLNt1oazupdMmVYnxsWV3E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\nfVHSs5ZYr8i8eHHZebbxTyx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+ "text": [ + "" + ] + } + ], + "prompt_number": 107 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and we can plot the mean of the conditional" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.plot(x, y, 'rx')\n", + "plt.plot(x_pred, mu_f, 'b-')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 108, + "text": [ + "[]" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 108 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "as well as the associated error bars. These are given (similarly to the Bayesian parametric model from the last lab) by the standard deviations of the marginal posterior densities. The marginal posterior variances are given by the diagonal elements of the posterior covariance," + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "var_f = np.diag(C_f)[:, None]\n", + "std_f = np.sqrt(var_f)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 109 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "They can be added to the underlying mean function to give the error bars," + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.plot(x, y, 'rx')\n", + "plt.plot(x_pred, mu_f, 'b-')\n", + "plt.plot(x_pred, mu_f+2*std_f, 'b--')\n", + "plt.plot(x_pred, mu_f-2*std_f, 'b--')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 110, + "text": [ + "[]" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 110 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This gives us a prediction from the Gaussian process. Remember machine learning is \n", + "$$\n", + "\\text{data} + \\text{model} \\rightarrow \\text{prediction}.\n", + "$$\n", + "Here our data is from the olympics, and our model is a Gaussian process with two parameters. The assumptions about the world are encoded entirely into our Gaussian process covariance. The GP covariance assumes that the function is highly smooth, and that correlation falls off with distance (scaled according to the length scale, $\\ell$). The model sustains the uncertainty about the function, this means we see an increase in the size of the error bars during periods like the 1st and 2nd World Wars when no olympic marathon was held. \n", + "\n", + "## Exercises\n", + "\n", + "Now try changing the parameters of the covariance function (and the noise) to see how the predictions change.\n", + "\n", + "Now try sampling from this conditional density to see what your predictions look like. What happens if you sample from the conditional density in regions a long way into the future or the past? How does this compare with the results from the polynomial model?\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Importance of the Covariance Function\n", + "\n", + "The covariance function encapsulates our assumptions about the data. The equations for the distribution of the prediction function, given the training observations, are highly sensitive to the covariation between the test locations and the training locations as expressed by the matrix $\\mathbf{K}_*$. We defined a matrix $\\mathbf{A}$ which allowed us to express our conditional mean in the form,\n", + "$$\n", + "\\boldsymbol{\\mu}_f = \\mathbf{A}^\\top \\mathbf{y},\n", + "$$\n", + "where $\\mathbf{y}$ were our *training observations*. In other words our mean predictions are always a linear weighted combination of our *training data*. The weights are given by computing the covariation between the training and the test data ($\\mathbf{K}_*$) and scaling it by the inverse covariance of the training data observations, $\\left[\\mathbf{K} + \\sigma^2 \\mathbf{I}\\right]^{-1}$. This inverse is the main computational object that needs to be resolved for a Gaussian process. It has a computational burden which is $O(n^3)$ and a storage burden which is $O(n^2)$. This makes working with Gaussian processes computationally intensive for the situation where $n>10,000$. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from IPython.display import YouTubeVideo\n", + "YouTubeVideo('ewJ3AxKclOg')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + " \n", + " " + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 111, + "text": [ + "" + ] + } + ], + "prompt_number": 111 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Improving the Numerics\n", + "\n", + "In practice we shouldn't be using matrix inverse directly to solve the GP system. One more stable way is to compute the *Cholesky decomposition* of the kernel matrix. The log determinant of the covariance can also be derived from the Cholesky decomposition." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def update_inverse(self):\n", + " # Perform Cholesky decomposition on matrix\n", + " self.R = sp.linalg.cholesky(self.K + self.sigma2*self.K.shape[0])\n", + " # compute the log determinant from Cholesky decomposition\n", + " self.logdetK = 2*np.log(np.diag(self.R)).sum()\n", + " # compute y^\\top K^{-1}y from Cholesky factor\n", + " self.Rinvy = sp.linalg.solve_triangular(self.R, self.y)\n", + " self.yKinvy = (self.Rinvy**2).sum()\n", + " \n", + " # compute the inverse of the upper triangular Cholesky factor\n", + " self.Rinv = sp.linalg.solve_triangular(self.R, np.eye(self.K.shape[0]))\n", + " self.Kinv = np.dot(self.Rinv, self.Rinv.T)\n", + "\n", + "GP.update_inverse = update_inverse" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 112 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Capacity Control\n", + "\n", + "Gaussian processes are sometimes seen as part of a wider family of methods known as kernel methods. Kernel methods are also based around covariance functions, but in the field they are known as Mercer kernels. Mercer kernels have interpretations as inner products in potentially infinite dimensional Hilbert spaces. This interpretation arises because, if we take $\\alpha=1$, then the kernel can be expressed as\n", + "$$\n", + "\\mathbf{K} = \\boldsymbol{\\Phi}\\boldsymbol{\\Phi}^\\top \n", + "$$\n", + "which imples the elements of the kernel are given by,\n", + "$$\n", + "k(\\mathbf{x}, \\mathbf{x}^\\prime) = \\boldsymbol{\\phi}(\\mathbf{x})^\\top \\boldsymbol{\\phi}(\\mathbf{x}^\\prime).\n", + "$$\n", + "So we see that the kernel function is developed from an inner product between the basis functions. Mercer's theorem tells us that any valid *positive definite function* can be expressed as this inner product but with the caveat that the inner product could be *infinite length*. This idea has been used quite widely to *kernelize* algorithms that depend on inner products. The kernel functions are equivalent to covariance functions and they are parameterized accordingly. In the kernel modeling community it is generally accepted that kernel parameter estimation is a difficult problem and the normal solution is to cross validate to obtain parameters. This can cause difficulties when a large number of kernel parameters need to be estimated. In Gaussian process modelling kernel parameter estimation (in the simplest case proceeds) by maximum likelihood. This involves taking gradients of the likelihood with respect to the parameters of the covariance function. \n", + "\n", + "## Gradients of the Likelihood\n", + "\n", + "The easiest conceptual way to obtain the gradients is a two step process. The first step involves taking the gradient of the likelihood with respect to the covariance function, the second step involves considering the gradient of the covariance function with respect to its parameters. The relevant terms of the negative log likelihood are given by\n", + "$$\n", + "E(\\boldsymbol{\\theta}) = \\frac{1}{2}\\log |\\hat{\\mathbf{K}}| + \\frac{1}{2} \\mathbf{y}^\\top \\hat{\\mathbf{K}}^{-1} \\mathbf{y}\n", + "$$\n", + "where $\\hat{\\mathbf{K}} = \\mathbf{K} + \\sigma^2 \\mathbf{I}$ is the noise corrupted covariance matrix. The gradient with respect to that matrix can be computed as\n", + "$$\n", + "\\frac{\\text{d}E(\\boldsymbol{\\theta})}{\\text{d}\\hat{\\mathbf{K}}} = \\frac{1}{2}\\hat{\\mathbf{K}}^{-1} - \\frac{1}{2}\\hat{\\mathbf{K}}^{-1}\\mathbf{y}\\mathbf{y}^\\top \\hat{\\mathbf{K}}^{-1}\n", + "$$\n", + "The can then be combined with gradients of the covariance function with respect to any parameters, $\\frac{\\text{d}\\hat{\\mathbf{K}}}{\\text{d}\\theta}$ using the chain rule. Mathematically that is written as\n", + "$$\n", + "\\frac{\\text{d}E(\\boldsymbol{\\theta})}{\\text{d}\\theta} = \\text{tr}\\left(\\frac{\\text{d}E(\\boldsymbol{\\theta})}{\\text{d}\\hat{\\mathbf{K}}}\\frac{\\text{d}\\hat{\\mathbf{K}}}{\\text{d}\\theta}\\right),\n", + "$$\n", + "where the two gradient matrices are multiplied together. In in implementation, however, that is inefficient. It is more efficient to perform an element by element multiplication of the two matrices.\n", + "\n", + "### Overall Process Scale\n", + "\n", + "In general we won't be able to find parameters of the covariance function through fixed point equations, we will need to do graident based optimization, however there is one parameter that does have a fixed point update. Imagine the covariance $\\hat{\\mathbf{K}}$ has an overall scale such that $\\hat{\\mathbf{K}} = \\alpha \\boldsymbol{\\Sigma}$. In this case the gradient of the covariance matrix with respect to $\\alpha$ is simply $\\mathbf{C}$ and $\\hat{\\mathbf{K}}^{-1}\\mathbf{C} = \\alpha^{-1}$. This means we can write,\n", + "$$\n", + "\\frac{\\text{d}E(\\boldsymbol{\\theta})}{\\text{d}\\alpha} = \\frac{1}{2\\alpha}\\left(n - \\frac{\\mathbf{y}^\\top\\mathbf{C}^{-1}\\mathbf{y}}{\\alpha}\\right)\n", + "$$\n", + "which implies a fixed point updated is given by\n", + "$$\n", + "\\alpha = \\frac{\\mathbf{y}^\\top\\mathbf{C}^{-1}\\mathbf{y}}{n}.\n", + "$$\n", + "The availability of a fixed point update for the overall scale means that sometimes, if we have a process of the form,\n", + "$$\n", + "\\hat{\\mathbf{K}} = \\alpha \\mathbf{K} + \\sigma^2 \\mathbf{I}\n", + "$$\n", + "where $\\mathbf{K}$ might be an exponentiated quadratic, or another covariance, that represents the signal, and $\\sigma^2$ represents the contribution from the noise. Rather than representing directly in this form we might represent the model as\n", + "$$\n", + "\\hat{\\mathbf{K}} = \\sigma^2\\left(\\hat{\\alpha}\\mathbf{K} + \\mathbf{I})\\right)\n", + "$$\n", + "where $\\hat{\\alpha} = \\frac{\\alpha^2}{\\sigma^2}$ is a signal to noise ratio. Although some care will need to be taken if the actual noise is very low as numerical instabilities are likely to occur.\n", + "\n", + "## Capacity Control and Data Fit\n", + "\n", + "The objective function can be decomposed into two terms, a capacity control term, and a data fit term. \n", + "$$\n", + "E(\\boldsymbol{\\theta}) = \\frac{1}{2}\\log |\\hat{\\mathbf{K}}| + \\frac{1}{2} \\mathbf{y}^\\top \\hat{\\mathbf{K}}^{-1} \\mathbf{y}\n", + "$$\n", + "The capacity control term is the log determinant of the covariance, $\\log |\\hat{\\mathbf{K}}|$. The data fit term is the matrix inner product between the data and the inverse covariance, $\\frac{1}{2} \\mathbf{y}^\\top \\hat{\\mathbf{K}}^{-1} \\mathbf{y}$.\n", + "\n", + "The log determinant term has an interpretation as a log volume. The determinant of the covariance is related to Gaussian density's 'footprint'. Recall that the determinant is the product of the eigenvalues, and the eigenvalues represent a set of axes which describe the correlations of the Gaussian densities (the directions being given by the corresponding eigenvectors). The product of these eigenvalues gives the area (or volume) of the Gaussian density. Roughly speaking it represents the diversity of different functions the Gaussian process can represent. If the number is large, then the process can represent many functions. If it is small then the process can represent fewer functions. Although the terms 'many' and 'few' are badly defined here because the space is continuous and the Gaussian process represents a continuum of different functions. However, the intuition is maybe useful. \n", + "\n", + "The data fit term is a little like a quadratic well, trying to locate the data at the lowest point. The data fit term can be driven to zero by increasing the scale of the covariance. However, this causes the capacity term to also increase, so a penalty is paid for this. Ideally, the data fit term should be reduced by matching correlations seen in the data with a corresponding correlation in the covariance function." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 112 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/lab_classes/mlss/index.ipynb b/lab_classes/mlss/index.ipynb new file mode 100644 index 0000000..bdd79f7 --- /dev/null +++ b/lab_classes/mlss/index.ipynb @@ -0,0 +1,100 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:43e13b0d3446c3bca3497c75aa3b092226d220c8b4dcd5f679f4e662bfd988e9" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Machine Learning Summer School, Sydney\n", + "\n", + "### February 2015\n", + "\n", + "### Neil D. Lawrence\n", + "\n", + "## Introduction\n", + "\n", + "Welcome to the lab for the Gaussian process section at the Machine Learning Summer School in Sydney.\n", + "\n", + "This notebook provides you with the guide to your lab classes for Gaussian processes. The lab classes are intended to help get you familiar with modeling with Gaussian processes as\n", + "\n", + "The lab classes are based on our two software packages, `pods` which is used for access to datasets and `GPy` (release 21st November 2014) for Gaussian processes. You can install the GPy framework with\n", + "\n", + "```sh\n", + "pip install GPy\n", + "```\n", + "As well as the GPy software we use our `pods` software for ['open data science'](http://inverseprobability.com/2014/07/01/open-data-science/) for access to data sets and other resources.\n", + "\n", + "```sh\n", + "pip install -pre pods\n", + "```\n", + "\n", + "on some systems you may need to use ```pip install -pre pods``` to allow the prerelease to install.\n", + "\n", + "As well as these lab classes here are a range of tutorials on how to use `GPy`, many of which are written by members of the Sheffield research group. `GPy` is under active development and is released under a BSD license, you'd also be very welcome to contribute!\n", + "\n", + "\n", + "\n", + "## Review\n", + "\n", + "Before you start, if you aren't familiar with probabilistic processes, the following lab classes from the GPRS schools might be useful. The first session will allow you to become familiar with the Jupyter (the ipython notebook) and start to work with Gaussian processes.\n", + "\n", + "* [Welcome to `Jupyter`](./gprs/jupyter introduction.ipynb) A quick introduction to `Jupyter`, `python` and `numpy`. \n", + "* [Introduction to Probabilistic Regression](./gprs/probabilistic interpretations of regression.ipynb) A review of least squares, basis function modelling and the probabilistic interpretation of least squares.\n", + "* [Introduction to Bayesian Regression](./gprs/bayesian approach to regression.ipynb) Introducing priors over parameters and averaging over solutions.\n", + "\n", + "## Gaussian Processes\n", + "\n", + "The second day will focus on Gaussian process models and developing covariance functions. \n", + " \n", + "* [Introduction to Gaussian Processes](./gaussian process introduction.ipynb) We move from the Bayesian regression with polynomials to Gaussian process perspectives by looking at the priors over the function directly.\n", + "* [GPy: Introduction through Covariance Functions](./GPy introduction covariance functions.ipynb) `GPy` is a Python Gaussian process framework that implements many of the ideas we'll see in the course. In this session we introduce its covariance functions and sample from the associated Gaussian processes.\n", + "* [Gaussian Process Regression with GPy](./GPy gaussian process regression.ipynb) In this example we show how to do a simple regression model using Gaussian processes in GPy.\n", + "* [Optimizing Gaussian Processes](./GPy optimizing gaussian processes.ipynb) The parameters of the covariance function can be optimized. In this example we show how to optimize the parameters of the covariance function. (TODO HMC)\n", + "\n", + "# Advanced Topics\n", + "\n", + "Things we haven't had time to cover in the MLSS can be found below.\n", + "\n", + "### Structured Outputs with Gaussian Processes\n", + "\n", + "Gaussian processes for learning vector valued functions.\n", + "\n", + "* [Multiple Output GPs](./gprs/multiple outputs.ipynb)\n", + "* [TODO Differential Equations and Gaussian Processes](./gprs/GP differential equation.ipynb)\n", + "\n", + "\n", + "### Approximations\n", + "\n", + "These examples look at approximations for speeding up inference in Gaussian processes and/or making inference tractable.\n", + "\n", + "* [Low Rank Approximations for Gaussian Processes](./gprs/low rank approximations.ipynb)\n", + "* [Non Gaussian Likelihoods](./gprs/non gaussian likelihoods.ipynb)\n", + "* [Low Rank and Non Gaussian](./gprs/low rank and non gaussian.ipynb)\n", + "\n", + "### Dimensionality Reduction\n", + "\n", + "These examples look at dimensionality reduction with Gaussian processes.\n", + "\n", + "* [Dimensionality Reduction with Gaussian Processes](./gprs/dimensionality reduction with gaussian processes.ipynb) " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file