{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>This notebook is a demonstration of two types of feature engineering methods:<br><br>\n",
    "<ul>\n",
    "    <li>Creating non-linear transformations of individual features</li>\n",
    "    <li>Transforming continuous or discrete features in binary bins - aka \"binning\"</li>\n",
    "</ul><br><br>\n",
    "\n",
    "The first thing we do is write a few functions that make transformations.\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "Binning vs transformation\n",
    "'''\n",
    "\n",
    "from sklearn import linear_model\n",
    "import math\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def genY(x, err, betas):\n",
    "    '''\n",
    "    Goal: generate a Y variable as Y=XB+e \n",
    "    Input\n",
    "    1. an np array x of length n\n",
    "    2. a random noise vector r of length n\n",
    "    3. a (d+1) x 1 vector of coefficients b - each represents ith degree of x\n",
    "    '''\n",
    "    d = pd.DataFrame(x, columns=['x'])    \n",
    "    y = err\n",
    "    for i,b in enumerate(betas):\n",
    "        y = y + b*x**i\n",
    "    d['y'] = y\n",
    "    return d\n",
    "\n",
    "\n",
    "def makePolyFeat(d, deg):\n",
    "    '''\n",
    "    Goal: Generate features up to X**deg\n",
    "    1. a data frame with two features X and Y\n",
    "    4. a degree 'deg' (from which we make polynomial features \n",
    "    \n",
    "    '''\n",
    "    #Generate Polynomial terms\n",
    "    for i in range(2, deg+1):\n",
    "        d['x'+str(i)] = d['x']**i\n",
    "    return d\n",
    "\n",
    "\n",
    "\n",
    "def makeBin(d, bins):\n",
    "    '''\n",
    "    This takes in a dataframe with a feature X and makes evenly spaced bin features\n",
    "    using the pandas get_dummies function\n",
    "    '''\n",
    "    d['g'] = np.floor(bins*(d['x']-d['x'].min())/(d['x'].max()-d['x'].min())).astype(int)\n",
    "    d['g']=-1*(d['g']==bins)+d['g'] #Puts the highest entry into the right bin\n",
    "    #Note that the get_dummies function makes k dummy features if there are k\n",
    "    #discrete values. In modeling you should always use k-1 bins\n",
    "    dummies = pd.get_dummies(d['g'], prefix='bin')\n",
    "    d_m = pd.merge(d, dummies, left_index=True, right_index=True, how='inner')\n",
    "    del d_m['g'] #we don't need this\n",
    "    del d_m['bin_0'] #we don't need this either\n",
    "    return d_m\n",
    "    \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Now that we've created the functions, let's generate some data. Again, the goal is to generate an X-Y relationship with noise, but where we know the underlying data generating distribution.\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "betas = [0, 4, -3.5, 1]\n",
    "n=200\n",
    "sig=2.2\n",
    "sp=20\n",
    "\n",
    "x_init = np.random.uniform(0,1,n)\n",
    "e_init = np.random.normal(0, sig, n)\n",
    "\n",
    "dat = genY(x_init, e_init, betas)\n",
    "dat = makePolyFeat(dat, 6)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Now we want to see the effect of fitting polynomial curves of different degrees to our noisy data set. Ultimately, we want to illustrate how model specification (and feature engineering) affects the bias-variance tradeoff.\n",
    "\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def PlotLinDeg(X_train, y_train, X_test, y_test, i, t):\n",
    "    '''\n",
    "    This function builds a regression model on the simulated data\n",
    "    1. plots the test data\n",
    "    2. plots the fitted line\n",
    "    3. Shows sum-square error\n",
    "    '''\n",
    "    regr = linear_model.LinearRegression(fit_intercept=True)\n",
    "    regr.fit(X_train, y_train)\n",
    "    y_hat=regr.predict(X_train)\n",
    "    y_hat_test=regr.predict(X_test)\n",
    "    ss_train=((y_train-y_hat)**2).mean()\n",
    "    ss_test=((y_test-y_hat_test)**2).mean()\n",
    "    #Plot train X vs. Predicted Y_train\n",
    "    plt.subplot(2, 3, i)\n",
    "    plt.plot(X_train['x'], y_train, 'b.')\n",
    "    plt.plot(X_train['x'], y_hat, 'r.')\n",
    "    plt.title('{}\\n Train MSE={}'.format(t,round(ss_train,4)))\n",
    "    #Plot test X vs. Predicted Y_test\n",
    "    plt.tick_params(axis='x', which='both', bottom='off', top='off', labelbottom='off')\n",
    "    plt.subplot(2,3,i+3)\n",
    "    plt.plot(X_test['x'], y_test, 'b.')\n",
    "    plt.plot(X_test['x'], y_hat_test, 'r.')\n",
    "    plt.title('Test MSE={}'.format(round(ss_test,4)))\n",
    "    plt.tick_params(axis='x', which='both', bottom='off', top='off', labelbottom='off')\n",
    "    \n",
    "    \n",
    "def PlotLinBin(X_train, y_train, X_test, y_test, i, t, x, x_t):\n",
    "    '''\n",
    "    This function builds a regression model on the simulated data\n",
    "    1. plots the test data\n",
    "    2. plots the fitted line\n",
    "    3. Shows sum-square error\n",
    "    '''\n",
    "    regr = linear_model.LinearRegression(fit_intercept=True)\n",
    "    regr.fit(X_train, y_train)\n",
    "    y_hat=regr.predict(X_train)\n",
    "    y_hat_test=regr.predict(X_test)\n",
    "    ss_train=((y_train-y_hat)**2).mean()\n",
    "    ss_test=((y_test-y_hat_test)**2).mean()\n",
    "    #Plot train X vs. Predicted Y_train\n",
    "    plt.subplot(2, 3, i)\n",
    "    plt.plot(x, y_train, 'b.')\n",
    "    plt.plot(x, y_hat, 'r.')\n",
    "    plt.title('{}\\n Train MSE={}'.format(t,round(ss_train,4)))\n",
    "    #Plot test X vs. Predicted Y_test\n",
    "    plt.tick_params(axis='x', which='both', bottom='off', top='off', labelbottom='off')\n",
    "    plt.subplot(2,3,i+3)\n",
    "    plt.plot(x_t, y_test, 'b.')\n",
    "    plt.plot(x_t, y_hat_test, 'r.')\n",
    "    plt.title('Test MSE={}'.format(round(ss_test,4)))\n",
    "    plt.tick_params(axis='x', which='both', bottom='off', top='off', labelbottom='off')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x720 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sp = 20\n",
    "\n",
    "f1=['x']; f3=['x', 'x2', 'x3']; f6=['x', 'x2', 'x3', 'x4', 'x5', 'x6']\n",
    "\n",
    "fig=plt.figure(figsize=(12,10))\n",
    "\n",
    "j=1\n",
    "for plot in [f1,f3,f6]:\n",
    "    PlotLinDeg(dat[plot][:sp], dat['y'][:sp], dat[plot][sp:], dat['y'][sp:], j, 'Degree '+str(len(plot)))\n",
    "    j+=1\n",
    "\n",
    "fig.tight_layout()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The above plot is a great illustration of bias-variance tradeoffs. The top row shows an nth-degree model fit to a sparse training set. The bottom row shows this fitted model against the test data (with actuals in blue and predicted in red). We can see multiple things here:<br>\n",
    "<ul>\n",
    "    <li>MSE gets much better on training data as we increase the degree to 6</li>\n",
    "    <li>MSE gets notably worse on test data as we increase the degree from 3 to 6</li>\n",
    "    <li>A linear model is notably biased (has the worst training error), but the error from bias is better than the error induced from overfitting (i.e., the high variance model)</li>\n",
    "</ul><br>\n",
    "\n",
    "Now let's do a similar experiment with the bin features.\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x720 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def getBinName(vl, pre):\n",
    "    l=[]\n",
    "    for v in vl:\n",
    "        if (pre in v):\n",
    "            l.append(v)\n",
    "    return l\n",
    "\n",
    "plt.figure(figsize=(14,10))\n",
    "\n",
    "j=1\n",
    "for binvals in [2,10,20]:  ## Arbitrary bin values can be chosen here\n",
    "\n",
    "    d = makeBin(dat,binvals); g = getBinName(d.columns.values,'bin')\n",
    "    PlotLinBin(d[g][:sp], d['y'][:sp], d[g][sp:], d['y'][sp:], j, 'Bins='+str(binvals), d['x'][:sp], d['x'][sp:])\n",
    "    j+=1\n",
    "\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}