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Last active May 23, 2016 04:28
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Machine Learning by Andrew Ng: II. Linear Regression with One Variable (Week 1)
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"\n",
"# Machine Learning by Andrew Ng\n",
"# https://class.coursera.org/ml-005/lecture\n",
"# II. Linear Regression with One Variable (Week 1)\n",
"# https://d396qusza40orc.cloudfront.net/ml/docs/slides/Lecture2.pdf\n",
"\n",
"import random\n",
"import math\n",
"import numpy as np\n",
"from functools import partial\n",
"\n",
"import matplotlib\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def make_h(theta0, theta1):\n",
" def h(x):\n",
" return theta0 + theta1 * x\n",
" return h\n",
"\n",
"def gradient_descent(data_x, data_y, alpha, max_iteration=1000):\n",
" isclose = partial(math.isclose, rel_tol=0.0002)\n",
" theta = [0, 0]\n",
" m = len(data_x)\n",
" assert m == len(data_y)\n",
" samples = list(zip(data_x, data_y))\n",
" r = []\n",
" for i in range(max_iteration):\n",
" h = make_h(theta[0], theta[1])\n",
" t0 = theta[0] - alpha * sum(h(x) - y for x, y in samples) / m\n",
" t1 = theta[1] - alpha * sum((h(x) - y) * x for x, y in samples) / m\n",
" r.append((t0, t1))\n",
" if isclose(t0, theta[0]) and isclose(t1, theta[1]):\n",
" print('local minimum found. iteration:', i)\n",
" break\n",
" theta[0] = t0\n",
" theta[1] = t1\n",
" else:\n",
" print('giveup! local minimum not found.')\n",
" return r"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"dist = 6\n",
"N = 6\n",
"data_x = np.array([random.random() * dist for _ in range(N)])\n",
"data_y = np.array([random.random() * dist for _ in range(N)])"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"local minimum found. iteration: 557\n",
"alpha = 0.022\n",
"local minimum(red): h(x) = 1.389830 + (0.520244 x)\n",
"global minimum(blue): h(x) = 1.436739 + (0.510031 x)\n"
]
},
{
"data": {
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p3KQzmzRolVJqLnr4YT5+9HP5vQ3rWN6Z5BE7xtsq/8jt7f/gtL96I6992xsZ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\nrgzwf1IwiXsp0S8d7HXfyTXj4StSZ7t17cbuTSG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ElVwy8H9awtbHKdErYevXXGCb7Nfz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FScOSzO2VhXxLpTixpxyXoEPNFJA09wuxeV52I4RbQdT7VLZG+1cmYEtjc9vl6N4CS4Y7wGJWP7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\nNTMzO0T/A+DgYgkvR+hPAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f5800b62828>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
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BW0vmKpSycAvsFgnu8koBbtDUnVLCW5VdE+2RkWcI7HbF/J5uEN4hlOLUDcK7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\nSGArpZRSEfT/AYMflJtXJSePAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f58004b9e48>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8, 6), dpi=50)\n",
"plt.plot(data_x, data_y, 'rx')\n",
"\n",
"# local minimum by gradient descent algorithm\n",
"alpha = 0.022\n",
"gda_spotting = gradient_descent(data_x, data_y, alpha)\n",
"for t0, t1 in gda_spotting:\n",
" h = make_h(t0, t1)\n",
" plt.plot([0, dist], [h(0), h(dist)], alpha=0.1)\n",
"t0, t1 =gda_spotting[-1]\n",
"print('alpha = {}'.format(alpha))\n",
"print('local minimum(red): h(x) = {:4f} + ({:4f} x)'.format(t0, t1))\n",
"h = make_h(t0, t1)\n",
"plt.plot([0, dist], [h(0), h(dist)], color='r', linewidth=1.5)\n",
"\n",
"# global minimum by least-squares solution\n",
"A = np.vstack([data_x, np.ones(len(data_x))]).T\n",
"t1, t0 = np.linalg.lstsq(A, data_y)[0]\n",
"print('global minimum(blue): h(x) = {:4f} + ({:4f} x)'.format(t0, t1))\n",
"h = make_h(t0, t1)\n",
"plt.plot([0, dist], [h(0), h(dist)], color='b', linewidth=1.5, linestyle='--')\n",
"plt.axis([0, dist, 0, dist])\n",
"plt.title(\"h(x)\")\n",
"\n",
"plt.figure(figsize=(8, 6), dpi=50)\n",
"samples = list(zip(data_x, data_y))\n",
"def rms(t0, t1):\n",
" h = make_h(t0, t1)\n",
" return np.sqrt(np.sum(np.power(h(x) - y, 2) for x, y in samples) / len(samples))\n",
"delta = 0.1\n",
"x = np.arange(-4.0, 4.01, delta)\n",
"y = np.arange(-4.0, 4.01, delta)\n",
"X, Y = np.meshgrid(x, y)\n",
"plt.contourf(X, Y, rms(X, Y), 32, alpha=0.8)\n",
"plt.axis([-4, 4, -2, 2])\n",
"plt.plot(*zip(*gda_spotting), 'rx', alpha=0.6, markersize=4.0)\n",
"plt.title(\"J(theta0, theta1)\")\n",
"\n",
"plt.show()"
]
}
],
"metadata": {
"kernelspec": {
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