{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "The real data for these problems wasn't posted before class (and these problems were not the class activity as the description suggests), so I generated my own simple data and used it for the problem." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import scipy.optimize" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Generate Sample Data" ] }, { "cell_type": "code", "collapsed": false, "input": [ "class RealModel(object):\n", " def __init__(self):\n", " self.params = (2, 3, -3, 1)\n", "\n", " def predict(self, x):\n", " b0, b1, b2, b3 = self.params\n", " return b0 + (b1 * x) + (b2 * x**2) + (b3 * x**3)\n", "\n", "REAL_MODEL = RealModel()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [ "np.random.seed(7)\n", "\n", "DATA_X = np.linspace(0, 2, num=10)\n", "REAL_Y = REAL_MODEL.predict(DATA_X)\n", "DATA_SIGMA = 0.15\n", "DATA_Y = REAL_Y + np.random.normal(scale=DATA_SIGMA, size=len(REAL_Y))\n", "\n", "xs = np.linspace(0, 2, num=500)\n", "plt.plot(xs, REAL_MODEL.predict(xs), label='Real')\n", "plt.scatter(DATA_X, DATA_Y, label='Noisy Measurement')\n", "plt.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 14, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAs4AAAH0CAYAAAAt5at6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Define Models" ] }, { "cell_type": "code", "collapsed": false, "input": [ "class LinearModel(object):\n", " FEATURE_FUNCS = [\n", " np.vectorize(lambda v: 1),\n", " lambda v: v,\n", " lambda v: v**2,\n", " lambda v: v**3,\n", " lambda v: v**4,\n", " lambda v: v**5,\n", " lambda v: v**6,\n", " lambda v: v**7,\n", " lambda v: v**8,\n", " lambda v: v**9,\n", " lambda v: v**10,\n", " lambda v: v**11,\n", " lambda v: v**12,\n", " lambda v: v**13,\n", " lambda v: v**14,\n", " lambda v: v**15,\n", " lambda v: v**16,\n", " lambda v: v**17,\n", " lambda v: v**18,\n", " lambda v: v**19,\n", " lambda v: v**20]\n", "\n", " def __init__(self, criterion=None):\n", " assert criterion in ('aic', 'bic', None)\n", " self.criterion = criterion\n", " self.feature_funcs = []\n", " self.params = None\n", "\n", " def fit(self, x, y, sigma, param_0_guess=1):\n", " # Try adding each of the parameters to the current model. Keep only those\n", " # that pass the AIC/BIC criterion.\n", " param_guess = []\n", " last_chisq = float('inf')\n", " for i, feature_func in enumerate(self.FEATURE_FUNCS):\n", " # Try adding another parameter\n", " self.feature_funcs.append(feature_func)\n", " if len(param_guess) == 0:\n", " param_guess = [param_0_guess]\n", " else:\n", " param_guess = list(param_guess) + [0]\n", " params_fit, chisq = self._fit(x, y, sigma, param_guess)\n", " delta_chisq = last_chisq - chisq\n", " #print 'params_fit', params_fit\n", " delta_loglikelihood = delta_chisq / 2.0\n", " #print 'chisq:', chisq, '--', 'delta_loglikelihood', delta_loglikelihood\n", "\n", " # Decide if the parameter is worth keeping.\n", " \n", " use_param = True\n", " if self.criterion == 'aic' and delta_loglikelihood <= 1:\n", " use_param = False\n", " if self.criterion == 'bic' and delta_loglikelihood <= (0.5 * np.log(len(x))):\n", " use_param = False\n", " if use_param:\n", " #print(\"Using parameter {0}\".format(i))\n", " best_params = params_fit.copy()\n", " best_chisq = chisq\n", " param_guess = params_fit\n", " last_chisq = chisq\n", " else:\n", " #print(\"Not using parameter {0}\".format(i))\n", " self.feature_funcs.pop()\n", " param_guess = params_fit[:-1]\n", "\n", " self.params = best_params\n", " self.chisq = best_chisq\n", " return self\n", "\n", " def predict(self, x):\n", " return self._predict(self.params, x)\n", "\n", " def _fit(self, x, y, sigma, params_guess):\n", " func = lambda params: self._chisquare(params, x, y, sigma)\n", " fit = scipy.optimize.fmin(func, params_guess, maxfun=10000, maxiter=10000, disp=False)\n", " chisq = func(fit)\n", " return fit, chisq\n", "\n", " def _chisquare(self, params, x, y, sigma):\n", " return np.sum(((self._predict(params, x) - y) / sigma)**2)\n", "\n", " def _predict(self, params, x):\n", " featurized_x = (np.array([f(x) for f in self.feature_funcs]).T)\n", " params_matrix = np.tile(params, (len(x), 1))\n", " prediction = (params_matrix * featurized_x).sum(axis=1)\n", " return prediction" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Fit the Models" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_model(model, name='Model', *args, **kwargs):\n", " xs = np.linspace(0, 2, num=500)\n", " chisq = model.chisq\n", " plt.scatter(DATA_X, DATA_Y, label='Data')\n", " plt.plot(xs, REAL_MODEL.predict(xs), label='Real')\n", " plt.plot(xs, model.predict(xs), color='red', label='Fit', *args, **kwargs)\n", " plt.legend()\n", " plt.title(\"{0} ($\\\\chi^2 {1}$ -- {2} params)\".format(name, chisq, len(model.params)))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fit a model with the AIC criterion." ] }, { "cell_type": "code", "collapsed": false, "input": [ "aic_model = LinearModel('aic').fit(DATA_X, DATA_Y, DATA_SIGMA)\n", "plot_model(aic_model)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAs4AAAIDCAYAAAAUmphGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYx4RbD73QgAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fit a model with the BIC criterion." ] }, { "cell_type": "code", "collapsed": false, "input": [ "bic_model = LinearModel('bic').fit(DATA_X, DATA_Y, DATA_SIGMA)\n", "plot_model(bic_model)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAs4AAAIDCAYAAAAUmphGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYx4RbD73QgAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just for fun, fit a model with all models (i.e., no criteron for rejecting parameters)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "overfit_model = LinearModel(None).fit(DATA_X, DATA_Y, DATA_SIGMA)\n", "plot_model(overfit_model)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAs4AAAIDCAYAAAAUmphGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 19 } ], "metadata": {} } ] }