{ "metadata": { "name": "", "signature": "sha256:74238c9afc0b8970af816fc53e0703f86da1266c50d08834bed9615215012794" }, "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 the package\n", "# source at http://github.com/jakevdp/supersmoother\n", "# or use ``pip install 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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MYYVi8EMtFbM4sGcdHnvsr9i0aQMAv5/3pJNOwtlnX4DaaUuQk6sKq4mGE7DR\nFBAJJZ7CCtHOoc05PEfb7U4sopXrh2y2uYaUhATCm7Sj8Q8WqOXoNtrg9fpXD/G0XgT811GlUkGl\nUuPyiZNgsrpwuMuErl5/pHxZYQ7mTMzDtxu3o9egR093Bw41N0Hf2YL9+3/E999/OywnXCZXQFNY\nDrFEim+OmoGiijrMnTMPXm/kay0Rs1Dn+mMaTNbEgvfKCnOGuGOS7d5IlFT5uMPd606ee5sjlVpz\nqJUoVkggE4IikrYYywuGbz+dvVbojXbk58qGVMviHuqernY07tyIP338Kg7sbwQAnHLKaTjh9BWo\nn3IUzjl5Frq7h9c7TvQBT3bwVjRzyHdMsYiJecEwElWlqkC0cejLKtaId5XSL9BFMfRQjgTfeKpK\nVSgu1GByw4wh23ILI6vViv+s/gZHWg/iSOtBNO7TwWxoRUdbC7weN1oP7gEAvABArsxD3cwT4Fqw\nCIXlU5CbVwCZhIVYzECj8gtiqYSFx+Mb0poz3msfzr3Bt6gLzakHkNKa66lqMxkpjzweuIU55++P\nZ0EcZHK3jbRtKCSQiTGBvt8OvXHAX+r1Yd/hPthdHtSU5mHTls149fm/Y923nwPwa1HHn3w2Ll15\nHc46aVHMEbd8mqBEwoaN8E518Fa4Yx480o+egZcyyzIYX6JKSRR3iWbwJT8kbSzGiHeuY1aJRjli\nD+Vo4cYjirKLlFKpRNWEyaiaMBkAsKfFgLqKfHT12uBxu6GV9KJxzw5s27YFWzasxQ/fr8YP368G\nAGiLKzB1+lwsXLQImnENKCqtCMxNwLWSwLWPxb0RmlMvkYye+uCHu0zQG+0xLy5DK+pxrqZYrXOc\nyf29R875PKYBgAQyITDCCbNYhUTofvQDwTNyqf+Wtzk8+OjTL/H5u89h60a/v7B64lRMmT4fKy66\nHGUVVZBI4os85osUlUtE6O7z+wv5alnHErw1EtHO4aJp49DaZQbDMMhVSNKyEAj2D6a7fy6nqQcL\nnlj9laFIgszyIrEYE+umYsrU6bj26qvx3Ps/oL1lD0rEXViz9mvodm/FN2tW45s1fgGdry3GzFnz\nMW3GPEi1k1BcVpPW9J6a0jxs2tMZ+Mzna04WkXzchxK4D8KlScWT3hhJi0+X+Z8EMiEoouneFM9+\nvF4f1LkyGM0ONOs2Y/XTr+LHvVsAAHPmL8aKS6+DtmIqGIZBWXHimmKw5uWDL6yfi9P04g3e4iPa\nOVTKxZh5rwF8AAAgAElEQVQxsRC9ZgdkEpEgcj2b2oxo6bbAYnEkPUAnWFNPFnk5Ut72iQBQpFWh\nSHs0rjxtCs6+8CocbOuDx9KOrkO78Mnna/HD9o1Yu+Z9rF3jrx2Ro1Jj7eLFWLBgMRYuXITp02dA\nLE7dKzpS5H+y4Xzc7oEG2cla/PHd61WlqrQv9pIFCWRCUOwZEFTcSy5aIcHn6wnWALR5Mjidbnzx\nvyew5as3AQDT5xyDlVfdgEsvOBW7mw04MBDUlYyXRbDmxb2Eggmul5wMv1UokTpgBZPM0pmxENxh\nibMYBKcLAdEF6MRCqkyy0bZPZEUi1NQ14OxlS7DopAvh8/nQeuggdmzbiHXrvodu9xZ8/PGH+Pjj\nDwH4u2jNmzc/ECk+a9aclJUHDY1UTgWlWmXAt5vMxV/ovR6vpq+QDb//uYV5Kp5RPkggE4JDJhWF\n7d4UC5wG4PV48P3ad/HeWy+go7UJBaXVuPa2B3DisQsDL4ZoBViySZbfKpRIHbAyRXD3K76IW7PN\nBVlIBHwiATqRiFRnOlbibZ/IMAwqqyagsmoCpi84AwAwvYLF+vXfY/36dVi//jt89dWX+OqrLwEA\nUqkUs2bNwcKFi7FgwSLMn380cnMTX2TojXaYClKfk5ys5zqUZN3rZYU5Q+qycJH84dIYU5ErLown\nlRjVxNM1KBk0tRmxY9devPXcvWjZ7y9lOX3B6Tjh3OuwZMGUIVpwMgVYaBBYuJV3qVaJ1m7zsH9L\nt98qFeQqJGFNxOF8dZ0GK8YXj47AonipqKjE8uUrsHz5CgBAT08PNmzwC+d1677Hpk0bsGHDOgD+\n4MPp02egrmE2jpo1H9NnzgMQe+43X4vSVOckC5VgVxO3IElW5kc0kEAmRiX7Dhnw4gv/xLP/eBhu\nlwNzFy3DWRdeDUleOcQsi8njNWkbS+jKmzOJZ1u95GjgSkaarS7ojfaYzMTKCAuXbBcOoaVRo6Ww\nsBBnnHEWzjjDXx7UZOrHpk0bsG7d91i37jts374VO3Zsw39ffRYAUFZZi7nzFuC0k4/HwoWLUVZW\nnpTxp2sRnWmG1KpPUiR/LJBAJjJCMk2GoRw+fAjX/Gwldu3YhJzcfFz483tw4sl+kyCXDpEuMy7X\nvclqdw+JaOWI5LfKNjjTXn6ODPD5NS++YizhIm4XTRs3JC+VW7h8vvkw2nss6LM4IBGxKQnOSiV8\npVE5k3CsL32VKg8nnHAyTjjhZACAzWbD/z76Ej9s24gftm/Czh2b8e7bL+Pdt18GAIwfX42FCxdh\n/MQZmDFrPsorq8EwQ6tb8y0QYslJDq2JPdq6TCUr8yMaSCATgiG4/my8Avu991bjlltuhNHYhyXH\nnYql596E3Lz0acPhCBfRGs5vlY2E62UbWqEsUlWpmtI86E3OQPrXEGHmA1xuv2lbCDWXoyXcvHBB\nfYmgUCgwc/YCzJy9AADQ1GqA03gIHc27sGHD94HSr8ArAABtQRFmzJqP8885FdOmzYHXm4MCtXxI\nil8sOcmRKmVlQsNMBXxpjKl6RkkgE6MCq9WKu+/+DV588XkolUrccc9DWHry+di6rzuwTbz5iamG\nz28lNJJdLzhcZLJSLsbEinz0Ga1QysVhG1IIxYRdolGioVormDQbsViC2qkzccEZJ+AXv7gRXq8X\njY17sfrDz7Fj2wb8sG0jvvz8A3z5+QcAAGWOCnUNs3HaycdDopmEqtopMUUqR6qUNVoKjQDpe0ZJ\nIBNZz+7du7Bq1Urs26fDtGlH4Zln/o2JEycNWdVOKFdjarUWH61vyeBI+cm03yoYPl9htLWxg017\nVrs7UHe6rDBn2MtZJhVhfkMJAOFEgfORDJcKf5nS1JWpDIZlWTQ0TAWU43Du8svg8/nQ1toCp/EA\nPv10Ddas/QrbN/n/AwC5XIF5847GxCmzcNSs+agpOQEKhWKEo4x+0vWMCvdJILKCWIM9OLN0MvD5\nfHjuuWfw+9/fBYfDgauvvhZ33/1HyGR+LTi0ElGyGO2BLaFEG2XKmfZMVic8Xi9YVoxijQLjCvxm\n+XjMmHzCTMiWBD74SqMmW3vkUslGypNlGAYVldVYev5SnHnmcny0vgUGfSeUzkP48NMvsGPbRnzz\nzVp8881aAMDtEglmzpyNiVNmoa5+GpQnH4OqqkE/dDj/ajZdHyFBAplIOakI4NLr9fjlL6/DJ598\nhIKCAjz33Is4+eRTh2yTzkpEsZKOQgyZoKY0Dx6vL1COkyNeM2aoMON6LGfakhAroaVRk1mmMjSv\nO9Y8WW1BCU5bMB/1s07wjzXPhzff+ww/bNuIH/duxdatmwNdz/5wJ1BUVIw5c+aisnI8Jk2qh1I7\nHk6XFlKZYlRkEIRGxKczSE1YbymCiIJvv/0a1133c3R0HMExxxyHJ598BiUlpZkeVtTwmYCP6C1w\nuZNTkSrZxBJlqpSLkT/QUjC0/WK8cMKMZRmolJJA5Hq8jPTbVPTXTWZp1FBGqsEcfD4N1doRz0er\nLcCSpcuwZOkyNFRrYTab8PaHX6Lpx71oO7gHmzdvDFQT45BI5aifvgC9Jx0L/by5UGhrkJOEoiXp\nhi8iPhltIqOFBDKRNbhcLjz00AN47LFHIBKJcNddf8D1198Elk3Oiz9eYhUOkaKRhUis9cX5NP5E\nzJiBSljMyNsmKkxDK6fF249bKITz/8/Ljb4EZ26uCnPnL8Hc+UsC93pnZyeOHGlDY+Ne7Nr1A976\n32rs2rIWu7asBQBIZTIsXHwili5ZiJkzZ0GaPx65ucJP5Yvknoni9kuY7LvDiDFJS0szrrnmZ9iy\nZRPGj6/G008/izlz5mV6WDHBmWud7uG1rTNJiUY5oik5ltKiBWo5uo2DrWCTZcYcKf842uCzSAih\n40+sROqktK+1b9j2LpcXPx7uRbkm/mCtkpISlJSUYObM2QAuwaIzroWhpwP5TBe2bduC115/DV99\n8SG++mJQk64cPwH1U6ZjYv1UnHTsAsyePScppT9HEySQCcEQ7Lsxmp0oUPtX8atXv4Vbb70JJlM/\nzj9/Of7yl0eRl5cev06wxlVSbECBMvbShKEks2Vcuoi1tKhKKYGIZZLSTjJa0lniMJRMpviEdlJK\nRp5srFYfhmFQUDQOpy1YgDPPPBvnX3ojOo60wtJzANu3b8P36zdCt3cnPv/kHXz+yTv4x+P+CPAp\nU6aiZHwDJk6egfri01BTM2FY4ZJ0whdEyC1uUtmekoMEMpFSQqv4RNoueJWvzpXCYbfi+huuxRuv\nvwylMgePP/4UVqz4Sdoe2FCNq9/sREeXKWHzZawt47Ixqru8MFdwzS2iIVsrp3HlRUMj0MP5/ydV\namA122M6RizBmQzDYFxZJRoWzcDZZ5+HPc0GeL1etB1uRtP+RnS36rB580bs2LENu3fvxBcfvY5n\nHr0DhYWFmDt3PnKLJmHRcWdi9vRJMY0xXoLjEkIj4tNpGcmeJ4XIOvhMiLsO6GF1uCBi2SHpGaHa\nTWvLj3jqodvQ0daMo46aiaeffha1tbE/nIloLqnUuJLVMo4jFYFI2UYiJQ71RjscLg+KNQr08Jjb\nhU5wJ6XgCPRw/v8chSRmgZwoLMsGuls1VF8KAHA6nXjmtU/R1LgDlp4fsWnTYMDY+2/+C8cedwqm\nHjUbvlNPwOTJUyASpT66PjQiPp2QQCZSRqhAO6K3wOpwo9Ngg1wqgsfrw+ebD2PRtHGBbXw+Hz5/\n/2W88cJf4XG78f9+chX++uADgdzi0UIyu0uNhfKF0RBr8BlHe49lSMcjlVKK1i4zNHnysC9kToAD\nkS0/QiBTrUWjQSqVorZuOmrrpuO0BVUAgCNH2nHPnx/HZ++9hE8/ehuffvQ2Hn3QH1w2Z85czJt3\nNObNOxpz5sxNiesqlRHxI0ECmUgbdqcnUDQC8AuKfosLa7e3oapEBZfTgf8+ey+2ff8hZHIlLr/m\nLtxz+42Q8ZgR00E6i8onwlgpXxgN8Qif0IAomUSEArUcYhHL+0IOFsZA6voHJwsh9saOxLhxZTjv\n4mtxzopVYB3d2PXDFrQd3IWNG9cP6Q/NMAwmT27AvHlHo2LCNCw69iQAqbNmpCM/WfhXh8ha+ASa\n1+uDXDr0tnO7vdilO4AH77kerQf3oKxqCi6/4UFMqq3CEb0lqTd+JAEV6hsL1bikEhY1MZgvs9H3\nm+2kQ/hQ/+DkEu6ZZFkWVTUTUVUzEQ3V1wLwFwTasmUjNm3aiE2bNmDbti3Yu3c3AKBkXDnu/O1d\nqJg0F0D0aV3RECk/OZn3GQlkIm5G8luGCrRcpQTqXBmM5sF8W7GIwf7G7XjqoVth7O3B5Dkn47SL\nbkOOWgWX25v0Gz9WIRmsccUTCBML8Ra8GM3lC7l7rKvXFtBckw1fIFe6ak1nkmgDLoVEQUEBli07\nDcuWnQbAX5tg9+6d+Mtf/4bPP16NG2+8FgzDYOa8paiqbcDSY4/BjFlHJ1yrIF0R/JmtqEBkLeH8\nllb7UPNfTWkeRCwDEcugrCAHVrsLJqsLNocbIpbB7g0f4qHf/QwmowEX/fRXOPPSO1CgyQPDMOg1\n+QU3d+NnAk7jqipVIYcnJUII1Jarh7XPm1qtzZj/mJuvRAm9x9S5UgCAw5ncimZlhTkQsYOR+1zU\ne7j5S7R/MB/JmrNoaWwxDHt+WzpMSZ/bVCMZqLV91x//hude/QT33HMf6iZPx7aNa7H61Sdx87UX\n4+Jzj8FzT/8Vhw8fyvRwR4Q0ZGJE+BpIRLtiPKK3wOP1wWR14lCnCeNLVDBanHB73Hjn5Uewfs1/\noVKpcee9/4eiqhlobOlN/QmlkExFOws5cCdeIvURTjbaPBkM/Y6oak1feko9djcbsH5XB4DUNItI\nNf0W57Dvst3sPqG2HmeeuBDHnX4Jvlm3GYzTgMYd3+Ht/72F/zz7OF5+/u8499wLcOq5l2Ni3dSY\n9h0pPzmZkIZMpIxgDcfl9sLm8KDX5IBaweCL1/6E9Wv+i6qaSXju5fcxe94SAIBE7L8lRSwDjcof\nWS3EQCo+orUapIJgTT4W035DtRanLaga8/5uiTi2yNpgy0823JuphDN9t/dYBGH6ZhgGVRMm45jj\nTsGjjz6Btz/ahF/f/RfU1dXjrbfewM8vOxM/v2QZXnzxefT3Rzfe2nL1kNrsnBUq2XEKJJCJuBhp\nxbin2cBbKtHU34cXHr0J+374BpOnzcMTz76FpQtmBEyuKqUUUjGLYo0CEjGb8I3fUK1Nm7CJZDXI\nBOk891SQzj7CsZqMuU5iJVol773Z1GaEvt8Ofb9dEEIqlLwc6bDv4pnbcIvQaE3fnEUp2LKUbBQK\nJU4760KsXbsOr7zyX5x00jIcONCEW2+9EQ1TJ+K6n1+Eu++4Bc+++Bq83vBlbUu1ypRXnyOTNREX\nseZ8SsQsWpr24MmHboNR344ZRy/DDbc/gOkTKwAMmlxFLIPJVZqA/3g0aR/ZLByTCTcPI9W2Dr3H\nxCLhmIYjBUQ1tRmx73AfTANmYa7yk5C6eU2u0qKja7AyXLxm90RS7iLVHk8FDMPgpJNOQdnEebi6\nsx1ffPIO3n/3v9izYz0A4JvP38YzTz6CuUcfC6PJBjHjwnFLFmDmzFloaJiWlvzkuPZaX1/PAngS\nwFEAHACu0ul0TckcGJFe+PzEIzGS3zI4evWwbj1ef+Z3cDmdWHDypTj34l9gYmVB4MYOTlfJy5EG\nVvDZkDfJkS15y9lE8EKtVKsUxKImXPtMTrvc19oHm2NQ+PpdNXb4fD5MrMhP+li4BQFftHgkakrz\nsGlPZ+BzOmo1B5NJi1JxSRnO/8kqnHfR1di2sxHGvh589dHL2LRuLQ426QLbffju6wD8BUwmTJyC\nk866HFUXXJCyccX7tjsXgFSn0y2qr68/GsAjA9/xYjab4zwMIVQ4AR4p57OsMAc+AN999jo+eO1v\nkMrkuPzGB1E26WgU5sffaUaoxFspCiDtORzBCzWhVB0bKdjM7hiuCXu8Plh4fpcIoQsDm8MNvdEe\ntdmZM7tzn+OBbxHabbTB5nCjqc0o+DKuDMOgqLQCRaUVOP7YY2C32/D1t98CPh+mTKqCqfsAtm3b\niu3bt2LHjm1o3HMr3n/jHzjxhOPxk59chunTZyR1PPH6kBcD+BgAdDrdBgBzI228fPly+Hy+OA9F\npJtQ/29Lhyls44NIeDwevPDU/Xj/1UeRm6fFm29+gBNOPBUalQwSsTBersmmpjQPYhGbkTq4hDBQ\nyIbf2yKWgSonuWlzfAsDj9eX1kjp0JS7bqMNRWpFIDgzkk85XZHL4eA7vkqVg5NPPAnTZy9G7aQp\n+MlPLsNDDz2Kzz77Cr/70/9BU1CM1sPNePbZZ3Diicfg+OMX45//fAomU3K0+ng15DwAwSPw1NfX\nszqdjtcj/sknn+CvT/4D5194OfJypJhcRdpAKigqit+/lt9rD+wj+DMA5ObIhu2f2ybcsSWHe/D7\n3/wCa7/4GJXVk3DH/c/gzDOOw9tf/Ih+mwu5OTLkq5XD9qk3OZGvVobdbyYIPtdoxjPD5o+qrqrU\nRLXfZJ1jMvYXaR/R7p/v3mhsMaCjz/99idWFyVXasPtr77UPuTeC74tozi3cfsPd40sHttuxr5v3\n30OptLrQb3ZCLve/0NVqBfrtblQU5aKoSIV508uwXdcF8YBQUufJUKhVwuXyBM4hdI6C5ypa1N0W\nwAcYzIMpTHKbGzk5sojnHnys4Gd7pGsf7hrMy5Vj10H/Ar6iNA9yqTgwJrXabwnTm0woCTl2UZEK\n2/d1BbYtKszBzLpiAEDujz3+4w68C6K957jzCB5r6Hlxf8+oK+I9/o593TA7PMPO9fzlKzBjwSkY\nX5KDIwe24LnnnsP777+PO+/8Nf72t4fx61//GqtWrUJubm7Y6zsS8QrkfgDBMxRWGAOAKk+Nx/7y\nB0xpmI+yiqqktLAjhlJUpEJ3d+xaLEef0b+q7u42DfkMAGaLY8jfwdtzBP/bgQNNWPH/zkfr4YM4\n9tjjcfG1f4Iyxz8+s8UBm90Fs8WBPqN12D657/n2myliHU/o/CW6XbQkY3+R9hHreXGs394Kk9UF\ny8B9dLjNiI4uU6D5Rbhjcd8H3xfxzn9TmzFg9bFZHYHyl3z3NN8zEEyBUoKOLhPsdr+GarU6UKiS\nwm53orvbhAKlBJocKTwev1VQkyOFXCpCS4cpcA7c/kMD3GK5dl6n2z+v1sHKdy6nGyrZ8DkNPR/u\nfRH8bI907SNdg7wBbdNhd8FhGxyTcaBzliXMc61RSOBwuAKfQ9858TxLwWNdv711yHWvLVcP2Zbv\n+OHOlfveYpViwYLjsGDBceju7sZ//vMcnnjiMdx222247777cNVV1+CYZSswo64o4pj5iNdk/R2A\n0wGgvr5+AYAfIm38qzvvh91mxcP33w6Px5PRVBAitezatRNnnXUKWg8fxIpLr8arr74JZU7mtVwi\nc0SKxE0HfEFYiValGikPefJ4TSA4cfL4yJaSeAk1F4tFLEq0yoz62sOZocP5tSPlz+uN9oRSotp7\nLCOmZMWbv89RVFSEW2/9NbZu3YXbb78DDMPg4Yf/jBXnLI55X0D8Avl/AOz19fXfwR/QdXOkjZed\nfh6WHHcqdu3YhP+98e84D0lkgliS/jdsWI9zzz0dPT3d+OXt9+LaG++ARCLMcpPEcNKRE5oJUlHx\na6Q8ZKVcjMnjNZg8XpNSS2BwzIIQam8nq4wrX0etWIvshHbxAlK3ENRotLjttt9gy5bd+OMf70du\nbnxKSFx3ik6n8wG4NtrtGYbBjbfdi107NuHfTz+M8klzMHvGUWhqMwo6Ai9b2NNsQH6vHWWa5Hc4\niTZP8IsvPsPKlZfC5XLhySf/iSlzTgr8m1ByR4nwRLrWiQoUoTW/OKK34IjeChHLpO0dlKoo+uAo\ndKGQjDKufB21UtHMIdnk5ubimmuux5JlF8X1+7RU6pJKWORrCnDFdffA5XLipSfvgYjxprW0IBE7\n0eYJrvn0XVx66Qr4fD688MIruOCCCyPut0SjDPsSibfjEZEYqcwJDac1zaor4r3WM8J8Hy/BZlR9\nvx02hydQmjVZ76BYq6KFbp+sqmpCeH5CzcDBVheumEo64MvLTsZCsKXDNGJRm3i7S6VFIE+q1EAi\nYTF97lKccMp5+FG3C6/+50kAmS0tSPhJxFT5zlsv4b67b4JCocQbb6zGySefOmpNn0T8ZDIdLHhB\n4HR5IRYxgdKsAL2DUglfrnRLh2nEBRBfR61YU6LKCnME1QUtGtIikHMUEkyt1mJ8iQo33HIPtIWl\neOX5v2Nf4850HJ6IQKSAl0h5gj6fDy/9++949MG7kK8pwOrVH2DBgkVRB9Bke53lZCCkOUhmTijf\neSUaPBMvXE49tyAQsUygGAaResL570daABWo5cNaYsZT0z7b6gKktbmESiFBTm4ebr/rL/B43Lj/\n97egqbUHZpuLNKkMEfrAHNFbcLjLjK0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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.span(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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RVYuKTnrOeXMLuO/WJQD0+UPfabp9/pMeJwLQ3OYDYPncApcrEZFIFs489k8D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\n1DZ3kZKcwL03LlLXu4iIA+K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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", "tfit = np.linspace(0, 1, 100)\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.span(tfit)\n", " span2 += model.span(tfit) ** 2\n", " \n", "mean = span / N\n", "std = np.sqrt(span2 / N - mean ** 2)\n", "plt.plot(tfit, mean)\n", "plt.fill_between(tfit, 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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F4blzw6gS8lXh2Da2Y+M4JXBt/JpCOOgnGtHpP3IIv7/5271VVWVooJ+hAUhn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\nRI11d3WyMXdh4V5f1/JB//L5JfJFhw8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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bass Enhancement\n", "\n", "The degree of smoothing can be tuned with the *bass enhancement* feature. This is a number $\\alpha$ which lies between 0 and 10, with 10 being a much smoother curve" ] }, { "cell_type": "code", "collapsed": false, "input": [ "rng = np.random.RandomState(0)\n", "t = rng.rand(200)\n", "dy = 0.5\n", "y = np.sin(5 * np.pi * t ** 2) + dy * rng.randn(200)\n", "\n", "plt.errorbar(t, y, dy, fmt='o', alpha=0.3)\n", "\n", "for alpha in [0, 8, 10]:\n", " smoother = SuperSmoother(alpha=alpha)\n", " smoother.fit(t, y, dy)\n", " plt.plot(tfit, smoother.predict(tfit),\n", " label='alpha = {0}'.format(alpha))\n", "plt.legend(loc=2);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Oxtme8dTfyRd+tsIk+aB/wsn+/jc5OXQOV3iEOBcDkyxSKTe3XI0p2IxFsfL2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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The effect of the smoothing is not linear: i.e. a change from 0 to 1 has much less effect than a change from 9 to 10." ] } ], "metadata": {} } ] }