{ "metadata": { "name": "", "signature": "sha256:79d5e2e537f340596115d1025a01340ff871db74f06f978e832d84c95d076624" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Example of the SuperSmoother\n", "\n", "This notebook gives an example for how to use the Python implementation of Friedman's Supersmoother at http://github.com/jakevdp/supersmoother/\n", "\n", "Supersmoother is a non-parametric locally-linear smooth in which the size of the local neighborhood is tuned to the characteristics of the data. It was introduced in 1984 by JH Friedman in a paper titled \"A Variable Span Smoother\" ([pdf](http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-3477.pdf))" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Use seaborn for plotting defaults.\n", "# This can be safely commented-out if seaborn is not installed\n", "import seaborn; seaborn.set()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "# Install supersmoother package from http://github.com/jakevdp/supersmoother\n", "from supersmoother import SuperSmoother, LinearSmoother" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generating the Data" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def make_test_set(N=200, rseed_x=None, rseed_y=None):\n", " \"\"\"Code to generate the test set from Friedman 1984\"\"\"\n", " rng_x = np.random.RandomState(rseed_x)\n", " rng_y = np.random.RandomState(rseed_y)\n", " x = rng_x.rand(N)\n", " dy = x\n", " y = np.sin(2 * np.pi * (1 - x) ** 2) + dy * rng_y.randn(N)\n", " return x, y, dy" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "# Generate and visualize the data\n", "t, y, dy = make_test_set(rseed_x=0, rseed_y=1)\n", "plt.errorbar(t, y, dy, fmt='o', alpha=0.3);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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3225YNwBBmtme7OyItfbnMlrlY7xx2SvM4HQMJv2/m22bf2/d1qfWYvjmB71ErE99/BaS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\n62kAfxtACkAEwF8wDOPtoHeMiIholfh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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is data generated the same way as in Friedman's paper. The nice part of this is that the data have a variety of errors, and the second derivative of the true model changes appreciably over the range:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fitting the SuperSmoother\n", "Here is how to fit the supersmoother to the data:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# fit the supersmoother model\n", "model = SuperSmoother()\n", "model.fit(t, y, dy)\n", "\n", "# find the smoothed fit to the data\n", "tfit = np.linspace(0, 1, 1000)\n", "yfit = model.predict(tfit)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we'll visualize this smoothed curve:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Show the smoothed model of the data\n", "plt.errorbar(t, y, dy, fmt='o', alpha=0.3)\n", "plt.plot(tfit, yfit, '-k');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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YsoCAhYcHWmxOas12Giw2nC43+2qaabE7yTak4bTYqTXbcLs9eIDcLD0Opzsp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\nqVRcec2dXH3DXezZs5u5c8/AZNrm/3u40nA+n6x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"text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exploring the component smooths\n", "The supersmoother is based on initial smooths where the size of each local neighborhood is some fraction $f$ of the total dataset.\n", "In analogy with audio frequencies, Friedman calls these the *tweeter* $(f = 0.05)$, the *midrange* $(f = 0.2)$, and the *woofer* $(f = 0.5)$. We can visualize these individual fits here:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.errorbar(t, y, dy, fmt='o', alpha=0.3)\n", "\n", "for smooth in model.primary_smooths:\n", " plt.plot(tfit, smooth.predict(tfit),\n", " label='span = {0:.2f}'.format(smooth.span))\n", "plt.legend();" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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GhUJHWhBP1zxekRXcxmJ6Yp3EUlFg9gI5o+FN5Srw+if7ppMpjeMtg5TNs3BL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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The final supersmoother value uses cross-validation to select the best smoothing value at each time for the dataset.\n", "We can show these smoothed span values as follows:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "t = np.linspace(0, 1, 1000)\n", "plt.plot(t, model.smoothed_spans.predict(t))\n", "plt.xlabel('t')\n", "plt.ylabel('smoothed span value');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "These spans are fit to the particular data realization.\n", "Friedman chose to use 1000 realizations of the smoother to get a better estimate of how the span varies.\n", "We'll do the same here:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "N = 1000\n", "span = span2 = 0\n", "\n", "for rseed in np.arange(N):\n", " t, y, dy = make_test_set(rseed_x=0, rseed_y=rseed)\n", " model = SuperSmoother().fit(t, y, dy)\n", " span += model.smoothed_span_vals\n", " span2 += model.smoothed_span_vals ** 2\n", " \n", "mean = span / N\n", "std = np.sqrt(span2 / N - mean ** 2)\n", "plt.plot(model.t, mean)\n", "plt.fill_between(model.t, mean - std, mean + std, alpha=0.3)\n", "plt.xlabel('t')\n", "plt.ylabel('resulting span');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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+hsmJSAfa2k6xnq4QCjZ2vLjrefyn7y1Qqbr85RdPa7y6dKz9BHvVsqwfoxbs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\nmKFVVB2X6eU0N+ZSzK9l8QC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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thanks for reading!" ] } ], "metadata": {} } ] }