06-engineering-numeric-predictors.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/nikolashahpazov/.pyenv/versions/3.9.2/lib/python3.9/site-packages/geopandas/_compat.py:106: UserWarning: The Shapely GEOS version (3.8.0-CAPI-1.13.1 ) is incompatible with the GEOS version PyGEOS was compiled with (3.9.1-CAPI-1.14.2). Conversions between both will be slow.\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib import cm\n",
    "from datetime import timedelta\n",
    "\n",
    "\n",
    "from sklearn.preprocessing import PowerTransformer\n",
    "\n",
    "# ggplot layers\n",
    "from plotnine import (ggplot, aes, geom_violin, coord_flip, geom_tile, geom_point, geom_segment,\n",
    "                      geom_boxplot, theme, element_blank, geom_path, geom_hline, xlim,\n",
    "                      scale_fill_manual, geom_errorbar, geom_line, geom_bar, scale_x_log10,\n",
    "                      scale_color_manual, geom_histogram, ggtitle, geom_density, geom_jitter,\n",
    "                      facet_wrap,  xlab, ylab, scale_x_discrete)\n",
    "\n",
    "# for setting plot size mainly\n",
    "import plotnine.options as ggplot_options\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An important transformation to an individual variable is for a variable that has values bounded between zero and one, such as proportions. The problem with modeling this type of outcome is that model predictions might may not be guaranteed to be within the same boundaries. For data between zero and one, the logit transformation could be used. If π is the variable, the logit transformations is\n",
    "\n",
    "$$\n",
    "logit(\\pi) = log(\\frac{\\pi}{1-\\pi})\n",
    "$$\n",
    "\n",
    "This transformation changes the scale from values between zero and one to values between negative and positive infinity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (321761898)>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_ = pd.DataFrame({'prop': np.random.uniform(0, 1, 1620)})\n",
    "from scipy.special import logit\n",
    "\n",
    "df = df_.assign(prop=lambda df: logit(df['prop']))\n",
    "ggplot(df) + aes(x='prop') + geom_density(fill=\"#336699\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Common Numerical Transformations\n",
    "\n",
    "* Box-Cox Power Transformation when the variable is positive\n",
    "* Yeo-Johnson Power Transformation when the variable can be negative as well\n",
    "* Centering and Scaling\n",
    "* $logit(\\pi)$ where $\\pi$ is a proportion\n",
    "* $arcsine(\\sqrt{\\pi})$ where $\\pi$ is a proportion\n",
    "* Range Scaling\n",
    "* Data Smoothing for time series, \n",
    "    - running mean\n",
    "    - running median (when having outliers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.random.normal(12, 7, 1000)\n",
    "y = (x - np.min(x)) / (np.max(x) - np.min(x))\n",
    "\n",
    "np.max(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These transformations are mostly innocuous and are typically needed when the model requires the predictors to be in common units. For example, when the distance or dot products between predictors are used, such as \n",
    "* K-nearest neighbors\n",
    "* support vector machines) or \n",
    "* when the variables are required to be a a common scale in order to apply a penalty (e.g., the lasso or ridge regression)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **1:Many Transformations**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **Many:Many Transformations**\n",
    "\n",
    "When creating new features from multiple predictors, there is a possibility of correcting a variety of issues such as \n",
    "* outliers\n",
    "* collinearity\n",
    "* reduce the dimensionality\n",
    "\n",
    "### **Linear Projection Methods**\n",
    "\n",
    "- Principal Component Analysis (**PCA**)\n",
    "- Kernel Principal Component Analysis (**KPCA**)\n",
    "- Independent Component Analysis (**ICA**)\n",
    "- Non-negative Matrix Factorization (**NNMF**)\n",
    "- Partial Least Squares (**PLS**)\n",
    "- Multidimensional Scaling (**MDS**)\n",
    "\n"
   ]
  }
 ],
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