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# SuperJohn/jupyter_notebook_test.ipynb

Last active Nov 15, 2017
jupyter_notebook_test
 { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Regression Week 4: Ridge Regression (interpretation)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook, we will run ridge regression multiple times with different L2 penalties to see which one produces the best fit. We will revisit the example of polynomial regression as a means to see the effect of L2 regularization. In particular, we will:\n", "* Use a pre-built implementation of regression (GraphLab Create) to run polynomial regression\n", "* Use matplotlib to visualize polynomial regressions\n", "* Use a pre-built implementation of regression (GraphLab Create) to run polynomial regression, this time with L2 penalty\n", "* Use matplotlib to visualize polynomial regressions under L2 regularization\n", "* Choose best L2 penalty using cross-validation.\n", "* Assess the final fit using test data.\n", "\n", "We will continue to use the House data from previous notebooks. (In the next programming assignment for this module, you will implement your own ridge regression learning algorithm using gradient descent.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Fire up graphlab create" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import graphlab\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Polynomial regression, revisited" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We build on the material from Week 3, where we wrote the function to produce an SFrame with columns containing the powers of a given input. Copy and paste the function polynomial_sframe from Week 3:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's use matplotlib to visualize what a polynomial regression looks like on the house data." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO] graphlab.cython.cy_server: GraphLab Create v2.1 started. Logging: /tmp/graphlab_server_1509441024.log\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "This non-commercial license of GraphLab Create for academic use is assigned to johnkirkhoughton1@gmail.com and will expire on April 06, 2018.\n" ] } ], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This non-commercial license of GraphLab Create for academic use is assigned to johnkirkhoughton1@gmail.com and will expire on April 06, 2018.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO] graphlab.cython.cy_server: GraphLab Create v2.1 started. Logging: /tmp/graphlab_server_1510595653.log\n" ] } ], "source": [ "sales = graphlab.SFrame('kc_house_data.gl/')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As in Week 3, we will use the sqft_living variable. For plotting purposes (connecting the dots), you'll need to sort by the values of sqft_living. For houses with identical square footage, we break the tie by their prices." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "sales = sales.sort(['sqft_living','price'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us revisit the 15th-order polynomial model using the 'sqft_living' input. Generate polynomial features up to degree 15 using polynomial_sframe() and fit a model with these features. When fitting the model, use an L2 penalty of 1e-5:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "l2_small_penalty = 1e-5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note: When we have so many features and so few data points, the solution can become highly numerically unstable, which can sometimes lead to strange unpredictable results. Thus, rather than using no regularization, we will introduce a tiny amount of regularization (l2_penalty=1e-5) to make the solution numerically stable. (In lecture, we discussed the fact that regularization can also help with numerical stability, and here we are seeing a practical example.)\n", "\n", "With the L2 penalty specified above, fit the model and print out the learned weights.\n", "\n", "Hint: make sure to add 'price' column to the new SFrame before calling graphlab.linear_regression.create(). Also, make sure GraphLab Create doesn't create its own validation set by using the option validation_set=None in this call." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def polynomial_sframe(feature, degree):\n", " # assume that degree >= 1\n", " # initialize the SFrame:\n", " poly_sframe = graphlab.SFrame()\n", " # and set poly_sframe['power_1'] equal to the passed feature\n", " poly_sframe['power_1'] = feature\n", " # first check if degree > 1\n", " if degree > 1:\n", " # then loop over the remaining degrees:\n", " # range usually starts at 0 and stops at the endpoint-1. We want it to start at 2 and stop at degree\n", " for power in range(2, degree+1): \n", " # first we'll give the column a name:\n", " name = 'power_' + str(power)\n", " # then assign poly_sframe[name] to the appropriate power of feature\n", " poly_sframe[name] = feature**power\n", " return poly_sframe" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def polynomial_regression(sframe, cols, target, deg, l2_penalty):\n", " global poly_data\n", " poly_data = polynomial_sframe(sframe[cols], deg)\n", " my_features = poly_data.column_names()\n", " poly_data[target] = sframe[target]\n", " model = graphlab.linear_regression.create(poly_data, target=target, features = my_features,\n", " l2_penalty=l2_penalty,\n", " validation_set=None,verbose=False)\n", " return model" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def print_coefficients(model): \n", " # Get the degree of the polynomial\n", " deg = len(model.coefficients['value'])-1\n", "\n", " # Get learned parameters as a list\n", " w = list(model.coefficients['value'])\n", "\n", " # Numpy has a nifty function to print out polynomials in a pretty way\n", " # (We'll use it, but it needs the parameters in the reverse order)\n", " print 'Learned polynomial for degree ' + str(deg) + ':'\n", " w.reverse()\n", " print np.poly1d(w)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_poly_predictions(data, model): \n", " plt.plot(poly_data['power_1'],poly_data['price'],'.',\n", " poly_data['power_1'], model.predict(poly_data),'-')\n", " plt.xlabel('x')\n", " plt.ylabel('y')" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "ename": "NameError", "evalue": "name 'l2_small_penalty' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mmodel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpolynomial_regression\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msales\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'sqft_living'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'price'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m15\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ml2_small_penalty\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mNameError\u001b[0m: name 'l2_small_penalty' is not defined" ] } ], "source": [ "model = polynomial_regression(sales, 'sqft_living', 'price', 15, l2_small_penalty)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "ename": "NameError", "evalue": "name 'model' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mprint_coefficients\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mNameError\u001b[0m: name 'model' is not defined" ] } ], "source": [ "print_coefficients(model)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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3Ft3J6AGjOTXnVH8NURpEIuYVlLqmo0TkHuAJY8zmENf6G2PWRcs4vxGR+k7X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\nRBNSsCIiogkpWBER0YQUrIiIaMKfBt7hVm+vzmcAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_poly_predictions(poly_data, model)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***QUIZ QUESTION: What's the learned value for the coefficient of feature power_1?***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "answer = 103.1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Observe overfitting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recall from Week 3 that the polynomial fit of degree 15 changed wildly whenever the data changed. In particular, when we split the sales data into four subsets and fit the model of degree 15, the result came out to be very different for each subset. The model had a *high variance*. We will see in a moment that ridge regression reduces such variance. But first, we must reproduce the experiment we did in Week 3." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, split the data into split the sales data into four subsets of roughly equal size and call them set_1, set_2, set_3, and set_4. Use .random_split function and make sure you set seed=0. " ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [], "source": [ "(semi_split1, semi_split2) = sales.random_split(.5,seed=0)\n", "(set_1, set_2) = semi_split1.random_split(0.5, seed=0)\n", "(set_3, set_4) = semi_split2.random_split(0.5, seed=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, fit a 15th degree polynomial on set_1, set_2, set_3, and set_4, using 'sqft_living' to predict prices. Print the weights and make a plot of the resulting model.\n", "\n", "Hint: When calling graphlab.linear_regression.create(), use the same L2 penalty as before (i.e. l2_small_penalty). Also, make sure GraphLab Create doesn't create its own validation set by using the option validation_set = None in this call." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": true }, "outputs": [], "source": [ "model = polynomial_regression(set_1, 'sqft_living', 'price', 15, l2_small_penalty)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Learned polynomial for degree 15:\n", " 15 14 13 12\n", "-2.338e-53 x + 1.527e-49 x + 3.8e-45 x + 2.851e-41 x \n", " 11 10 9 8\n", " - 1.627e-37 x - 6.838e-33 x - 6.928e-29 x + 1.593e-25 x\n", " 7 6 5 4 3\n", " + 1.069e-20 x + 5.975e-17 x - 3.798e-13 x - 1.529e-08 x + 0.0001415 x\n", " 2\n", " - 0.3973 x + 585.9 x + 9306\n" ] } ], "source": [ "print_coefficients(model)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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DMpIr8MKSvhpGFIS8mhUrEsOrSU+HgQODtSESqspTC5/izVVvsviaxRbCnuD0\nb9efpVuX8u2P39KofqOgzakQEyzDiIKQV7N8uROrRPRqgubbH7/l+inXs2DTAqZeNpWmh1Qno5tR\nExxS7xCOan0U8/Pn8/NOPw/anAqxIUHDiJKQV2NiVZqV21Yy4OkBKMq8q+fRo0WPoE0yoiSZhgVN\nsAzDqBbjlo7jxOdP5OaBN/P8uc8nxdCSUUwybehY4cLhuowtHDaMsvmh4AduevcmZn45k9cvep2j\n2hwVtElGFdj+3XY6PdqJHbftIC0lNrNEgS0cNgzDCOeLHV9w3DPHseP7HSz47QITqySm+aHN6dCk\nA0u2LAnalAoxwTIMj0RZGJzoTFw5keOeOY6r+lzFq798lcYNGgdtklFNkmVDRxMswyCxFgYnKj8W\n/shN797ELdNu4e1L3+b3/X9vYeu1hGTZ0NEEyzBIrIXBicj63es58bkTWbtzLZ/+9lP6tesXtElG\nDAlFCib6nL0JlmEQ/3RHiTbcWBl73l79Nv2e6seFPS9k0rBJNDukWfwNNGqUjk06kiqpfLGzoj15\ng8UWDhsG8V0YHBpuDPUddDqlaO0pKCrg/2b+Hy8vfZkJF09gUMagmjfWqBH8Gzp2adYlaHPKxDws\nw/CI18LgRBtujMaeTXs3cfKLJ/Pp15+y8LcLTazqAMkQeGGCZdQaEm3YLURWFvToAamp0L179Ycb\n/c9ZlWeuaPjz4/Ufc+yTx3JKp1N451fv0LJRy+oZbCQFyRB4YUOCRq0g0YbdIhGLgDr/c/bwsh+t\nWlW5Zy5v+HP80vHc8O4NvHjei5zR9YzqG2wkDb1b9mbLvi1s/XYrrRq1CtqciJiHZdQKEm3Yzc+y\nZU5UCgogL696tvmfc+XK4n4r+8zhw5+qyl8//Cu3v3c77w1/z8SqDpKaksrxHY5P6LyCcRUsEWkg\nIvNEZJGILBWRu73ypiIyTUTyRGSqiDTxtRkpImtEZKWInOYr7ysiS0RktYg84iuvLyI5Xps5IpLh\nuzbCq58nIsN95ZkiMte7Nl5EzNNMchJ5U8NY2ubvq2dP52VVt9/9Bfu5fNLlvLXqLeZeNZcjWx9Z\ndQONpCbRN3SMey5BETlUVb8TkVTgY+AG4EJgu6o+ICK3AU1V9XYR6QW8AvQD2gMzgK6qqiIyD/i9\nqn4iIlOAR1V1qohcC/xUVa8TkaHA+ao6TESaAguAvoAAnwJ9VXW3iLwKvKGqr4vIWGCxqv4ngu2W\nSzCJ2Ls/JPsdAAAgAElEQVQ3cbf/iKVt/r6gev1+8903XPDqBbQ4tAUvnf+SJa6t48z6aha3TLuF\n+b+ZX61+kjaXoKp+5502wM2ZKXAu8IJX/gJwnnd+DpCjqgWqug5YA/QXkTZAuqp+4tV70dfG39cb\nwEne+RBgmqruVtVdwDTgdO/aScAE3/3Pj8GjGgFTXpRf0AEZsYxA9PdVnX7zvslj4NMDOb7D8bxx\n8RsmVgb92vVjxbYV7PtxX9CmRCTugiUiKSKyCNgMTPdEp7WqbgFQ1c1AaIavHbDB1zzfK2sHbPSV\nb/TKSrRR1UJgt4g0K6svEWkO7FTVIl9fbWPxrEYwVCRGiZJ2KWjR9PP+l+9z4vMncsfgO7j/lPtJ\nEZvONqBhWkOObnM08zbOC9qUiMR97sYThj4i0hh4U0R647ysEtVieMto3NCoXdVRo0YdPM/OziY7\nO7vyFhlxI5rowEgBGTW9vXwiRTE+s/AZ7ph5BzkX5iTFLrNGzRJK03Ry55OjbpObm0tubm78jPKo\nsWADVd0jIrm4YbktItJaVbd4w31bvWr5QAdfs/ZeWVnl/jabvHmyxqq6Q0TygeywNu+r6nYRaSIi\nKZ6Y+vsqhV+wjNizd68TlKysqr3AoxGjUKDCihUlgxP89w71VVU7YmFnvCnSIkbOGMnEVROZdcUs\nujXvFpf7VPd3agTLoIxBPDL3kYor+gj/Y3706NExtspDVeN2AC2AJt75IcCHwJnAGOA2r/w24H7v\nvBewCKgPdAI+pzgwZC7QH+cdTQFO98qvAx73zofh5sAAmgJfAE1854d7114FhnrnY4HflWG/GvFj\nzx7Vo45STUtzP/fsqXof9eqV38eePapz5hRfz89X7dLF3Tsryx3VsSNWdsaLffv36fk55+uJz52o\n33z7TdzuE4vfqREsO77boYfde5j+WPBjlfvw3p2x15R4dHqwc/gpsBBYDCwB7vTKm+EiAPNwwRCH\n+9qM9IRqJXCar/wYYCkuEONRX3kD4DWvfC6Q6bt2uVe+GhjuK+8EzPPKXwXqlWF/lX9hRsXMnu1e\nbOBe5HPmVK2fcDGKpn6XLu6+oJqaGhs7Ym1nrMjfk6/H/OcYHfHmCP3hwA9xvVesfqdGsGQ9nqXz\nN86vcvt4CVbcw9qTGQtrjy+heZ3QUF1NzevMmePuW1joPnfuDIce6hb11qQdNcGirxdxbs65XHvs\ntdw+6Pa4718V1O/UiC3XvX0dXZt15ebjbq5S+3iFtZtglYMJVvwJYu2UPwAiMxM++MDdO1HXcFWV\niSsncs3/ruHxMx/not4X1dh9E3k9nBEd45aOY8LKCUy4eELFlSNgghUAJljBUBOT9rX5pVpYVMif\nZ/6ZccvGMeHiCRzb9tgK21ighOFn/e71HPvksWz5f1uq5JUn7cJhw6gMFa2ZitVapnhtJRI027/b\nzhmvnMH8TfNZ8JsFUYtVIqxTMxKHjCYZHFLvENbsWBO0KSUwwTISivKS2NqLtXwWfb2IY586lqNa\nH8XUy6ZGvS1IIicONoIjtB4rkTDBMuJGrPdqshdr2bz02Uuc9vJpjDllDH8/7e+kpUS/xDKREwcb\nwTGowyBmrU+sDR1tDqscbA6r6lQns0NZ80tlRaDV5fmXA4UHuGXaLbzz+Tu8OfRNslplVamf2jyn\nZ1SNZVuXcf6r57PmD5UfFrSgiwAwwao6c+a4obuCAveX+4cfVi+zQ0iUOnaE9euLX6yJlPKoplm/\nez3D3hhGs0Oa8fIFL3N4w8ODNsmoRRRpES0eaMGK61fQ5rA2lWprQRdGUuEfZureHfbtq/qck3/u\n6swzISPDiVdIxOI9TJhISWtDvLnyTfo91Y/ze5zP5Esmm1gZMSdFUhJuQ0cTLCMuhLZhf+cd9/mM\nM6oeKOEXpeXL4Wc/Kw686Ngx9vMvfoFKhEAPvz37ftzHbyb/hv83/f8xadgkbj3hVsu0bsSNRNvQ\n0f6lG3EjPd1lkKjqNu4h/N5aZiasW1fc3/r1Thg//DA2w4HhAjVvXrCBHn57jjn7E44e25cCLWDx\nNYsZ2D522XMT0Ys0gifRIgVNsIwqEe0LLlYRaP/4h/PWPvigdH+xXFMVPsQoEp398XrhL1sGy1YU\nUjDwPtb0+wVXdPwbz537HOkNYjdRlwhepJGYHNv2WFZ9s4q9+xPkH0U8EhTWlgNLfhuRsjJy79nj\nkp+GJ3etTtLXSPeKZxLZSFnVQ/fLzy/7+eKVoXzhV6u10e8Hq1yerT0Hro/LM1vCWqM8Bj87WKd9\nPq1SbYhT8lvzsIxKEynQoby/0qvjAUW6V6w8qkheUWjuzT/EmJ7uPKszz4z8fPEI/CgoKuCBjx/g\n1Jzj+PMvL2DWb2cwb1qHuERA2josozwGZSTOeiwTLKPSRHrBxfKlHRKSTZtg2zYXFRiLaMPwe5Q3\nDBa+mqG854v1C/+zzZ8x4OkBTF87nU9+8wm3/+wmTjguNW7h+pFE2jBCDM4YzAdffpQYc5zxcNtq\ny4ENCZZJ+LBcWUNpkYbQKur3qKPcHlUNGujBPasyM1V79ar8sFtZNoQPg82Y4cry88se7ixvA8ZY\nDFN+f+B7vfO9O7XlAy312YXPalFRUdU7M4wYsX7rTk258zBNrf9j1P/3SMYNHJP9MMGqHP6XdrTz\nXOGf/ULiPyqzyWKoz7LEJ1QnJED+HYdDuxBHuk9ZolQVYQ5nxhcztMe/euj5Oefrpj2bqt6RYcSY\n2bNV5ezfKYdtinqO0wTLBCupiDSRHy5ikQTFX8fvYfXsWexhZWWVLQ5+D61tW/ezLJELCdD06cW2\nhkQr2q3sqxtw8eXOL/WCVy/QTo900jdXvmlelZFwVDS6EIl4CZbNYRlVprxQ7kiZLsLXNL39duSA\nilmz3LF2LcyYUXykpJSeWwpn2TJYutTtJrxpU/Guwt27l55bCgVvDBhQbGvv3i50Ptr5nKrO3X13\n4Dvufv9ujnnyGPq06cPy65ZzXo/z4r4jsGFUloSa44yHCtaWA/OwyiQaz2LPHjc3FBpu69lTtXPn\n4r/UQh5WNH+5RRt6nZ+vWr++lhpOnDGj4ucJn5ObPt0d5dlV2b8+i4qK9LVlr2nGwxk69PWhun7X\n+vIbGEYSQjIOCQLtgZnAcmApcINX3hSYBuQBU4EmvjYjgTXASuA0X3lfYAmwGnjEV14fyPHazAEy\nfNdGePXzgOG+8kxgrndtPJBWhv0x+eXVRqIVkPA5qdRUN+SWn++uRxusEK0wzJ5dPAwYOsobQizr\nXllZ0beP9hkWfb1Is5/P1iPHHqm5X+ZGb5BhJBnJKlhtgKO988M84egBjAH+5JXfBtzvnfcCFgFp\nnqh8TnFG+XlAP+98CjDEO78WeNw7HwrkaLEofgE0AQ4PnXvXXgUu8s7HAteUYX9sfnu1kGgFxD+n\nFBKAtLTSwQzRBC1EIwx+z69zZ9XJkys/rxQueuH2VpbV36zWoa8P1Tb/aKP/nv9vPVB4oOqdGUYS\nkJSCVepm8BZwCrAKaK3ForbKO78duM1X/x1ggFdnha98GDDWO38XGOCdpwJbw+tosTAN9c63ASne\n+UDg3TLsreavrXZTGe9o8uTiIIqGDUt6WKEhw2g8oWjEraoh5v7owsp4WGWxYfcG/c3k32iLB1ro\n3z78m+7bv6/ynRhGEhIvwYp+W9JqIiKZwNG4objWqrrFU4TNItLKq9YON6wXIt8rKwA2+so3euWh\nNhu8vgpFZLeINPOX+/sSkebATlUt8vXVNhbPWNcIBS2EE76hYno6tGhRHABRWOiS1rZt6wIxli1z\n5cuWwfz5cPLJke8X7d5XZdlVHuF9T50KK1e6a/37V26i+ZvvvuG+Wffx3OLn+O0xvyXv93k0O6RZ\n5QyKAXV5Y0ujdlIjgiUihwFvADeq6j4RCY/1iuUuidGEWUUdijVq1KiD59nZ2WRnZ1feojpEWaIS\nihoM7RZclWwQkSLyqrMpZHl9r19ftnCWxZ79e3h4zsP8c/4/Gdp7KMuvW84R6UfExsBKUpc3tjRq\nntzcXHJzc+N/o3i4bf4DJ4rv4sQqVLaSkkOCKzXykOC7FA8JrvSVRzsk+ISvzRMUDwlupeSQ4Dtl\n2F4Npzh5iTTsFu08k39NUzQLb0NDgqmpkYfe/PetynqQaJ+zOn1v+mavXv/KA9rygVZ62cTL9Isd\nX1TLllhgCW2NICFZ57CAF4GHwsrGhISJyEEX9YFOlAy6mAv0x3lHU4DTvfLrKA66GEbkoIvQ+eHe\ntVd94jUW+F0Ztsfid5dUlJUdPZrFsZWNrgu1mT7dhZ1HkwU9Vpnaq9J3uKjs/H6n3jntL5o2sqXK\nRRdrt0FLq2RXPLK9x1rcDaMyJKVgAScAhcBiT4gWAqcDzYAZuKjBaSEh8dqM9IQqPKz9GFxo/Brg\nUV95A+A1r3wukOm7drlXvpqSYe2dcFGHqz3xqleG/bH57SURkf4yr0oIe0qKC7Qoj4pe1PH0Eirb\nt9/W3v226i1TRmqzMc30zCdHaGqrVdWyMV7PGStxN4zKkpSClexHXRSs/PzSqYmi/Ws9P9+Fkod7\nWGUNd4UPH86YUXKxbln3zc9XffRR1UmTyu+/PCoTlj99urtfatONypCblNua6vnP/E7X7lgbE0/G\nvCGjtmGCZYIVd/xrpvyLe0PXIs0/hc8BpaQUC1ZIhEKeSVZWSTHyDx926+Yysoc+d+7s7h9+3/z8\nkjkGu3cvDouvSHgizctVNASYlaXK4WuVX1yj3NZUU864WXsN2FgqI0akIc3KfvfmDRm1BRMsE6y4\n418wW9Fi2fDhPL+3FDoaNnRekL88Uv2UFNU2bUq2DYnW9Okld/p99NGSdVJSyk9wG26rXzTD64QL\n2rjpK1XOH678qZly0h2akr5Vn3qqZPqmeO00bBjJTLwEy5LfGgfp2NElgAVIS3MbJ5ZFeBi4iAuf\nTk0trnPgAHz1FfToUVweXr9ePcjMhM2bS99j7VoYMgR+8hO30eKAAfDggyXr/OQnzlZwyXG3bi2Z\njHfvXhg/vtjWZcvg9NOhb1+XHDdUx7+Z4+y1n3Hx6xdzw8ITaZnaFR77Amb+jV4dWzJ0aHF4eDx2\nGo435SUsNoyEJx4qWFsO6qCHVZk9p7KynIeTmek8qfz8ksluGzYs9momT3Y/w+fG5sxxbf1eU8uW\npb2tSEebNq6tP42SfzjTP0wpUrp9ly7FnlVamirt5qpcera2uO8I/cfH/9C9+/fqnj3umWbMKOnp\nhb6DZJp7Mo/QqCmwIUETrHgTzQvYn76oe/eSAtCzZ/EQ3pNPlg6omDRJ9bHHisXEP//Vs2dJIQqf\nC4skWP45svCEt+3alR6OjNR+9uwinbI8Vw+77hTl5gxtd96/deuO78v8biJtSFnW3FNlgkFivQ4r\nErY2y6gpTLBMsGqEkNjk5UUOUvAnlo0kAuGbM4Z29PULUrdurr3/5T99etki1aFDyWuRohBnzCht\nU+fOJb29evWKtzhJq1eknU6bogOfPEG7PNZF/z37GX1n2v4SQSFl7YQcbRh8eQuiw+vWhOeTbB6h\nkbyYYJlgxYVIkX6pqcXDef4X2/TpxZ5MJAHxi03I6wjt6BvuAfmH8ELDbf59rFJTi+8R2gU4fOgv\nFJkXsj8/33lWfvF87LHi/ufMUd21u1Bf+XSidn+or/b8Z28dt2ScHig8UCowIzzysKyXvd/j9Avc\n9Okln7O8/bhq0vOxaESjJjDBMsGKOSEvwB89Fz6E5hcfv5dUv75q167uvFUr1bFjS27OGO6Z+UPY\nI0UDhs9FtWrl5sb8mz2G5sdCXtv48aU9tdA6Mv8c2lFHOaGasGKCHjn2SO3zRB99c+WbWlhUeNBG\nv2ikpkYWkPCXfXkCHz4vV94i6sp4Y4aRDJhgmWBVm/BhrnAvICfHvXjBBSn4xSd8j6hQsEXoc4MG\nkddv+e89eXLJNv4jM7OkIPrFzL8VyfTprp/w+bNwYTk4hyaFmpr1hv7kHz/VY/5zjE5eNVmLiooi\n2ucfwgwPEIlE+OaUfjsq42GF/+FggmUkOyZYJlgVUt7Evd/zKMsLeOyxYlFKTdUSa47Cs1h07hx5\nWDBcOMqaB4p0XH116bLQerCK5s9CEX8hdu0u1I5nvK5cl6WH3Hisvrr4v7p7d5FOn+6eu6y1WKF7\nRTN05rcpNEfmH0KM1muyYAijtmGCZYJVLuVN3O/Z417oflEJDa+Fyjp2dIEWZc3ThIa+MjNVH3jA\n1Y3kLdWvr/rpp04QevYsfmHn5amOGePalDWfFSn0PDW1OACkrPmztm2LvbDCokJ9ddmr2uPRLM24\np5/+30v/0927i0oJLlScOqqi7zskfv45sspk0gj/3VkwhFFbMMEywSqX8L/SZ8woDgZ49NGSL/nO\nnV2Z39tJTS2eKwqfp/nPf0pnq8jKUh09OrLw1KtXWnz87du2Ve3Vq/zADf/RurXqhx+WLOva1bUP\nDRkWFBZoztIc7f3v3nrkP/trWs+3FYq0YUMneH7B9tsUKXWUP4CirJROsdiR2I8FQxi1CRMsE6xy\niTQHk5paMu9eaK4oJBbhohJp/6rQwtt69UoLTKg8GtEJP3JyVG+7rWRZamrZ4fJNm5b8/Je/OFt3\n7irQ8UvHa69/99IBTw3QNz6bom3bFZWoe/vtkb26SIEm/gCKSNGCqqXn8ypKY2UYdY14CZalZqol\npKe7XWU//BAefhhWrXJb0e/fX1wnJQWuuw5Wr4aiIve6DZGWVnIn4FBKo2XLXN0DB9zP+vWL2xQV\nuXukVOFf0YYNcPTRLkVTiFGj4J13oFu30vV37iz5+fv9hTw4bTyd//FTxuQ+ykOnPcScq+bQ9tsz\n2Px1caf168NFF0GnTu4ZO3eGnByYMQNmz3bpnvwppQoL4YcfXLqllSvd91hQ4NIu5eS47yUrC3r2\nLLalR4+q7aBsGEblCG2OaERARDRZvp+9e524ZGW5z8cf7z6H062be3GvWuUEJ8Rjj8Hllzvh27vX\nvcjz8tyL/MCB4noiJYUuJaVkP9GQlgbt2zvRKiwsLk9NdfZPmQLTpsEtt8COHWGNpRA58lV08D3w\nfVPIHQVfnMqnnwr797t8iGee6Z79iCNg0iS48kr3uVMn+OAD94yh7yr0vPPnw003ue8lLc3Z1b27\nu2WorKCgeLt5cG0A+ve37ecNw4+IoKpScc1K9pssL+QgSBbBCiVvXb68+IX69ttwySWR62dmwvr1\nLvFsYaHzEGbPdteWLXMJa/1tW7aEbdvcebhgVRYRaN06crJbcDZ9+KG7x4knOpEQgTZtC9ncIofU\nn99Dm8bN2fjyKFh7Cm4Damfjzp3u+adMcc+XkQH/+x9cf73rp14958HdckvJ7yokNnv3uvKMjOL2\nK1Y4T+uPfyzu48MPYeDAqn8HhlHbiZdgpcW6Q6PmCc8aPn8+3Hln2fU3bCgezhs7FoYOdeUDB7qX\n8+GHl6x/xhnw4ovuvKpiJeI8qFat4Ouvy6/XrJkTjB49YGVeASlH5vD1cX+lQWELhjX9Fx+/fDKs\nLfl/YccO9zzLlzux/tnP3PHll05kRNyQp2rpDOsh8UlPL3ke+iOgRw935OWVHDY1DKOGicfEWG05\nSJKgi/Cw6PJSIbVsGXlRbE5O5Pqg2r592deiPVJSXHRgNHUzMlRT6x3Qdme+qK3+0k25cpDSaYZC\nUam6Ii5i0J8zMDW1ZJqntLTiNWXRhpBHiroMOoov2vD7mkikaxjlgUUJmmCV9yIKX/QaCtUO3xix\nffvi0PVQ+HZ+fuQNFKMNOy/vqFfP2dGuXdkiWuJIOaAc9YLyh64qVw7Wv7/xnvbOKi1UoaNNGxe2\nXiK7RVid8EXFlVkUnChro6JNkFtTiXQNozySUrCAZ4AtwBJfWVNgGpAHTAWa+K6NBNYAK4HTfOV9\ngSXAauARX3l9IMdrMwfI8F0b4dXPA4b7yjOBud618UBaOfbH4FcXGyqbvif0Us7Pd9nO/S/wyZOd\nFxbqr6xQ8qqGrPvD5UWct1Oh+KUcUI56XvlDF+XyE5XMmdq1W1HEjBzhR2jhcHjmiVDS3EipoqL9\nzoP2qkJEmw3DsmYYiUCyCtYg4OgwwRoD/Mk7vw243zvvBSzCzatlAp9THBQyD+jnnU8Bhnjn1wKP\ne+dDgRwtFsUvgCbA4aFz79qrwEXe+VjgmnLsj8XvrlqEvKrwl3Z5uenC23fsWLJt586lM59X15Py\nH82aVaJ+yo9Kn6eVGzorI7KVzJkaGvqrV895T/4cg2lpZW/GmJ/vhHjGDNfuySdLilW4h5pMQ2fR\nenyJ5hkadZOkFCxnNx3DBGsV0No7bwOs8s5vB27z1XsHGODVWeErHwaM9c7fBQZ456nA1vA6WixM\nQ73zbUCKdz4QeLcc26v5a6se5eXPmzw5cjaGSPn7/N5Nixalxapbt0qKTNgh4vqN1usC1bQG+5Vj\n/qPc1FEZfrLS8YOI7UaMKPm5adPSi4hDzxHKlXhwz6sI24OE79eVTENnlUn1lCieoVE3iZdgBREl\n2EpVt3hqsFlEWnnl7XDDeiHyvbICYKOvfKNXHmqzweurUER2i0gzf7m/LxFpDuxU1SJfX21j9mQx\nxh/9t369W/T61VduLdVtt7kFwN26uQi41auha1cXibdqVXHIdvPm7pUeYseOkp8LC13b6qAK33xT\ncR0AUvdD32coGHQ/bOsFE16BDSeU2e6FF0p+Dl9AHKJpUxcRWFjoIh1DhCIBVUtGB779dtnRguH4\n17gFud7KH8UYi3qGkWwkQli7VlwlaqKJ+6/U2oBRo0YdPM/OziY7O7tyFlWDrCwnPCtWuHDq0Pqi\nrVvh3HNdHf/LeeVKJ1iFhcUv4fnzSwpUZRf5xoy076Hv0zBoDGw+Gl57HfIHlKomAoceCt9+W4mu\n05xgRRLNDh2Kw9D93+VZZ5X8XFaoeqQ1bgDz5rmfAwbYomHDyM3NJTc3N+73CUKwtohIa1XdIiJt\ngK1eeT7QwVevvVdWVrm/zSYRSQUaq+oOEckHssPavK+q20WkiYikeF6Wv6+I+AWrpgmlWwotZl2x\nouI27drBxo3u58KF8Le/la5T3cW/laLhLjh2LAx4DPL7Q85bsOnYMqurRidWaWnwz386Qfn+e/jL\nX1x5Sor7rtatc58bNHA//d9l796RP0ci0hq3m24qziKSleUWXQclWoni/Rl1m/A/5kePHh2fG8Vj\nnNF/4AIolvo+j8GbqyJy0EV9oBMlgy7mAv1x3tEU4HSv/DqKgy6GETnoInR+uHftVYrns8YCvyvH\n9mqM4saO8Ozg3boVJ7UNj77zbxEf6JG+UTn1/yl/aqacf5nSaklM+3/oodK7IIP7niZNKrl7cChA\nJT/fZZ6vTNRgRWvcgkx8ayHsRqJCMgZdAOOATcB+YD1whScgM3Dh5tNCQuLVH+kJVXhY+zHAUlz4\n+qO+8gbAa175XCDTd+1yr3w1JcPaO+GiDld74lWvHPtj8ssri7Ki1CIFToTv9hu4IJV1tFipnHOl\ncltT5fQblSbr4nKfli1LR06mproF0GPGuMXHofLOnd0eXaHdlBs2rLxo+de4xXprkapiIexGohIv\nwbJcguUQz1yC4XMjU6a4IadvvoGRI91cVWamy323apXLh7fRCz2pSsLZ+KLQ6X0Y8Ci0nwufXA/z\nr4fvm8ftjikpLqnt008Xl6WmuuPHH0vXb9Gi5BzXU0/B1VeX3X95Q22hZLkQbOLb0L+h0DycPy+i\nYQSJJb8NgHgK1pw5xcldw+dd/ISyhCck9b6FI1+GAf8EFObdAEt+DQcODdqyUvjFrGFD+OILaFtG\nfGikQItEFYJQwt7y5uEMo6aJl2DZflgB0by5SwQLzluKJFaQoGJ1+Jdw6q1wc0fo+g688yg8vgw+\nvSbmYnXrrc7LSUtz24VURGhfqxAZGS75bVYWLF3qPKvyxApKB1osX169Z4gnoRB2EyujLmAeVjnE\ny8NauNCFQyekGJVF2g/Q4y3o8wwcsQgWj3BDfzs7x+2WmZmwZIk7X768ZDi/nwYN3HfZvTsMGwZ3\n3VV87Z//hGOPrZwHYkNthlE9bEgwAOIhWJs2uU0Gk0asWi1166d+Og62HAULr4ZV50FBw7jetn17\neO892L695EaLxx/v1pt16AD33+/WbIUWUffsCRMmwFFHuV2DKxr6g7LnqmyozTCqju2HVUv43/+S\nQKwO/xKyXoWs8XDodlh0BTw9L27eVGqqEyBwgSUZGW792IUXlszakZ7u1jz5hWTOHFizxi2Wzstz\nmTy++AImTnT9lCc25c1VWbYIw0g8TLDiSPhf73v3VpzCKDDS86HXBCdSzT6HlRfCO4/B+kGgqRW3\nrwaFhXDggNvYMSPDeUaXXebKwQlKTo4b7ktPd+IS+l5D2UCWL3eea7NmbijvP/8pLXbhRJqrMpEy\njMTFhgTLoTpDgqG/3pctc97Dr37lJvy3bq24bc2gbi6q+2To9l84fB2sOQuWXuK2ni+qF5hlofRS\n4CIo09Lc5549YepUOPNM97127AgPP+x2Az7rrOLdhQ8cKG5f3pb2NldlGPHB5rACoDqCNWMGDBmS\nYOulGm2BzFzo/B50neIi+vLOhrxzXALaosRwuDMz3dBgKAzd/yt47DG4+eZiQQI3R7V1a+mh1rS0\nisPSba7KMGKPzWElEXv3wg03JIBYNdoCHWa7Rb2Z70OTDbDuZ7Du5zD7FtjePWADHeFrzYqK4N57\n4Y47SooVODHr1Ak+/7y4bNMmqF/f9RPyxrp3h0ceqXhhr81VGUbyYB5WOVTVw5oxA04/vaQXEHfS\nvocjFkL7edBunvvZYLdLOLvu57D2ZNjcJ2G8KCg/CW9mppvT2r/f1UtNdUN/s2e78qwsN/QXIi0N\nxo51w4Xr15vHZBhBYkOCAVAVwQqFXoeyecectO+hRR60XA4tV7ij1XJovAG29YaNA9y2HRsHwI6u\noIHoK1EAAAkvSURBVMm5Njy0ALiw0J0/8QQMHVocGRjKEgLRDf0ZhlFz2JBgErB3L4wf76LTqk29\n76DFypKi1HIFNN4IO7rA1t5uA8Sllzqh2tEFCuvH4Mbxo2nT0hswpqQ4b+qrr0p6pB07ujVWeXku\nICIkVlByn7Boh/4Mw0h+zMMqh8p4WJs2uYizL790L+GohwPTvoeWK6HVMuc1hYTpsK+dhxQSpm29\nPGH6SaARfFWhaVNo0sSJUvjX2aULfPCBWwx8001O7DMzXVl6etkBERYsYRiJiw0JBkC0grV3Lxx5\nZNn5AA+SvsnNLx2xyAlUq2VuKG9HV9ia5URpa28nTDs7J9R8U3VITXXzUOFRfB07ujmpUCYKEyHD\nqB2YYAVAtII1eXKEHHdS6ISp08ziIIjU/S4I4uu+sPWnTqS2d006jykSzZu7LBNpaaWDIXr0cOcr\nV5ZcXzVtGpx8cs3bahhGfDHBCoBoBKuEd3XoNugxCX4y1QnVvjbw5Umw4XgXCLGzE27T5NpF584u\n4GH9epdp4qyz3PCff34JireXD81LWZCEYdROTLACIBrBmvjOdi78vwnQ63VoNx8+Px3WnOmyRext\nV0OWxp9QBgk/qaluTdQHH5RMMFve0J4N+xlG7ceiBBOUpXtmQaf3YMHvIGdSQm5eGA033gjHHefO\nt26FE05wkXnr1rkgiLffdp7RTTfBhg3lR+eVtxjXFuoahlFV6qyHJSKnA4/gNrF8RlXHRKgT1ZDg\nsce67S2SgXr1XPBD8+bw8stOfM48M/IWHJG8IfOQDMOoCNtxOIaISArwL2AI0Bu4RER6VLW/U06J\nlWXVp3FjJ0qOXC6/HD791GXfmDHDeUyzZ8PatS7X4dVXl71fVKTdbGtqh9vc3Nz43iDOmP3BYvbX\nTuqkYAH9gTWq+pWqHgBygAh72ZZPKNv32LExt+8gjRqV/JyaCvfcA+++6wIcRNyWHDk5TpA2bnSi\n9NRT8Mc/5vLcc9C3r4vGO/lkJ07JsKV6sv+HNfuDxeyvndTVOax2wAbf5404EasUof2UIi2G/eqr\n0kEK4YjAlVfCtm1wxhmun3ffdYEM7dq5LUnS0yE3FxYvdvtE/epXxR7RunWRh+fS053nNGpUZZ/I\nMAwjcamrghUTwlME3XuvSyfUv7/zvqZMcTnv3nsPRo6EPXvgiCOcN5SXF3nu6NprS9/n7LPdEY4F\nMBiGUZeok0EXIjIQGKWqp3ufbwc0PPBCROrel2MYhhEDbB1WjBCRVCAPOBn4GpgPXKKqKwM1zDAM\nwyiTOjkkqKqFIvJ7YBrFYe0mVoZhGAlMnfSwDMMwjOSjroa1l4uInC4iq0RktYjcFrQ9IUSkvYjM\nFJHlIrJURG7wypuKyDQRyRORqSLSxNdmpIisEZGVInKar7yviCzxnvGRGnyGFBFZKCKTk9D2JiLy\numfPchEZkGT23ywiy7x7vyIi9RPZfhF5RkS2iMgSX1nM7PWeP8drM0dEMmrA/gc8+xaLyAQRaZxM\n9vuu3SIiRSLSrEbtV1U7fAdOxD8HOgL1gMVAj6Dt8mxrAxztnR+Gm4frAYwB/uSV3wbc7533Ahbh\nhn4zvecKedXzgH7e+RRgSA09w83Ay8Bk73My2f48cIV3ngY0SRb7gbbAWqC+9/lVYEQi2w8MAo4G\nlvjKYmYvcC3wuHc+FMipAftPAVK88/uB+5LJfq+8PfAu8CXQzCvrWRP2x/0/ebIdwEDgHd/n24Hb\ngrarDFvf8v4DrAJae2VtgFWRbAfeAQZ4dVb4yocBY2vA3vbAdCCbYsFKFtsbA19EKE8W+9sCXwFN\nvZfK5GT4t4P7w9H/wo+ZvbiX7gDvPBXYFm/7w66dB7yUbPYDrwM/paRg1Yj9NiRYmkiLihMu7bqI\nZOL++pmL+w+8BUBVNwOtvGrhz5LvlbXDPVeImnrGh4FbAf/EabLY3gn4RkSe84Y0nxSRQ0kS+1V1\nE/AgsN6zZbeqziBJ7PfRKob2HmyjqoXALv8QVw1wJc7jKGGLR0LaLyLnABtUdWnYpRqx3wQrCRGR\nw4A3gBtVdR8lBYAInwNHRM4CtqjqYsrfFCzhbPdIA/oC/1bVvsC3uL8qE/67BxCRw3HpxzrivK1G\nIvIrksT+coilvTW2WZ2I3AkcUNXxsew2hn2V7lzkEOAO4O543aKiCiZYpckH/JN/7b2yhEBE0nBi\n9ZKqTvKKt4hIa+96G2CrV54PdPA1Dz1LWeXx5ATgHBFZC4wHThKRl4DNSWA7uL8MN6jqAu/zBJyA\nJcN3D274b62q7vD+mn0TOJ7ksT9ELO09eE3c2szGqrojfqY7RORy4EzgUl9xMtj/E9z81Gci8qVn\ny0IRaUXZ782Y2m+CVZpPgC4i0lFE6uPGXCcHbJO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_poly_predictions(poly_data, model)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": true }, "outputs": [], "source": [ "model = polynomial_regression(set_2, 'sqft_living', 'price', 15, l2_small_penalty)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Learned polynomial for degree 15:\n", " 15 14 13 12\n", "1.301e-50 x - 1.004e-46 x - 1.024e-42 x - 9.413e-40 x \n", " 11 10 9 8\n", " + 6.517e-35 x + 6.218e-31 x - 2.713e-29 x - 4.597e-23 x\n", " 7 6 5 4 3\n", " - 2.064e-19 x + 2.512e-15 x + 6.843e-12 x - 1.152e-07 x + 0.0004388 x\n", " 2\n", " - 0.7678 x + 783.5 x - 2.512e+04\n" ] } ], "source": [ "print_coefficients(model)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YH2rkhu76/Ul3645dB+o8l9gs8f6PgWAoe6yAxgtUaewPisZ8x01N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\nbMIOn7YwbiNTWNBFCGRCsKqqoivs5uR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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_poly_predictions(poly_data, model)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": true }, "outputs": [], "source": [ "model = polynomial_regression(set_3, 'sqft_living', 'price', 15, l2_small_penalty)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Learned polynomial for degree 15:\n", " 15 14 13 12\n", "-2.858e-51 x + 3.556e-47 x + 2.426e-43 x - 1.066e-39 x \n", " 11 10 9 8\n", " - 2.968e-35 x - 1.72e-31 x + 1.243e-27 x + 2.571e-23 x\n", " 7 6 5 4 3\n", " + 4.088e-20 x - 2.082e-15 x - 2.261e-12 x + 1.154e-07 x - 0.0005283 x\n", " 2\n", " + 1.029 x - 759.3 x + 4.624e+05\n" ] } ], "source": [ "print_coefficients(model)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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dHTZsgOOPr9/RPRMCKNoKH+z8gPFPjueQXodw72n3kpNlSxw7IiZYacAEq+OS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\nRkZggmUYhmFkBCZYhmEYRkbw/wFFndpIXC7+JwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_poly_predictions(poly_data, model)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": true }, "outputs": [], "source": [ "model = polynomial_regression(set_4, 'sqft_living', 'price', 15, l2_small_penalty)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Learned polynomial for degree 15:\n", " 15 14 13 12\n", "4.395e-50 x - 6.029e-46 x - 1.799e-42 x + 2.334e-38 x \n", " 11 10 9 8\n", " + 2.399e-34 x + 1.602e-31 x - 1.324e-26 x - 7.999e-23 x\n", " 7 6 5 4 3\n", " + 4.215e-19 x + 4.818e-15 x - 2.202e-11 x - 6.383e-08 x + 0.0005553 x\n", " 2\n", " - 1.225 x + 1248 x - 1.702e+05\n" ] } ], "source": [ "print_coefficients(model)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Gdu/dzaf7P+WTfZ8gInQs6sjBnQ6mtKSU0pJS+hzUh2NKj2HYwcMokOwGbRq7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\n/3epMuYOpfDTBnaFvZvwJOP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_poly_predictions(poly_data, model)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The four curves should differ from one another a lot, as should the coefficients you learned.\n", "\n", "***QUIZ QUESTION: For the models learned in each of these training sets, what are the smallest and largest values you learned for the coefficient of feature power_1?*** (For the purpose of answering this question, negative numbers are considered \"smaller\" than positive numbers. So -5 is smaller than -3, and -3 is smaller than 5 and so forth.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "smallest power_1 = - 759 & largest power_1 = 1248\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Ridge regression comes to rescue" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generally, whenever we see weights change so much in response to change in data, we believe the variance of our estimate to be large. Ridge regression aims to address this issue by penalizing \"large\" weights. (Weights of model15 looked quite small, but they are not that small because 'sqft_living' input is in the order of thousands.)\n", "\n", "With the argument l2_penalty=1e5, fit a 15th-order polynomial model on set_1, set_2, set_3, and set_4. Other than the change in the l2_penalty parameter, the code should be the same as the experiment above. Also, make sure GraphLab Create doesn't create its own validation set by using the option validation_set = None in this call." ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": true }, "outputs": [], "source": [ "l2_penalty_big=1e5" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": true }, "outputs": [], "source": [ "model = polynomial_regression(set_1, 'sqft_living', 'price', 15, l2_penalty_big)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Learned polynomial for degree 15:\n", " 15 14 13 12\n", "3.601e-58 x + 5.845e-54 x + 9.392e-50 x + 1.498e-45 x \n", " 11 10 9 8\n", " + 2.382e-41 x + 3.789e-37 x + 6.066e-33 x + 9.861e-29 x\n", " 7 6 5 4 3\n", " + 1.65e-24 x + 2.896e-20 x + 5.422e-16 x + 1.06e-11 x + 1.749e-07 x\n", " 2\n", " + 0.001274 x + 2.587 x + 5.303e+05\n" ] } ], "source": [ "print_coefficients(model)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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8wbYf48e7MiUlcOKJsQSI5ma3aO3gwS4RY/VqZ1+9GlauhIsuSny/dPe+SuZX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\nNUpdZ+lGfPkWGXaUw4cP62v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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_poly_predictions(poly_data, model)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": true }, "outputs": [], "source": [ "model = polynomial_regression(set_2, 'sqft_living', 'price', 15, l2_penalty_big)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Learned polynomial for degree 15:\n", " 15 14 13 12\n", "4.715e-55 x + 4.427e-51 x + 4.183e-47 x + 3.985e-43 x \n", " 11 10 9 8\n", " + 3.842e-39 x + 3.767e-35 x + 3.777e-31 x + 3.901e-27 x\n", " 7 6 5 4 3\n", " + 4.16e-23 x + 4.531e-19 x + 4.808e-15 x + 4.435e-11 x + 2.931e-07 x\n", " 2\n", " + 0.001131 x + 2.045 x + 5.192e+05\n" ] } ], "source": [ "print_coefficients(model)" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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FyJny+vfLFI2jLXR266g9NDY16in3n6LTnpkWdVOKCmwdlgmWkfpiHjIkdX3W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\nRo9OnZsKbh8yZ07qM5SUOGs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4FXAaMB74nIiMLdT9Pv1p99IvJN//vnNMEHFzRKWlzmKa\nPt25eN95p7OI1q515+vWpXrZXXRRqvBMmAD33+8cRo49FpYuXZhyv67sAr5w4cKom1A0WF8ksb4o\nPF1SsICJwBpVXaeq+4FZQMEG7QYPds4YBx+cTCspcc4I117rhtVKSpzAjB3rRKck8M2UhuzgIUNc\n2ujRbj+t2lr48Y/hhReco8ebbzovumXL4NvfduJz6aWuHYMHJ88rK+GnP83NIrL/jEmsL5JYXySx\nvig8XXVIcAiwIfD3RpyIFYzKSref0oknOutm3Di44gpnoVxxRXOHhGHDkhG/q6qcAD33HHzlK3DI\nIemH43yrB2z+yDCMzkdXFaxIGDwYXnyxudgEhQbSi85nP+uOcB7DMIyuQpf0EhSRY4Fpqnq69/fV\ngIYdL0Sk63WOYRhGHjC39jwhIgmgFjgZeAt4Hvicqq7KWtAwDMOIjC45JKiqjSLyP8A8km7tJlaG\nYRhFTJe0sAzDMIz40VXd2rMiIqeLyKsislpEroq6PYVARIaKyNMiskJEXhGRy7z0PiIyT0RqRWSu\niPQKlJkqImtEZJWInBpInyAiy7z+mhHF87QXESkRkRdFZI73d5fsBwAR6SUiv/eeb4WITOqq/SEi\nV4rIcu85HhSR8q7SFyJyl4hsEZFlgbS8PbvXl7O8MktEZFiLjVJVOwIHTsRfA4YDZcDLwNio21WA\n5xwEHOWdH4Sb0xsL3AB8x0u/CrjeOx8HvIQbRh7h9ZFvoT8HHOOdPwGcFvXztaE/rgR+C8zx/u6S\n/eC1/V7gYu+8FOjVFfsDGAy8AZR7fz8MXNRV+gL4D+AoYFkgLW/PDnwVuM07/ywwq6U2mYXVnA5d\nVBwVqrpZVV/2zt8BVgFDcc96n5ftPuBc7/xs3D+oBlVdC6wBJorIIKBCVV/w8t0fKBMLRGQocAbw\nm0Byl+sHABHpCZygqvcAeM+5iy7aH0ACOFBESoEDgDq6SF+o6t+BHaHkfD57sK5HcU5wWTHBak66\nRcVDImpLhyAiI3C/pJ4FBqrqFnCiBgzwsoX7pc5LG4LrI5849tcvgW8DwQndrtgPACOBf4vIPd4Q\n6R0i0oMu2B+qugn4BbAe91y7VHUBXbAvAgzI47N/UEZVG4GdItI3281NsLo4InIQ7tfN5Z6lFfbC\n6dReOSJyJrDFszazrRvp1P0QoBSYANyqqhOAd4Gr6WL/LgBEpDfOChiOGx48UEQuoAv2RRby+ewt\nrtsywWpOHRCc/BvqpXU6vGGOR4EHVHW2l7xFRAZ61wcBW730OuDQQHG/XzKlx4XjgbNF5A3gIeAk\nEXkA2NzF+sFnI7BBVf/p/f0YTsC62r8LgI8Db6jqds8C+ANwHF2zL3zy+ewfXPPWxvZU1e3Zbm6C\n1ZwXgNEiMlxEyoEpwJyI21Qo7gZWqupNgbQ5wBe984uA2YH0KZ5nz0hgNPC8NyywS0QmiogAFwbK\nFD2q+l1VHaaqo3Df9dOq+gXgT3ShfvDxhns2iIgfEvlkYAVd7N+Fx3rgWBHp7j3DycBKulZfCKmW\nTz6ffY5XB8D5wNMttiZqT5RiPIDTcV5za4Cro25PgZ7xeKAR5wX5EvCi99x9gQXe888DegfKTMV5\n/6wCTg2kHw284vXXTVE/Wzv65ESSXoJduR8+hPvh9jLwOM5LsEv2B3CN91zLcA4CZV2lL4DfAZuA\nvTjxvhjok69nB7oBj3jpzwIjWmqTLRw2DMMwYoENCRqGYRixwATLMAzDiAUmWIZhGEYsMMEyDMMw\nYoEJlmEYhhELTLAMwzCMWGCCZRiGYcQCEyzDMAwjFphgGUaMEJH/T0T+5YXAOdDbXHBc1O0yjI7A\nIl0YRswQkWtxezMdgAtUe0PETTKMDsEEyzBihoiU4WL9vQ8cp/af2Ogi2JCgYcSP/sBBQAXQPeK2\nGEaHYRaWYcQMEZmN27trJDBYVb8RcZMMo0MojboBhmHkjoh8AdinqrNEpAT4h4jUqOrCiJtmGAXH\nLCzDMAwjFtgclmEYhhELTLAMwzCMWGCCZRiGYcQCEyzDMAwjFphgGYZhGLHABMswDMOIBSZYhmEY\nRiwwwTIMwzBiwf8P80+Gych0pokAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_poly_predictions(poly_data, model)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": true }, "outputs": [], "source": [ "model = polynomial_regression(set_3, 'sqft_living', 'price', 15, l2_penalty_big)" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Learned polynomial for degree 15:\n", " 15 14 13 12\n", "1.917e-55 x + 1.912e-51 x + 1.911e-47 x + 1.915e-43 x \n", " 11 10 9 8\n", " + 1.927e-39 x + 1.954e-35 x + 2.004e-31 x + 2.093e-27 x\n", " 7 6 5 4 3\n", " + 2.247e-23 x + 2.501e-19 x + 2.876e-15 x + 3.209e-11 x + 2.776e-07 x\n", " 2\n", " + 0.001259 x + 2.269 x + 5.229e+05\n" ] } ], "source": [ "print_coefficients(model)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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gXii/BKjydZYDI0P3ZvrytcBFofxyYIW/9wBQlKL/nVkzZ6RBsr3qwotnKypU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\nc52CF30q62bu3MSLOuwWDOq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ITM2z8V0hIut83+4XkZI4j09E/iAi20RkbSgvY+Px30+V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\ngv8Hz3yqiJRcH2cAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_poly_predictions(poly_data, model)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": true }, "outputs": [], "source": [ "model = polynomial_regression(set_4, 'sqft_living', 'price', 15, l2_penalty_big)" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Learned polynomial for degree 15:\n", " 15 14 13 12\n", "2.679e-54 x + 2.275e-50 x + 1.94e-46 x + 1.663e-42 x \n", " 11 10 9 8\n", " + 1.436e-38 x + 1.253e-34 x + 1.108e-30 x + 9.957e-27 x\n", " 7 6 5 4 3\n", " + 9.065e-23 x + 8.25e-19 x + 7.205e-15 x + 5.501e-11 x + 3.128e-07 x\n", " 2\n", " + 0.001101 x + 1.91 x + 5.137e+05\n" ] } ], "source": [ "print_coefficients(model)" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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XKKcKc4Uz2oKL32fl901lm+F3113pJ4wNT6Xkz0o+d27rvqpcpz0K2xEU36oq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\nU3dZmcv+C3aoByfbDYrBvHn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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_poly_predictions(poly_data, model)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These curves should vary a lot less, now that you applied a high degree of regularization.\n", "\n", "***QUIZ QUESTION: For the models learned with the high level of regularization in each of these training sets, what are the smallest and largest values you learned for the coefficient of feature power_1?*** (For the purpose of answering this question, negative numbers are considered \"smaller\" than positive numbers. So -5 is smaller than -3, and -3 is smaller than 5 and so forth.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "smallest power_1 = 1.91 & largest power_1 = 2.587" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Selecting an L2 penalty via cross-validation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just like the polynomial degree, the L2 penalty is a \"magic\" parameter we need to select. We could use the validation set approach as we did in the last module, but that approach has a major disadvantage: it leaves fewer observations available for training. **Cross-validation** seeks to overcome this issue by using all of the training set in a smart way.\n", "\n", "We will implement a kind of cross-validation called **k-fold cross-validation**. The method gets its name because it involves dividing the training set into k segments of roughtly equal size. Similar to the validation set method, we measure the validation error with one of the segments designated as the validation set. The major difference is that we repeat the process k times as follows:\n", "\n", "Set aside segment 0 as the validation set, and fit a model on rest of data, and evalutate it on this validation set
\n", "Set aside segment 1 as the validation set, and fit a model on rest of data, and evalutate it on this validation set
\n", "...
\n", "Set aside segment k-1 as the validation set, and fit a model on rest of data, and evalutate it on this validation set\n", "\n", "After this process, we compute the average of the k validation errors, and use it as an estimate of the generalization error. Notice that all observations are used for both training and validation, as we iterate over segments of data. \n", "\n", "To estimate the generalization error well, it is crucial to shuffle the training data before dividing them into segments. GraphLab Create has a utility function for shuffling a given SFrame. We reserve 10% of the data as the test set and shuffle the remainder. (Make sure to use seed=1 to get consistent answer.)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "(train_valid, test) = sales.random_split(.9, seed=1)\n", "train_valid_shuffled = graphlab.toolkits.cross_validation.shuffle(train_valid, random_seed=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once the data is shuffled, we divide it into equal segments. Each segment should receive n/k elements, where n is the number of observations in the training set and k is the number of segments. Since the segment 0 starts at index 0 and contains n/k elements, it ends at index (n/k)-1. The segment 1 starts where the segment 0 left off, at index (n/k). With n/k elements, the segment 1 ends at index (n*2/k)-1. Continuing in this fashion, we deduce that the segment i starts at index (n*i/k) and ends at (n*(i+1)/k)-1." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With this pattern in mind, we write a short loop that prints the starting and ending indices of each segment, just to make sure you are getting the splits right." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 (0, 1938)\n", "1 (1939, 3878)\n", "2 (3879, 5817)\n", "3 (5818, 7757)\n", "4 (7758, 9697)\n", "5 (9698, 11636)\n", "6 (11637, 13576)\n", "7 (13577, 15515)\n", "8 (15516, 17455)\n", "9 (17456, 19395)\n" ] } ], "source": [ "n = len(train_valid_shuffled)\n", "k = 10 # 10-fold cross-validation\n", "\n", "def get_segments(data, k):\n", " n = len(data)\n", " for i in xrange(k):\n", " start = (n*i)/k\n", " end = (n*(i+1))/k-1\n", " print i, (start, end)\n", " # return i, (start, end)\n", " \n", "get_segments(train_valid_shuffled, 10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us familiarize ourselves with array slicing with SFrame. To extract a continuous slice from an SFrame, use colon in square brackets. For instance, the following cell extracts rows 0 to 9 of train_valid_shuffled. Notice that the first index (0) is included in the slice but the last index (10) is omitted." ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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longsqft_living15sqft_lot15
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-122.270224562590.010445.0
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\n", "" ], "text/plain": [ "Columns:\n", "\tid\tstr\n", "\tdate\tdatetime\n", "\tprice\tfloat\n", "\tbedrooms\tfloat\n", "\tbathrooms\tfloat\n", "\tsqft_living\tfloat\n", "\tsqft_lot\tint\n", "\tfloors\tstr\n", "\twaterfront\tint\n", "\tview\tint\n", "\tcondition\tint\n", "\tgrade\tint\n", "\tsqft_above\tint\n", "\tsqft_basement\tint\n", "\tyr_built\tint\n", "\tyr_renovated\tint\n", "\tzipcode\tstr\n", "\tlat\tfloat\n", "\tlong\tfloat\n", "\tsqft_living15\tfloat\n", "\tsqft_lot15\tfloat\n", "\n", "Rows: 10\n", "\n", "Data:\n", "+------------+---------------------------+----------+----------+-----------+\n", "| id | date | price | bedrooms | bathrooms |\n", "+------------+---------------------------+----------+----------+-----------+\n", "| 2780400035 | 2014-05-05 00:00:00+00:00 | 665000.0 | 4.0 | 2.5 |\n", "| 1703050500 | 2015-03-21 00:00:00+00:00 | 645000.0 | 3.0 | 2.5 |\n", "| 5700002325 | 2014-06-05 00:00:00+00:00 | 640000.0 | 3.0 | 1.75 |\n", "| 0475000510 | 2014-11-18 00:00:00+00:00 | 594000.0 | 3.0 | 1.0 |\n", "| 0844001052 | 2015-01-28 00:00:00+00:00 | 365000.0 | 4.0 | 2.5 |\n", "| 2658000373 | 2015-01-22 00:00:00+00:00 | 305000.0 | 4.0 | 2.0 |\n", "| 3750603471 | 2015-03-27 00:00:00+00:00 | 239950.0 | 3.0 | 2.5 |\n", "| 2114700540 | 2014-10-21 00:00:00+00:00 | 366000.0 | 3.0 | 2.5 |\n", "| 2596400050 | 2014-07-30 00:00:00+00:00 | 375000.0 | 3.0 | 1.0 |\n", "| 4140900050 | 2015-01-26 00:00:00+00:00 | 440000.0 | 4.0 | 1.75 |\n", "+------------+---------------------------+----------+----------+-----------+\n", "+-------------+----------+--------+------------+------+-----------+-------+------------+\n", "| sqft_living | sqft_lot | floors | waterfront | view | condition | grade | sqft_above |\n", "+-------------+----------+--------+------------+------+-----------+-------+------------+\n", "| 2800.0 | 5900 | 1 | 0 | 0 | 3 | 8 | 1660 |\n", "| 2490.0 | 5978 | 2 | 0 | 0 | 3 | 9 | 2490 |\n", "| 2340.0 | 4206 | 1 | 0 | 0 | 5 | 7 | 1170 |\n", "| 1320.0 | 5000 | 1 | 0 | 0 | 4 | 7 | 1090 |\n", "| 1904.0 | 8200 | 2 | 0 | 0 | 5 | 7 | 1904 |\n", "| 1610.0 | 6250 | 1 | 0 | 0 | 4 | 7 | 1610 |\n", "| 1560.0 | 4800 | 2 | 0 | 0 | 4 | 7 | 1560 |\n", "| 1320.0 | 4320 | 1 | 0 | 0 | 3 | 6 | 660 |\n", "| 1960.0 | 7955 | 1 | 0 | 0 | 4 | 7 | 1260 |\n", "| 2180.0 | 10200 | 1 | 0 | 2 | 3 | 8 | 2000 |\n", "+-------------+----------+--------+------------+------+-----------+-------+------------+\n", "+---------------+----------+--------------+---------+-------------+\n", "| sqft_basement | yr_built | yr_renovated | zipcode | lat |\n", "+---------------+----------+--------------+---------+-------------+\n", "| 1140 | 1963 | 0 | 98115 | 47.68093246 |\n", "| 0 | 2003 | 0 | 98074 | 47.62984888 |\n", "| 1170 | 1917 | 0 | 98144 | 47.57587004 |\n", "| 230 | 1920 | 0 | 98107 | 47.66737217 |\n", "| 0 | 1999 | 0 | 98010 | 47.31068733 |\n", "| 0 | 1952 | 0 | 98118 | 47.52930128 |\n", "| 0 | 1974 | 0 | 98001 | 47.26533057 |\n", "| 660 | 1918 | 0 | 98106 | 47.53271982 |\n", "| 700 | 1963 | 0 | 98177 | 47.76407345 |\n", "| 180 | 1966 | 0 | 98028 | 47.76382378 |\n", "+---------------+----------+--------------+---------+-------------+\n", "+---------------+---------------+-----+\n", "| long | sqft_living15 | ... |\n", "+---------------+---------------+-----+\n", "| -122.28583258 | 2580.0 | ... |\n", "| -122.02177564 | 2710.0 | ... |\n", "| -122.28796 | 1360.0 | ... |\n", "| -122.36472902 | 1700.0 | ... |\n", "| -122.0012452 | 1560.0 | ... |\n", "| -122.27097145 | 1310.0 | ... |\n", "| -122.28506088 | 1510.0 | ... |\n", "| -122.34716948 | 1190.0 | ... |\n", "| -122.36361517 | 1850.0 | ... |\n", "| -122.27022456 | 2590.0 | ... |\n", "+---------------+---------------+-----+\n", "[10 rows x 21 columns]" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "train_valid_shuffled[0:10] # rows 0 to 9" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let us extract individual segments with array slicing. Consider the scenario where we group the houses in the train_valid_shuffled dataframe into k=10 segments of roughly equal size, with starting and ending indices computed as above.\n", "Extract the fourth segment (segment 3) and assign it to a variable called validation4." ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": true }, "outputs": [], "source": [ "validation4 = train_valid_shuffled[5818:7757]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To verify that we have the right elements extracted, run the following cell, which computes the average price of the fourth segment. When rounded to nearest whole number, the average should be $536,234." ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "536353\n" ] } ], "source": [ "#### Why isn't this value lining up with the above? \n", "\n", "print int(round(validation4['price'].mean(), 0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After designating one of the k segments as the validation set, we train a model using the rest of the data. To choose the remainder, we slice (0:start) and (end+1:n) of the data and paste them together. SFrame has append() method that pastes together two disjoint sets of rows originating from a common dataset. For instance, the following cell pastes together the first and last two rows of the train_valid_shuffled dataframe." ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+------------+---------------------------+-----------+----------+-----------+\n", "| id | date | price | bedrooms | bathrooms |\n", "+------------+---------------------------+-----------+----------+-----------+\n", "| 2780400035 | 2014-05-05 00:00:00+00:00 | 665000.0 | 4.0 | 2.5 |\n", "| 1703050500 | 2015-03-21 00:00:00+00:00 | 645000.0 | 3.0 | 2.5 |\n", "| 4139480190 | 2014-09-16 00:00:00+00:00 | 1153000.0 | 3.0 | 3.25 |\n", "| 7237300290 | 2015-03-26 00:00:00+00:00 | 338000.0 | 5.0 | 2.5 |\n", "+------------+---------------------------+-----------+----------+-----------+\n", "+-------------+----------+--------+------------+------+-----------+-------+------------+\n", "| sqft_living | sqft_lot | floors | waterfront | view | condition | grade | sqft_above |\n", "+-------------+----------+--------+------------+------+-----------+-------+------------+\n", "| 2800.0 | 5900 | 1 | 0 | 0 | 3 | 8 | 1660 |\n", "| 2490.0 | 5978 | 2 | 0 | 0 | 3 | 9 | 2490 |\n", "| 3780.0 | 10623 | 1 | 0 | 1 | 3 | 11 | 2650 |\n", "| 2400.0 | 4496 | 2 | 0 | 0 | 3 | 7 | 2400 |\n", "+-------------+----------+--------+------------+------+-----------+-------+------------+\n", "+---------------+----------+--------------+---------+-------------+\n", "| sqft_basement | yr_built | yr_renovated | zipcode | lat |\n", "+---------------+----------+--------------+---------+-------------+\n", "| 1140 | 1963 | 0 | 98115 | 47.68093246 |\n", "| 0 | 2003 | 0 | 98074 | 47.62984888 |\n", "| 1130 | 1999 | 0 | 98006 | 47.55061236 |\n", "| 0 | 2004 | 0 | 98042 | 47.36923712 |\n", "+---------------+----------+--------------+---------+-------------+\n", "+---------------+---------------+-----+\n", "| long | sqft_living15 | ... |\n", "+---------------+---------------+-----+\n", "| -122.28583258 | 2580.0 | ... |\n", "| -122.02177564 | 2710.0 | ... |\n", "| -122.10144844 | 3850.0 | ... |\n", "| -122.12606473 | 1880.0 | ... |\n", "+---------------+---------------+-----+\n", "[4 rows x 21 columns]\n", "\n" ] } ], "source": [ "n = len(train_valid_shuffled)\n", "first_two = train_valid_shuffled[0:2]\n", "last_two = train_valid_shuffled[n-2:n]\n", "print first_two.append(last_two)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Extract the remainder of the data after *excluding* fourth segment (segment 3) and assign the subset to train4." ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": true }, "outputs": [], "source": [ "train4=train_valid_shuffled[0:5818].append(train_valid_shuffled[7758:19396])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To verify that we have the right elements extracted, run the following cell, which computes the average price of the data with fourth segment excluded. When rounded to nearest whole number, the average should be$539,450." ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "539450\n" ] } ], "source": [ "print int(round(train4['price'].mean(), 0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we are ready to implement k-fold cross-validation. Write a function that computes k validation errors by designating each of the k segments as the validation set. It accepts as parameters (i) k, (ii) l2_penalty, (iii) dataframe, (iv) name of output column (e.g. price) and (v) list of feature names. The function returns the average validation error using k segments as validation sets.\n", "\n", "* For each i in [0, 1, ..., k-1]:\n", " * Compute starting and ending indices of segment i and call 'start' and 'end'\n", " * Form validation set by taking a slice (start:end+1) from the data.\n", " * Form training set by appending slice (end+1:n) to the end of slice (0:start).\n", " * Train a linear model using training set just formed, with a given l2_penalty\n", " * Compute validation error using validation set just formed" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def get_RSS(prediction, output):\n", " residual = output - prediction\n", " # square the residuals and add them up\n", " RS = residual*residual\n", " RSS = RS.sum()\n", " return(RSS)\n", "\n", "def k_fold_cross_validation(k, l2_penalty, data, features_list):\n", " n = len(data)\n", " RSS = 0\n", " for i in xrange(k):\n", " start = (n*i)/k\n", " end = (n*(i+1))/k-1\n", " validation=data[start:end+1]\n", " train=data[0:start].append(data[end+1:n])\n", " model = graphlab.linear_regression.create(train, target='price', features = features_list, l2_penalty=l2_penalty,validation_set=None,verbose = False)\n", " predictions=model.predict(validation)\n", " A =get_RSS(predictions,validation['price'])\n", " RSS = RSS + A\n", " \n", " Val_err = RSS/k\n", " return Val_err" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once we have a function to compute the average validation error for a model, we can write a loop to find the model that minimizes the average validation error. Write a loop that does the following:\n", "* We will again be aiming to fit a 15th-order polynomial model using the sqft_living input\n", "* For l2_penalty in [10^1, 10^1.5, 10^2, 10^2.5, ..., 10^7] (to get this in Python, you can use this Numpy function: np.logspace(1, 7, num=13).)\n", " * Run 10-fold cross-validation with l2_penalty\n", "* Report which L2 penalty produced the lowest average validation error.\n", "\n", "Note: since the degree of the polynomial is now fixed to 15, to make things faster, you should generate polynomial features in advance and re-use them throughout the loop. Make sure to use train_valid_shuffled when generating polynomial features!" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " val_errs penalties\n", "0 3.258313e+14 1.000000e+01\n", "1 1.911928e+14 3.162278e+01\n", "2 1.063884e+14 1.000000e+02\n", "3 8.092771e+13 3.162278e+02\n", "4 8.128663e+13 1.000000e+03\n", "5 8.261466e+13 3.162278e+03\n", "6 9.071015e+13 1.000000e+04\n", "7 1.134137e+14 3.162278e+04\n", "8 1.522393e+14 1.000000e+05\n", "9 1.688055e+14 3.162278e+05\n", "10 1.724966e+14 1.000000e+06\n", "11 1.751939e+14 3.162278e+06\n", "12 1.765843e+14 1.000000e+07\n" ] } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "poly_data = polynomial_sframe(train_valid_shuffled['sqft_living'], 15)\n", "my_features = poly_data.column_names()\n", "poly_data['price'] = train_valid_shuffled['price']\n", "stuff = []\n", "columns = ['val_errs','penalties']\n", "#pd.DataFrame(columns = [['val_err','penalty']])\n", "for l2_penalty in np.logspace(1, 7, num=13):\n", " val_err = k_fold_cross_validation(15, l2_penalty, poly_data, my_features)\n", " # results.append([l2_penalty, Val_err])\n", " # val_errs.append(val_err)\n", " # penalties.append(l2_penalty)\n", " row = [val_err, l2_penalty]\n", " stuff.append(row)\n", "results = pd.DataFrame(stuff, columns=columns)\n", "print results" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [], "source": [ "max_err = results['val_errs'].max()\n", "min_err = results['val_errs'].min()\n", "results.loc[results['val_errs'] == min_err]" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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val_errspenalties
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38.092771e+13316.227766
\n", " \n", " \n", " \n", " \n", " \n", " \n", "\n", "" ], "text/plain": [ " val_errs penalties\n", "3 8.092771e+13 316.227766" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***QUIZ QUESTIONS: What is the best value for the L2 penalty according to 10-fold validation?***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You may find it useful to plot the k-fold cross-validation errors you have obtained to better understand the behavior of the method. " ] }, { "cell_type": "code", "execution_count": 106, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the l2_penalty values in the x axis and the cross-validation error in the y axis.\n", "# Using plt.xscale('log') will make your plot more intuitive.\n", "plt.plot(results['penalties'],results['val_errs'])\n", "plt.xlabel('penalties')\n", "plt.ylabel('val_errs')\n", "#plt.set(xlim=[0,2],ylim=[1,2])\n", "#plt.set_xlim(0,2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once you found the best value for the L2 penalty using cross-validation, it is important to retrain a final model on all of the training data using this value of l2_penalty. This way, your final model will be trained on the entire dataset." ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.21192264451e+14\n" ] } ], "source": [ "poly1_data = polynomial_sframe(train_valid_shuffled['sqft_living'], 15) # use equivalent of polynomial_sframe\n", "my_features = poly1_data.column_names() \n", "poly1_data['price'] = train_valid_shuffled['price']\n", "model1 = graphlab.linear_regression.create(poly1_data, target = 'price', features = my_features, verbose = False, validation_set = None, l2_penalty=1000)\n", "Val_err = k_fold_cross_validation(10, 1000, poly1_data, my_features)\n", "print Val_err" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***QUIZ QUESTION: Using the best L2 penalty found above, train a model using all training data. What is the RSS on the TEST data of the model you learn with this L2 penalty? ***" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.11" } }, "nbformat": 4, "nbformat_minor": 1 }