learning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning\n",
    "\n",
    "This notebook serves as supporting material for topics covered in **Chapter 18 - Learning from Examples** , **Chapter 19 - Knowledge in Learning**, **Chapter 20 - Learning Probabilistic Models** from the book *Artificial Intelligence: A Modern Approach*. This notebook uses implementations from [learning.py](https://github.com/aimacode/aima-python/blob/master/learning.py). Let's start by importing everything from the module:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from learning import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Contents\n",
    "\n",
    "* Machine Learning Overview\n",
    "* Datasets\n",
    "* Distance Functions\n",
    "* Plurality Learner\n",
    "* k-Nearest Neighbours\n",
    "* Naive Bayes Learner\n",
    "* Perceptron\n",
    "* Neural Network\n",
    "* MNIST Handwritten Digits\n",
    "    * Loading and Visualising\n",
    "    * Testing\n",
    "        * kNN Classifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Machine Learning Overview\n",
    "\n",
    "In this notebook, we learn about agents that can improve their behavior through diligent study of their own experiences.\n",
    "\n",
    "An agent is **learning** if it improves its performance on future tasks after making observations about the world.\n",
    "\n",
    "There are three types of feedback that determine the three main types of learning:\n",
    "\n",
    "* **Supervised Learning**:\n",
    "\n",
    "In Supervised Learning the agent observes some example input-output pairs and learns a function that maps from input to output.\n",
    "\n",
    "**Example**: Let's think of an agent to classify images containing cats or dogs. If we provide an image containing a cat or a dog, this agent should output a string \"cat\" or \"dog\" for that particular image. To teach this agent, we will give a lot of input-output pairs like {cat image-\"cat\"}, {dog image-\"dog\"} to the agent. The agent then learns a function that maps from an input image to one of those strings.\n",
    "\n",
    "* **Unsupervised Learning**:\n",
    "\n",
    "In Unsupervised Learning the agent learns patterns in the input even though no explicit feedback is supplied. The most common type is **clustering**: detecting potential useful clusters of input examples.\n",
    "\n",
    "**Example**: A taxi agent would develop a concept of *good traffic days* and *bad traffic days* without ever being given labeled examples.\n",
    "\n",
    "* **Reinforcement Learning**:\n",
    "\n",
    "In Reinforcement Learning the agent learns from a series of reinforcements—rewards or punishments.\n",
    "\n",
    "**Example**: Let's talk about an agent to play the popular Atari game—[Pong](http://www.ponggame.org). We will reward a point for every correct move and deduct a point for every wrong move from the agent. Eventually, the agent will figure out its actions prior to reinforcement were most responsible for it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Datasets\n",
    "\n",
    "For the following tutorials we will use a range of datasets, to better showcase the strengths and weaknesses of the algorithms. The datasests are the following:\n",
    "\n",
    "* [Fisher's Iris](https://github.com/aimacode/aima-data/blob/a21fc108f52ad551344e947b0eb97df82f8d2b2b/iris.csv): Each item represents a flower, with four measurements: the length and the width of the sepals and petals. Each item/flower is categorized into one of three species: Setosa, Versicolor and Virginica.\n",
    "\n",
    "* [Zoo](https://github.com/aimacode/aima-data/blob/a21fc108f52ad551344e947b0eb97df82f8d2b2b/zoo.csv): The dataset holds different animals and their classification as \"mammal\", \"fish\", etc. The new animal we want to classify has the following measurements: 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 4, 1, 0, 1 (don't concern yourself with what the measurements mean)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make using the datasets easier, we have written a class, `DataSet`, in `learning.py`. The tutorials found here make use of this class.\n",
    "\n",
    "Let's have a look at how it works before we get started with the algorithms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Intro\n",
    "\n",
    "A lot of the datasets we will work with are .csv files (although other formats are supported too). We have a collection of sample datasets ready to use [on aima-data](https://github.com/aimacode/aima-data/tree/a21fc108f52ad551344e947b0eb97df82f8d2b2b). Two examples are the datasets mentioned above (*iris.csv* and *zoo.csv*). You can find plenty datasets online, and a good repository of such datasets is [UCI Machine Learning Repository](https://archive.ics.uci.edu/ml/datasets.html).\n",
    "\n",
    "In such files, each line corresponds to one item/measurement. Each individual value in a line represents a *feature* and usually there is a value denoting the *class* of the item.\n",
    "\n",
    "You can find the code for the dataset here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%psource DataSet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Class Attributes\n",
    "\n",
    "* **examples**: Holds the items of the dataset. Each item is a list of values.\n",
    "\n",
    "* **attrs**: The indexes of the features (by default in the range of [0,f), where *f* is the number of features. For example, `item[i]` returns the feature at index *i* of *item*.\n",
    "\n",
    "* **attrnames**: An optional list with attribute names. For example, `item[s]`, where *s* is a feature name, returns the feature of name *s* in *item*.\n",
    "\n",
    "* **target**: The attribute a learning algorithm will try to predict. By default the last attribute.\n",
    "\n",
    "* **inputs**: This is the list of attributes without the target.\n",
    "\n",
    "* **values**: A list of lists which holds the set of possible values for the corresponding attribute/feature. If initially `None`, it gets computed (by the function `setproblem`) from the examples.\n",
    "\n",
    "* **distance**: The distance function used in the learner to calculate the distance between two items. By default `mean_boolean_error`.\n",
    "\n",
    "* **name**: Name of the dataset.\n",
    "\n",
    "* **source**: The source of the dataset (url or other). Not used in the code.\n",
    "\n",
    "* **exclude**: A list of indexes to exclude from `inputs`. The list can include either attribute indexes (attrs) or names (attrnames)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Class Helper Functions\n",
    "\n",
    "These functions help modify a `DataSet` object to your needs.\n",
    "\n",
    "* **sanitize**: Takes as input an example and returns it with non-input (target) attributes replaced by `None`. Useful for testing. Keep in mind that the example given is not itself sanitized, but instead a sanitized copy is returned.\n",
    "\n",
    "* **classes_to_numbers**: Maps the class names of a dataset to numbers. If the class names are not given, they are computed from the dataset values. Useful for classifiers that return a numerical value instead of a string.\n",
    "\n",
    "* **remove_examples**: Removes examples containing a given value. Useful for removing examples with missing values, or for removing classes (needed for binary classifiers)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Importing a Dataset\n",
    "\n",
    "#### Importing from aima-data\n",
    "\n",
    "Datasets uploaded on aima-data can be imported with the following line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "iris = DataSet(name=\"iris\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To check that we imported the correct dataset, we can do the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.1, 3.5, 1.4, 0.2, 'setosa']\n",
      "[0, 1, 2, 3]\n"
     ]
    }
   ],
   "source": [
    "print(iris.examples[0])\n",
    "print(iris.inputs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which correctly prints the first line in the csv file and the list of attribute indexes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When importing a dataset, we can specify to exclude an attribute (for example, at index 1) by setting the parameter `exclude` to the attribute index or name."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 2, 3]\n"
     ]
    }
   ],
   "source": [
    "iris2 = DataSet(name=\"iris\",exclude=[1])\n",
    "print(iris2.inputs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Attributes\n",
    "\n",
    "Here we showcase the attributes.\n",
    "\n",
    "First we will print the first three items/examples in the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[5.1, 3.5, 1.4, 0.2, 'setosa'], [4.9, 3.0, 1.4, 0.2, 'setosa'], [4.7, 3.2, 1.3, 0.2, 'setosa']]\n"
     ]
    }
   ],
   "source": [
    "print(iris.examples[:3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we will print `attrs`, `attrnames`, `target`, `input`. Notice how `attrs` holds values in [0,4], but since the fourth attribute is the target, `inputs` holds values in [0,3]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "attrs: [0, 1, 2, 3, 4]\n",
      "attrnames (by default same as attrs): [0, 1, 2, 3, 4]\n",
      "target: 4\n",
      "inputs: [0, 1, 2, 3]\n"
     ]
    }
   ],
   "source": [
    "print(\"attrs:\", iris.attrs)\n",
    "print(\"attrnames (by default same as attrs):\", iris.attrnames)\n",
    "print(\"target:\", iris.target)\n",
    "print(\"inputs:\", iris.inputs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will print all the possible values for the first feature/attribute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.7, 5.5, 6.3, 5.0, 4.9, 5.1, 4.6, 5.4, 4.4, 4.8, 5.8, 7.0, 7.1, 4.5, 5.9, 5.6, 6.9, 6.6, 6.5, 6.4, 6.0, 6.1, 7.6, 7.4, 7.9, 4.3, 5.7, 5.3, 5.2, 6.7, 6.2, 6.8, 7.3, 7.2, 7.7]\n"
     ]
    }
   ],
   "source": [
    "print(iris.values[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally we will print the dataset's name and source. Keep in mind that we have not set a source for the dataset, so in this case it is empty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "name: iris\n",
      "source: \n"
     ]
    }
   ],
   "source": [
    "print(\"name:\", iris.name)\n",
    "print(\"source:\", iris.source)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A useful combination of the above is `dataset.values[dataset.target]` which returns the possible values of the target. For classification problems, this will return all the possible classes. Let's try it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['versicolor', 'virginica', 'setosa']\n"
     ]
    }
   ],
   "source": [
    "print(iris.values[iris.target])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helper Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now take a look at the auxiliary functions found in the class.\n",
    "\n",
    "First we will take a look at the `sanitize` function, which sets the non-input values of the given example to `None`.\n",
    "\n",
    "In this case we want to hide the class of the first example, so we will sanitize it.\n",
    "\n",
    "Note that the function doesn't actually change the given example; it returns a sanitized *copy* of it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sanitized: [5.1, 3.5, 1.4, 0.2, None]\n",
      "Original: [5.1, 3.5, 1.4, 0.2, 'setosa']\n"
     ]
    }
   ],
   "source": [
    "print(\"Sanitized:\",iris.sanitize(iris.examples[0]))\n",
    "print(\"Original:\",iris.examples[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Currently the `iris` dataset has three classes, setosa, virginica and versicolor. We want though to convert it to a binary class dataset (a dataset with two classes). The class we want to remove is \"virginica\". To accomplish that we will utilize the helper function `remove_examples`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['versicolor', 'setosa']\n"
     ]
    }
   ],
   "source": [
    "iris2 = DataSet(name=\"iris\")\n",
    "\n",
    "iris2.remove_examples(\"virginica\")\n",
    "print(iris2.values[iris2.target])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also have `classes_to_numbers`. For a lot of the classifiers in the module (like the Neural Network), classes should have numerical values. With this function we map string class names to numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Class of first example: setosa\n",
      "Class of first example: 0\n"
     ]
    }
   ],
   "source": [
    "print(\"Class of first example:\",iris2.examples[0][iris2.target])\n",
    "iris2.classes_to_numbers()\n",
    "print(\"Class of first example:\",iris2.examples[0][iris2.target])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see \"setosa\" was mapped to 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we take a look at `find_means_and_deviations`. It finds the means and standard deviations of the features for each class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Setosa feature means: [5.006, 3.418, 1.464, 0.244]\n",
      "Versicolor mean for first feature: 5.936\n",
      "Setosa feature deviations: [0.3524896872134513, 0.38102439795469095, 0.17351115943644546, 0.10720950308167838]\n",
      "Virginica deviation for second feature: 0.32249663817263746\n"
     ]
    }
   ],
   "source": [
    "means, deviations = iris.find_means_and_deviations()\n",
    "\n",
    "print(\"Setosa feature means:\", means[\"setosa\"])\n",
    "print(\"Versicolor mean for first feature:\", means[\"versicolor\"][0])\n",
    "\n",
    "print(\"Setosa feature deviations:\", deviations[\"setosa\"])\n",
    "print(\"Virginica deviation for second feature:\",deviations[\"virginica\"][1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distance Functions\n",
    "\n",
    "In a lot of algorithms (like the *k-Nearest Neighbors* algorithm), there is a need to compare items, finding how *similar* or *close* they are. For that we have many different functions at our disposal. Below are the functions implemented in the module:\n",
    "\n",
    "### Manhattan Distance (`manhattan_distance`)\n",
    "\n",
    "One of the simplest distance functions. It calculates the difference between the coordinates/features of two items. To understand how it works, imagine a 2D grid with coordinates *x* and *y*. In that grid we have two items, at the squares positioned at `(1,2)` and `(3,4)`. The difference between their two coordinates is `3-1=2` and `4-2=2`. If we sum these up we get `4`. That means to get from `(1,2)` to `(3,4)` we need four moves; two to the right and two more up. The function works similarly for n-dimensional grids."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Manhattan Distance between (1,2) and (3,4) is 4\n"
     ]
    }
   ],
   "source": [
    "def manhattan_distance(X, Y):\n",
    "    return sum([abs(x - y) for x, y in zip(X, Y)])\n",
    "\n",
    "\n",
    "distance = manhattan_distance([1,2], [3,4])\n",
    "print(\"Manhattan Distance between (1,2) and (3,4) is\", distance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Euclidean Distance (`euclidean_distance`)\n",
    "\n",
    "Probably the most popular distance function. It returns the square root of the sum of the squared differences between individual elements of two items."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Euclidean Distance between (1,2) and (3,4) is 2.8284271247461903\n"
     ]
    }
   ],
   "source": [
    "def euclidean_distance(X, Y):\n",
    "    return math.sqrt(sum([(x - y)**2 for x, y in zip(X,Y)]))\n",
    "\n",
    "\n",
    "distance = euclidean_distance([1,2], [3,4])\n",
    "print(\"Euclidean Distance between (1,2) and (3,4) is\", distance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hamming Distance (`hamming_distance`)\n",
    "\n",
    "This function counts the number of differences between single elements in two items. For example, if we have two binary strings \"111\" and \"011\" the function will return 1, since the two strings only differ at the first element. The function works the same way for non-binary strings too."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hamming Distance between 'abc' and 'abb' is 1\n"
     ]
    }
   ],
   "source": [
    "def hamming_distance(X, Y):\n",
    "    return sum(x != y for x, y in zip(X, Y))\n",
    "\n",
    "\n",
    "distance = hamming_distance(['a','b','c'], ['a','b','b'])\n",
    "print(\"Hamming Distance between 'abc' and 'abb' is\", distance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mean Boolean Error (`mean_boolean_error`)\n",
    "\n",
    "To calculate this distance, we find the ratio of different elements over all elements of two items. For example, if the two items are `(1,2,3)` and `(1,4,5)`, the ration of different/all elements is 2/3, since they differ in two out of three elements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Boolean Error Distance between (1,2,3) and (1,4,5) is 0.6666666666666666\n"
     ]
    }
   ],
   "source": [
    "def mean_boolean_error(X, Y):\n",
    "    return mean(int(x != y) for x, y in zip(X, Y))\n",
    "\n",
    "\n",
    "distance = mean_boolean_error([1,2,3], [1,4,5])\n",
    "print(\"Mean Boolean Error Distance between (1,2,3) and (1,4,5) is\", distance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mean Error (`mean_error`)\n",
    "\n",
    "This function finds the mean difference of single elements between two items. For example, if the two items are `(1,0,5)` and `(3,10,5)`, their error distance is `(3-1) + (10-0) + (5-5) = 2 + 10 + 0 = 12`. The mean error distance therefore is `12/3=4`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Error Distance between (1,0,5) and (3,10,5) is 4\n"
     ]
    }
   ],
   "source": [
    "def mean_error(X, Y):\n",
    "    return mean([abs(x - y) for x, y in zip(X, Y)])\n",
    "\n",
    "\n",
    "distance = mean_error([1,0,5], [3,10,5])\n",
    "print(\"Mean Error Distance between (1,0,5) and (3,10,5) is\", distance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mean Square Error (`ms_error`)\n",
    "\n",
    "This is very similar to the `Mean Error`, but instead of calculating the difference between elements, we are calculating the *square* of the differences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Square Distance between (1,0,5) and (3,10,5) is 34.666666666666664\n"
     ]
    }
   ],
   "source": [
    "def ms_error(X, Y):\n",
    "    return mean([(x - y)**2 for x, y in zip(X, Y)])\n",
    "\n",
    "\n",
    "distance = ms_error([1,0,5], [3,10,5])\n",
    "print(\"Mean Square Distance between (1,0,5) and (3,10,5) is\", distance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Root of Mean Square Error (`rms_error`)\n",
    "\n",
    "This is the square root of `Mean Square Error`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root of Mean Error Distance between (1,0,5) and (3,10,5) is 5.887840577551898\n"
     ]
    }
   ],
   "source": [
    "def rms_error(X, Y):\n",
    "    return math.sqrt(ms_error(X, Y))\n",
    "\n",
    "\n",
    "distance = rms_error([1,0,5], [3,10,5])\n",
    "print(\"Root of Mean Error Distance between (1,0,5) and (3,10,5) is\", distance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plurality Learner Classifier\n",
    "\n",
    "### Overview\n",
    "\n",
    "The Plurality Learner is a simple algorithm, used mainly as a baseline comparison for other algorithms. It finds the most popular class in the dataset and classifies any subsequent item to that class. Essentially, it classifies every new item to the same class. For that reason, it is not used very often, instead opting for more complicated algorithms when we want accurate classification.\n",
    "\n",
    "![pL plot](images/pluralityLearner_plot.png)\n",
    "\n",
    "Let's see how the classifier works with the plot above. There are three classes named **Class A** (orange-colored dots) and **Class B** (blue-colored dots) and **Class C** (green-colored dots). Every point in this plot has two **features** (i.e. X<sub>1</sub>, X<sub>2</sub>). Now, let's say we have a new point, a red star and we want to know which class this red star belongs to. Solving this problem by predicting the class of this new red star is our current classification problem.\n",
    "\n",
    "The Plurality Learner will find the class most represented in the plot. ***Class A*** has four items, ***Class B*** has three and ***Class C*** has seven. The most popular class is ***Class C***. Therefore, the item will get classified in ***Class C***, despite the fact that it is closer to the other two classes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "Below follows the implementation of the PluralityLearner algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def PluralityLearner(dataset):\n",
    "    \"\"\"A very dumb algorithm: always pick the result that was most popular\n",
    "    in the training data.  Makes a baseline for comparison.\"\"\"\n",
    "    most_popular = mode([e[dataset.target] for e in dataset.examples])\n",
    "\n",
    "    def predict(example):\n",
    "        \"Always return same result: the most popular from the training set.\"\n",
    "        return most_popular\n",
    "    return predict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It takes as input a dataset and returns a function. We can later call this function with the item we want to classify as the argument and it returns the class it should be classified in.\n",
    "\n",
    "The function first finds the most popular class in the dataset and then each time we call its \"predict\" function, it returns it. Note that the input (\"example\") does not matter. The function always returns the same class."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example\n",
    "\n",
    "For this example, we will not use the Iris dataset, since each class is represented the same. This will throw an error. Instead we will use the zoo dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mammal\n"
     ]
    }
   ],
   "source": [
    "zoo = DataSet(name=\"zoo\")\n",
    "\n",
    "pL = PluralityLearner(zoo)\n",
    "print(pL([1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 4, 1, 0, 1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output for the above code is \"mammal\", since that is the most popular and common class in the dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## k-Nearest Neighbours (kNN) Classifier\n",
    "\n",
    "### Overview\n",
    "The k-Nearest Neighbors algorithm is a non-parametric method used for classification and regression. We are going to use this to classify Iris flowers. More about kNN on [Scholarpedia](http://www.scholarpedia.org/article/K-nearest_neighbor).\n",
    "\n",
    "![kNN plot](images/knn_plot.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how kNN works with a simple plot shown in the above picture.\n",
    "\n",
    "We have co-ordinates (we call them **features** in Machine Learning) of this red star and we need to predict its class using the kNN algorithm. In this algorithm, the value of **k** is arbitrary. **k** is one of the **hyper parameters** for kNN algorithm. We choose this number based on our dataset and choosing a particular number is known as **hyper parameter tuning/optimising**. We learn more about this in coming topics.\n",
    "\n",
    "Let's put **k = 3**. It means you need to find 3-Nearest Neighbors of this red star and classify this new point into the majority class. Observe that smaller circle which contains three points other than **test point** (red star). As there are two violet points, which form the majority, we predict the class of red star as **violet- Class B**.\n",
    "\n",
    "Similarly if we put **k = 5**, you can observe that there are four yellow points, which form the majority. So, we classify our test point as **yellow- Class A**.\n",
    "\n",
    "In practical tasks, we iterate through a bunch of values for k (like [1, 3, 5, 10, 20, 50, 100]), see how it performs and select the best one. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "Below follows the implementation of the kNN algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def NearestNeighborLearner(dataset, k=1):\n",
    "    \"\"\"k-NearestNeighbor: the k nearest neighbors vote.\"\"\"\n",
    "    def predict(example):\n",
    "        \"\"\"Find the k closest items, and have them vote for the best.\"\"\"\n",
    "        best = heapq.nsmallest(k, ((dataset.distance(e, example), e)\n",
    "                                   for e in dataset.examples))\n",
    "        return mode(e[dataset.target] for (d, e) in best)\n",
    "    return predict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It takes as input a dataset and k (default value is 1) and it returns a function, which we can later use to classify a new item.\n",
    "\n",
    "To accomplish that, the function uses a heap-queue, where the items of the dataset are sorted according to their distance from *example* (the item to classify). We then take the k smallest elements from the heap-queue and we find the majority class. We classify the item to this class."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example\n",
    "\n",
    "We measured a new flower with the following values: 5.1, 3.0, 1.1, 0.1. We want to classify that item/flower in a class. To do that, we write the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "setosa\n"
     ]
    }
   ],
   "source": [
    "iris = DataSet(name=\"iris\")\n",
    "\n",
    "kNN = NearestNeighborLearner(iris,k=3)\n",
    "print(kNN([5.1,3.0,1.1,0.1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output of the above code is \"setosa\", which means the flower with the above measurements is of the \"setosa\" species."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Naive Bayes Learner\n",
    "\n",
    "### Overview\n",
    "\n",
    "#### Theory of Probabilities\n",
    "\n",
    "The Naive Bayes algorithm is a probabilistic classifier, making use of [Bayes' Theorem](https://en.wikipedia.org/wiki/Bayes%27_theorem). The theorem states that the conditional probability of **A** given **B** equals the conditional probability of **B** given **A** multiplied by the probability of **A**, divided by the probability of **B**.\n",
    "\n",
    "$$P(A|B) = \\dfrac{P(B|A)*P(A)}{P(B)}$$\n",
    "\n",
    "From the theory of Probabilities we have the Multiplication Rule, if the events *X* are independent the following is true:\n",
    "\n",
    "$$P(X_{1} \\cap X_{2} \\cap ... \\cap X_{n}) = P(X_{1})*P(X_{2})*...*P(X_{n})$$\n",
    "\n",
    "For conditional probabilities this becomes:\n",
    "\n",
    "$$P(X_{1}, X_{2}, ..., X_{n}|Y) = P(X_{1}|Y)*P(X_{2}|Y)*...*P(X_{n}|Y)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Classifying an Item\n",
    "\n",
    "How can we use the above to classify an item though?\n",
    "\n",
    "We have a dataset with a set of classes (**C**) and we want to classify an item with a set of features (**F**). Essentially what we want to do is predict the class of an item given the features.\n",
    "\n",
    "For a specific class, **Class**, we will find the conditional probability given the item features:\n",
    "\n",
    "$$P(Class|F) = \\dfrac{P(F|Class)*P(Class)}{P(F)}$$\n",
    "\n",
    "We will do this for every class and we will pick the maximum. This will be the class the item is classified in.\n",
    "\n",
    "The features though are a vector with many elements. We need to break the probabilities up using the multiplication rule. Thus the above equation becomes:\n",
    "\n",
    "$$P(Class|F) = \\dfrac{P(Class)*P(F_{1}|Class)*P(F_{2}|Class)*...*P(F_{n}|Class)}{P(F_{1})*P(F_{2})*...*P(F_{n})}$$\n",
    "\n",
    "The calculation of the conditional probability then depends on the calculation of the following:\n",
    "\n",
    "*a)* The probability of **Class** in the dataset.\n",
    "\n",
    "*b)* The conditional probability of each feature occuring in an item classified in **Class**.\n",
    "\n",
    "*c)* The probabilities of each individual feature.\n",
    "\n",
    "For *a)*, we will count how many times **Class** occurs in the dataset (aka how many items are classified in a particular class).\n",
    "\n",
    "For *b)*, if the feature values are discrete ('Blue', '3', 'Tall', etc.), we will count how many times a feature value occurs in items of each class. If the feature values are not discrete, we will go a different route. We will use a distribution function to calculate the probability of values for a given class and feature. If we know the distribution function of the dataset, then great, we will use it to compute the probabilities. If we don't know the function, we can assume the dataset follows the normal (Gaussian) distribution without much loss of accuracy. In fact, it can be proven that any distribution tends to the Gaussian the larger the population gets (see [Central Limit Theorem](https://en.wikipedia.org/wiki/Central_limit_theorem)).\n",
    "\n",
    "*NOTE:* If the values are continuous but use the discrete approach, there might be issues if we are not lucky. For one, if we have two values, '5.0 and 5.1', with the discrete approach they will be two completely different values, despite being so close. Second, if we are trying to classify an item with a feature value of '5.15', if the value does not appear for the feature, its probability will be 0. This might lead to misclassification. Generally, the continuous approach is more accurate and more useful, despite the overhead of calculating the distribution function.\n",
    "\n",
    "The last one, *c)*, is tricky. If feature values are discrete, we can count how many times they occur in the dataset. But what if the feature values are continuous? Imagine a dataset with a height feature. Is it worth it to count how many times each value occurs? Most of the time it is not, since there can be miscellaneous differences in the values (for example, 1.7 meters and 1.700001 meters are practically equal, but they count as different values).\n",
    "\n",
    "So as we cannot calculate the feature value probabilities, what are we going to do?\n",
    "\n",
    "Let's take a step back and rethink exactly what we are doing. We are essentially comparing conditional probabilities of all the classes. For two classes, **A** and **B**, we want to know which one is greater:\n",
    "\n",
    "$$\\dfrac{P(F|A)*P(A)}{P(F)} vs. \\dfrac{P(F|B)*P(B)}{P(F)}$$\n",
    "\n",
    "Wait, **P(F)** is the same for both the classes! In fact, it is the same for every combination of classes. That is because **P(F)** does not depend on a class, thus being independent of the classes.\n",
    "\n",
    "So, for *c)*, we actually don't need to calculate it at all."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Wrapping It Up\n",
    "\n",
    "Classifying an item to a class then becomes a matter of calculating the conditional probabilities of feature values and the probabilities of classes. This is something very desirable and computationally delicious.\n",
    "\n",
    "Remember though that all the above are true because we made the assumption that the features are independent. In most real-world cases that is not true though. Is that an issue here? Fret not, for the the algorithm is very efficient even with that assumption. That is why the algorithm is called **Naive** Bayes Classifier. We (naively) assume that the features are independent to make computations easier."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "The implementation of the Naive Bayes Classifier is split in two; Discrete and Continuous. The user can choose between them with the argument `continuous`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Discrete\n",
    "\n",
    "The implementation for discrete values counts how many times each feature value occurs for each class, and how many times each class occurs. The results are stored in a `CountinProbDist` object."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the below code you can see the probabilities of the class \"Setosa\" appearing in the dataset and the probability of the first feature (at index 0) of the same class having a value of 5. Notice that the second probability is relatively small, even though if we observe the dataset we will find that a lot of values are around 5. The issue arises because the features in the Iris dataset are continuous, and we are assuming they are discrete. If the features were discrete (for example, \"Tall\", \"3\", etc.) this probably wouldn't have been the case and we would see a much nicer probability distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3333333333333333\n",
      "0.10588235294117647\n"
     ]
    }
   ],
   "source": [
    "dataset = iris\n",
    "\n",
    "target_vals = dataset.values[dataset.target]\n",
    "target_dist = CountingProbDist(target_vals)\n",
    "attr_dists = {(gv, attr): CountingProbDist(dataset.values[attr])\n",
    "              for gv in target_vals\n",
    "              for attr in dataset.inputs}\n",
    "for example in dataset.examples:\n",
    "        targetval = example[dataset.target]\n",
    "        target_dist.add(targetval)\n",
    "        for attr in dataset.inputs:\n",
    "            attr_dists[targetval, attr].add(example[attr])\n",
    "\n",
    "\n",
    "print(target_dist['setosa'])\n",
    "print(attr_dists['setosa', 0][5.0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we found the different values for the classes (called targets here) and calculated their distribution. Next we initialized a dictionary of `CountingProbDist` objects, one for each class and feature. Finally, we iterated through the examples in the dataset and calculated the needed probabilites.\n",
    "\n",
    "Having calculated the different probabilities, we will move on to the predicting function. It will receive as input an item and output the most likely class. Using the above formula, it will multiply the probability of the class appearing, with the probability of each feature value appearing in the class. It will return the max result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "setosa\n"
     ]
    }
   ],
   "source": [
    "def predict(example):\n",
    "    def class_probability(targetval):\n",
    "        return (target_dist[targetval] *\n",
    "                product(attr_dists[targetval, attr][example[attr]]\n",
    "                        for attr in dataset.inputs))\n",
    "    return argmax(target_vals, key=class_probability)\n",
    "\n",
    "\n",
    "print(predict([5, 3, 1, 0.1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can view the complete code by executing the next line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%psource NaiveBayesDiscrete"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Continuous\n",
    "\n",
    "In the implementation we use the Gaussian/Normal distribution function. To make it work, we need to find the means and standard deviations of features for each class. We make use of the `find_means_and_deviations` Dataset function. On top of that, we will also calculate the class probabilities as we did with the Discrete approach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.006, 3.418, 1.464, 0.244]\n",
      "[0.5161711470638634, 0.3137983233784114, 0.46991097723995795, 0.19775268000454405]\n"
     ]
    }
   ],
   "source": [
    "means, deviations = dataset.find_means_and_deviations()\n",
    "\n",
    "target_vals = dataset.values[dataset.target]\n",
    "target_dist = CountingProbDist(target_vals)\n",
    "\n",
    "\n",
    "print(means[\"setosa\"])\n",
    "print(deviations[\"versicolor\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see the means of the features for the \"Setosa\" class and the deviations for \"Versicolor\".\n",
    "\n",
    "The prediction function will work similarly to the Discrete algorithm. It will multiply the probability of the class occuring with the conditional probabilities of the feature values for the class.\n",
    "\n",
    "Since we are using the Gaussian distribution, we will input the value for each feature into the Gaussian function, together with the mean and deviation of the feature. This will return the probability of the particular feature value for the given class. We will repeat for each class and pick the max value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "setosa\n"
     ]
    }
   ],
   "source": [
    "def predict(example):\n",
    "    def class_probability(targetval):\n",
    "        prob = target_dist[targetval]\n",
    "        for attr in dataset.inputs:\n",
    "            prob *= gaussian(means[targetval][attr], deviations[targetval][attr], example[attr])\n",
    "        return prob\n",
    "\n",
    "    return argmax(target_vals, key=class_probability)\n",
    "\n",
    "\n",
    "print(predict([5, 3, 1, 0.1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The complete code of the continuous algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%psource NaiveBayesContinuous"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Examples\n",
    "\n",
    "We will now use the Naive Bayes Classifier (Discrete and Continuous) to classify items:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Discrete Classifier\n",
      "setosa\n",
      "versicolor\n",
      "versicolor\n",
      "\n",
      "Continuous Classifier\n",
      "setosa\n",
      "versicolor\n",
      "virginica\n"
     ]
    }
   ],
   "source": [
    "nBD = NaiveBayesLearner(iris, continuous=False)\n",
    "print(\"Discrete Classifier\")\n",
    "print(nBD([5, 3, 1, 0.1]))\n",
    "print(nBD([6, 5, 3, 1.5]))\n",
    "print(nBD([7, 3, 6.5, 2]))\n",
    "\n",
    "\n",
    "nBC = NaiveBayesLearner(iris, continuous=True)\n",
    "print(\"\\nContinuous Classifier\")\n",
    "print(nBC([5, 3, 1, 0.1]))\n",
    "print(nBC([6, 5, 3, 1.5]))\n",
    "print(nBC([7, 3, 6.5, 2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how the Discrete Classifier misclassified the second item, while the Continuous one had no problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Perceptron Classifier\n",
    "\n",
    "### Overview\n",
    "\n",
    "The Perceptron is a linear classifier. It works the same way as a neural network with no hidden layers (just input and output). First it trains its weights given a dataset and then it can classify a new item by running it through the network.\n",
    "\n",
    "Its input layer consists of the the item features, while the output layer consists of nodes (also called neurons). Each node in the output layer has *n* synapses (for every item feature), each with its own weight. Then, the nodes find the dot product of the item features and the synapse weights. These values then pass through an activation function (usually a sigmoid). Finally, we pick the largest of the values and we return its index.\n",
    "\n",
    "Note that in classification problems each node represents a class. The final classification is the class/node with the max output value.\n",
    "\n",
    "Below you can see a single node/neuron in the outer layer. With *f* we denote the item features, with *w* the synapse weights, then inside the node we have the dot product and the activation function, *g*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![perceptron](images/perceptron.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "First, we train (calculate) the weights given a dataset, using the `BackPropagationLearner` function of `learning.py`. We then return a function, `predict`, which we will use in the future to classify a new item. The function computes the (algebraic) dot product of the item with the calculated weights for each node in the outer layer. Then it picks the greatest value and classifies the item in the corresponding class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%psource PerceptronLearner"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the Perceptron is a one-layer neural network, without any hidden layers. So, in `BackPropagationLearner`, we will pass no hidden layers. From that function we get our network, which is just one layer, with the weights calculated.\n",
    "\n",
    "That function `predict` passes the input/example through the network, calculating the dot product of the input and the weights for each node and returns the class with the max dot product."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example\n",
    "\n",
    "We will train the Perceptron on the iris dataset. Because though the `BackPropagationLearner` works with integer indexes and not strings, we need to convert class names to integers. Then, we will try and classify the item/flower with measurements of 5, 3, 1, 0.1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "iris = DataSet(name=\"iris\")\n",
    "iris.classes_to_numbers()\n",
    "\n",
    "perceptron = PerceptronLearner(iris)\n",
    "print(perceptron([5, 3, 1, 0.1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The correct output is 0, which means the item belongs in the first class, \"setosa\". Note that the Perceptron algorithm is not perfect and may produce false classifications."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural Network\n",
    "\n",
    "### Overview\n",
    "\n",
    "Although the Perceptron may seem like a good way to make classifications, it is a linear classifier (which, roughly, means it can only draw straight lines to divide spaces) and therefore it can be stumped by more complex problems. We can extend Perceptron to solve this issue, by employing multiple layers of its functionality. The construct we are left with is called a Neural Network, or a Multi-Layer Perceptron, and it is a non-linear classifier. It achieves that by combining the results of linear functions on each layer of the network.\n",
    "\n",
    "Similar to the Perceptron, this network also has an input and output layer. However it can also have a number of hidden layers. These hidden layers are responsible for the non-linearity of the network. The layers are comprised of nodes. Each node in a layer (excluding the input one), holds some values, called *weights*, and takes as input the output values of the previous layer. The node then calculates the dot product of its inputs and its weights and then activates it with an *activation function* (sometimes a sigmoid). Its output is fed to the nodes of the next layer. Note that sometimes the output layer does not use an activation function, or uses a different one from the rest of the network. The process of passing the outputs down the layer is called *feed-forward*.\n",
    "\n",
    "After the input values are fed-forward into the network, the resulting output can be used for classification. The problem at hand now is how to train the network (ie. adjust the weights in the nodes). To accomplish that we utilize the *Backpropagation* algorithm. In short, it does the opposite of what we were doing up to now. Instead of feeding the input forward, it will feed the error backwards. So, after we make a classification, we check whether it is correct or not, and how far off we were. We then take this error and propagate it backwards in the network, adjusting the weights of the nodes accordingly. We will run the algorithm on the given input/dataset for a fixed amount of time, or until we are satisfied with the results. The number of times we will iterate over the dataset is called *epochs*. In a later section we take a detailed look at how this algorithm works.\n",
    "\n",
    "NOTE: Sometimes we add to the input of each layer another node, called *bias*. This is a constant value that will be fed to the next layer, usually set to 1. The bias generally helps us \"shift\" the computed function to the left or right."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![multilayer_perceptron](images/multilayer_perceptron.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "The `NeuralNetLearner` function takes as input a dataset to train upon, the learning rate (in (0, 1]), the number of epochs and finally the size of the hidden layers. This last argument is a list, with each element corresponding to one hidden layer.\n",
    "\n",
    "After that we will create our neural network in the `network` function. This function will make the necessary connections between the input layer, hidden layer and output layer. With the network ready, we will use the `BackPropagationLearner` to train the weights of our network for the examples provided in the dataset.\n",
    "\n",
    "The NeuralNetLearner returns the `predict` function, which can receive an example and feed-forward it into our network to generate a prediction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%psource NeuralNetLearner"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Backpropagation\n",
    "\n",
    "In both the Perceptron and the Neural Network, we are using the Backpropagation algorithm to train our weights. Basically it achieves that by propagating the errors from our last layer into our first layer, this is why it is called Backpropagation. In order to use Backpropagation, we need a cost function. This function is responsible for indicating how good our neural network is for a given example. One common cost function is the *Mean Squared Error* (MSE). This cost function has the following format:\n",
    "\n",
    "$$MSE=\\frac{1}{2} \\sum_{i=1}^{n}(y - \\hat{y})^{2}$$\n",
    "\n",
    "Where `n` is the number of training examples, $\\hat{y}$ is our prediction and $y$ is the correct prediction for the example.\n",
    "\n",
    "The algorithm combines the concept of partial derivatives and the chain rule to generate the gradient for each weight in the network based on the cost function.\n",
    "\n",
    "For example, if we are using a Neural Network with three layers, the sigmoid function as our activation function and the MSE cost function, we want to find the gradient for the a given weight $w_{j}$, we can compute it like this:\n",
    "\n",
    "$$\\frac{\\partial MSE(\\hat{y}, y)}{\\partial w_{j}} = \\frac{\\partial MSE(\\hat{y}, y)}{\\partial \\hat{y}}\\times\\frac{\\partial\\hat{y}(in_{j})}{\\partial in_{j}}\\times\\frac{\\partial in_{j}}{\\partial w_{j}}$$\n",
    "\n",
    "Solving this equation, we have:\n",
    "\n",
    "$$\\frac{\\partial MSE(\\hat{y}, y)}{\\partial w_{j}} = (\\hat{y} - y)\\times{\\hat{y}}'(in_{j})\\times a_{j}$$\n",
    "\n",
    "Remember that $\\hat{y}$ is the activation function applied to a neuron in our hidden layer, therefore $$\\hat{y} = sigmoid(\\sum_{i=1}^{num\\_neurons}w_{i}\\times a_{i})$$\n",
    "\n",
    "Also $a$ is the input generated by feeding the input layer variables into the hidden layer.\n",
    "\n",
    "We can use the same technique for the weights in the input layer as well. After we have the gradients for both weights, we use gradient descent to update the weights of the network."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "First, we feed-forward the examples in our neural network. After that, we calculate the gradient for each layer weights. Once that is complete, we update all the weights using gradient descent. After running these for a given number of epochs, the function returns the trained Neural Network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%psource BackPropagationLearner"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "iris = DataSet(name=\"iris\")\n",
    "iris.classes_to_numbers()\n",
    "\n",
    "nNL = NeuralNetLearner(iris)\n",
    "print(nNL([5, 3, 1, 0.1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output should be 0, which means the item should get classified in the first class, \"setosa\". Note that since the algorithm is non-deterministic (because of the random initial weights) the classification might be wrong. Usually though it should be correct.\n",
    "\n",
    "To increase accuracy, you can (most of the time) add more layers and nodes. Unfortunately the more layers and nodes you have, the greater the computation cost."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MNIST Handwritten Digits Classification\n",
    "\n",
    "The MNIST database, available from [this page](http://yann.lecun.com/exdb/mnist/), is a large database of handwritten digits that is commonly used for training and testing/validating in Machine learning.\n",
    "\n",
    "The dataset has **60,000 training images** each of size 28x28 pixels with labels and **10,000 testing images** of size 28x28 pixels with labels.\n",
    "\n",
    "In this section, we will use this database to compare performances of different learning algorithms.\n",
    "\n",
    "It is estimated that humans have an error rate of about **0.2%** on this problem. Let's see how our algorithms perform!\n",
    "\n",
    "NOTE: We will be using external libraries to load and visualize the dataset smoothly ([numpy](http://www.numpy.org/) for loading and [matplotlib](http://matplotlib.org/) for visualization). You do not need previous experience of the libraries to follow along."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loading MNIST digits data\n",
    "\n",
    "Let's start by loading MNIST data into numpy arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os, struct\n",
    "import array\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import Counter\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (10.0, 8.0)\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "plt.rcParams['image.cmap'] = 'gray'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def load_MNIST(path=\"aima-data/MNIST\"):\n",
    "    \"helper function to load MNIST data\"\n",
    "    train_img_file = open(os.path.join(path, \"train-images-idx3-ubyte\"), \"rb\")\n",
    "    train_lbl_file = open(os.path.join(path, \"train-labels-idx1-ubyte\"), \"rb\")\n",
    "    test_img_file = open(os.path.join(path, \"t10k-images-idx3-ubyte\"), \"rb\")\n",
    "    test_lbl_file = open(os.path.join(path, 't10k-labels-idx1-ubyte'), \"rb\")\n",
    "    \n",
    "    magic_nr, tr_size, tr_rows, tr_cols = struct.unpack(\">IIII\", train_img_file.read(16))\n",
    "    tr_img = array.array(\"B\", train_img_file.read())\n",
    "    train_img_file.close()    \n",
    "    magic_nr, tr_size = struct.unpack(\">II\", train_lbl_file.read(8))\n",
    "    tr_lbl = array.array(\"b\", train_lbl_file.read())\n",
    "    train_lbl_file.close()\n",
    "    \n",
    "    magic_nr, te_size, te_rows, te_cols = struct.unpack(\">IIII\", test_img_file.read(16))\n",
    "    te_img = array.array(\"B\", test_img_file.read())\n",
    "    test_img_file.close()\n",
    "    magic_nr, te_size = struct.unpack(\">II\", test_lbl_file.read(8))\n",
    "    te_lbl = array.array(\"b\", test_lbl_file.read())\n",
    "    test_lbl_file.close()\n",
    "\n",
    "#     print(len(tr_img), len(tr_lbl), tr_size)\n",
    "#     print(len(te_img), len(te_lbl), te_size)\n",
    "    \n",
    "    train_img = np.zeros((tr_size, tr_rows*tr_cols), dtype=np.int16)\n",
    "    train_lbl = np.zeros((tr_size,), dtype=np.int8)\n",
    "    for i in range(tr_size):\n",
    "        train_img[i] = np.array(tr_img[i*tr_rows*tr_cols : (i+1)*tr_rows*tr_cols]).reshape((tr_rows*te_cols))\n",
    "        train_lbl[i] = tr_lbl[i]\n",
    "        \n",
    "    test_img = np.zeros((te_size, te_rows*te_cols), dtype=np.int16)\n",
    "    test_lbl = np.zeros((te_size,), dtype=np.int8)\n",
    "    for i in range(te_size):\n",
    "        test_img[i] = np.array(te_img[i*te_rows*te_cols : (i+1)*te_rows*te_cols]).reshape((te_rows*te_cols))\n",
    "        test_lbl[i] = te_lbl[i]\n",
    "        \n",
    "    return(train_img, train_lbl, test_img, test_lbl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `load_MNIST()` loads MNIST data from files saved in `aima-data/MNIST`. It returns four numpy arrays that we are going to use to train and classify hand-written digits in various learning approaches."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_img, train_lbl, test_img, test_lbl = load_MNIST()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the shape of these NumPy arrays to make sure we have loaded the database correctly.\n",
    "\n",
    "Each 28x28 pixel image is flattened to a 784x1 array and we should have 60,000 of them in training data. Similarly, we should have 10,000 of those 784x1 arrays in testing data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training images size: (60000, 784)\n",
      "Training labels size: (60000,)\n",
      "Testing images size: (10000, 784)\n",
      "Training labels size: (10000,)\n"
     ]
    }
   ],
   "source": [
    "print(\"Training images size:\", train_img.shape)\n",
    "print(\"Training labels size:\", train_lbl.shape)\n",
    "print(\"Testing images size:\", test_img.shape)\n",
    "print(\"Training labels size:\", test_lbl.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing MNIST digits data\n",
    "\n",
    "To get a better understanding of the dataset, let's visualize some random images for each class from training and testing datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "classes = [\"0\", \"1\", \"2\", \"3\", \"4\", \"5\", \"6\", \"7\", \"8\", \"9\"]\n",
    "num_classes = len(classes)\n",
    "\n",
    "def show_MNIST(dataset, samples=8):\n",
    "    if dataset == \"training\":\n",
    "        labels = train_lbl\n",
    "        images = train_img\n",
    "    elif dataset == \"testing\":\n",
    "        labels = test_lbl\n",
    "        images = test_img\n",
    "    else:\n",
    "        raise ValueError(\"dataset must be 'testing' or 'training'!\")\n",
    "        \n",
    "    for y, cls in enumerate(classes):\n",
    "        idxs = np.nonzero([i == y for i in labels])\n",
    "        idxs = np.random.choice(idxs[0], samples, replace=False)\n",
    "        for i , idx in enumerate(idxs):\n",
    "            plt_idx = i * num_classes + y + 1\n",
    "            plt.subplot(samples, num_classes, plt_idx)\n",
    "            plt.imshow(images[idx].reshape((28, 28)))\n",
    "            plt.axis(\"off\")\n",
    "            if i == 0:\n",
    "                plt.title(cls)\n",
    "\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7b88++2yqV68OOMY0QJ48eYxhcuWVVwJw7NgxT8YXjP79+wNw3nnnmW2NGjUC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\neKSBlIiIiIhHGkiJiIiIePQ/B3zVmzgAI0oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3150035390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# takes 5-10 seconds to execute this\n",
    "show_MNIST(\"training\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PorLFQ4mKNaKwBBY5/PzzzwAmVyoQUQ6l3Lxnz54ZlChB9mvmhN9YkDu3c9uaPXt2UF/A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\n7og2hFijABPMK2rmKZlmRTpAzhEJJFV5jo2NBQJfPymQZM+ePVkgvK/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YAGDeD+K+jYqK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\nY7pw7U2ZM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2/U2dkpSfOmN/ORza7LBwMDAy64tQ/v8vLyQH92fHxcHz9+lOSdzpDmLzYP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\nEoEUAABASARSAAAAIf0HBztPDx0KfCcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3144b93320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# takes 5-10 seconds to execute this\n",
    "show_MNIST(\"testing\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's have a look at the average of all the images of training and testing data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "classes = [\"0\", \"1\", \"2\", \"3\", \"4\", \"5\", \"6\", \"7\", \"8\", \"9\"]\n",
    "num_classes = len(classes)\n",
    "\n",
    "def show_ave_MNIST(dataset):\n",
    "    if dataset == \"training\":\n",
    "        print(\"Average of all images in training dataset.\")\n",
    "        labels = train_lbl\n",
    "        images = train_img\n",
    "    elif dataset == \"testing\":\n",
    "        print(\"Average of all images in testing dataset.\")\n",
    "        labels = test_lbl\n",
    "        images = test_img\n",
    "    else:\n",
    "        raise ValueError(\"dataset must be 'testing' or 'training'!\")\n",
    "        \n",
    "    for y, cls in enumerate(classes):\n",
    "        idxs = np.nonzero([i == y for i in labels])\n",
    "        print(\"Digit\", y, \":\", len(idxs[0]), \"images.\")\n",
    "        \n",
    "        ave_img = np.mean(np.vstack([images[i] for i in idxs[0]]), axis = 0)\n",
    "#         print(ave_img.shape)\n",
    "        \n",
    "        plt.subplot(1, num_classes, y+1)\n",
    "        plt.imshow(ave_img.reshape((28, 28)))\n",
    "        plt.axis(\"off\")\n",
    "        plt.title(cls)\n",
    "\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average of all images in training dataset.\n",
      "Digit 0 : 5923 images.\n",
      "Digit 1 : 6742 images.\n",
      "Digit 2 : 5958 images.\n",
      "Digit 3 : 6131 images.\n",
      "Digit 4 : 5842 images.\n",
      "Digit 5 : 5421 images.\n",
      "Digit 6 : 5918 images.\n",
      "Digit 7 : 6265 images.\n",
      "Digit 8 : 5851 images.\n",
      "Digit 9 : 5949 images.\n"
     ]
    },
    {
     "data": {
      "image/png": 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7J8+LKVOGYRiGYRgtcCSVKR14DUTrofQQP/CBDwBoeIxTU1NiIdODLxaLYkHzs+iVDA4O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\nzhCdfwdoDjympaq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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3143051d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average of all images in testing dataset.\n",
      "Digit 0 : 980 images.\n",
      "Digit 1 : 1135 images.\n",
      "Digit 2 : 1032 images.\n",
      "Digit 3 : 1010 images.\n",
      "Digit 4 : 982 images.\n",
      "Digit 5 : 892 images.\n",
      "Digit 6 : 958 images.\n",
      "Digit 7 : 1028 images.\n",
      "Digit 8 : 974 images.\n",
      "Digit 9 : 1009 images.\n"
     ]
    },
    {
     "data": {
      "image/png": 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1zknfpI3A67C0tNR0mdaW+QzDMAzDMA4AB06Z6u3tFU9HB/PSogyX4bLZbMP2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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f31434f97b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_ave_MNIST(\"training\")\n",
    "show_ave_MNIST(\"testing\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing\n",
    "\n",
    "Now, let us convert this raw data into `DataSet.examples` to run our algorithms defined in `learning.py`. Every image is represented by 784 numbers (28x28 pixels) and we append them with its label or class to make them work with our implementations in learning module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60000, 784) (60000,)\n",
      "(60000, 785)\n"
     ]
    }
   ],
   "source": [
    "print(train_img.shape, train_lbl.shape)\n",
    "temp_train_lbl = train_lbl.reshape((60000,1))\n",
    "training_examples = np.hstack((train_img, temp_train_lbl))\n",
    "print(training_examples.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we will initialize a DataSet with our training examples, so we can use it in our algorithms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# takes ~8 seconds to execute this\n",
    "MNIST_DataSet = DataSet(examples=training_examples, distance=manhattan_distance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Moving forward we can use `MNIST_DataSet` to test our algorithms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### k-Nearest Neighbors\n",
    "\n",
    "We will now try to classify a random image from the dataset using the kNN classifier.\n",
    "\n",
    "First, we choose a number from 0 to 9999 for `test_img_choice` and we are going to predict the class of that test image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    }
   ],
   "source": [
    "from learning import NearestNeighborLearner\n",
    "\n",
    "# takes ~20 Secs. to execute this\n",
    "kNN = NearestNeighborLearner(MNIST_DataSet,k=3)\n",
    "print(kNN(test_img[211]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make sure that the output we got is correct, let's plot that image along with its label."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual class of test image: 5\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f314374b198>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3143f85400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Actual class of test image:\", test_lbl[211])\n",
    "plt.imshow(test_img[211].reshape((28,28)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hurray! We've got it correct. Don't worry if our algorithm predicted a wrong class. With this techinique we have only ~97% accuracy on this dataset. Let's try with a different test image and hope we get it this time.\n",
    "\n",
    "You might have recognized that our algorithm took ~20 seconds to predict a single image. How would we even predict all 10,000 test images? Yeah, the implementations we have in our learning module are not optimized to run on this particular dataset, as they are written with readability in mind, instead of efficiency."
   ]
  }
 ],
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