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Cynhard85 / MachineLearningTutorial

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机器学习 - 局部加权线性回归.ipynb 101.63 KB
一键复制 编辑 Web IDE 原始数据 按行查看 历史
Cynhard 提交于 2018-07-14 10:09 . add 局部加权线性回归
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 准备"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"import pandas as pd\n",
"import numpy as np"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 构造数据"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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JjwIXR0QnvF0JPFdqhJImQr/idIvWJc2qkUNWZh7KzCsz8xrgw8CfZ+avA48CH2xfth94uPQoJTVev+J0i9Ylzaoq+mR9HHgwIj4JPAHcV8F7SGqYTnH6xtqrfucladpFZv3lUPPz87m6ulr3MCRJkgaKiJOZOT/oOrfVkSRJqoAhS5IkqQKGLEmSpAoYsiRJkipgyJIkSaqAIUuSJKkChixJkqQKGLIkjV2rBUeOFI+SNKuq6PguaYa5IbQkFZzJkjRWbggtSQVDlqSxckNoSSq4XChprNwQWpIKhixpirVa9YSdhQXDlSQZsqQK1RVyOu9tAbok1ceQJVVkO0LOxhDXfdyrAN2QJUnbx5AlVaTqkLMxxB09CgcPvvZ45871YwvQJWl7GbKkinTusqsq5GwMccePv/b4zBkL0CWpToYsqSJV32W3McTt3QuPPfbaUGcBuiTVx5AltVVRpF5lyOkV4m64Yfi/Q51F+ZI0CyIz6x4D8/Pzubq6WvcwNMNm7U68Wfv7StI4RcTJzJwfdJ0d3yVmbyuYWfv7SlIdDFkSs7cVzKz9fSWpDtZkSczeVjCz9veVpDpYkyXVxMJzSZpMw9ZkOZMl1aBXI9EzZwxckjRNDFnSFg07A7XZdSsrcPYsrK3BT34CBw4UP3unnyRND0OWZspWl+h67Q24WeuDzvW7d792i5uN1+3eXYQqgEw4d6543Mr2Oy43SlKzGbI0M7baG6rX9d2tD37yEzh2bP01uq+PKELU2lrv4HTmDOzYUTwfARdcsD6TNcydfva5kqTms4WDZsZWe0P1un5xsWh7AMXM0/33F4Fn4/Vra8V1/VokLC7Crl3F8294A9x1Fxw+PHxYss+VJDWfM1maGVvdsLnX9QsLcOut8NnPri/zdWapNl6/WTF72RYKVW8+LUkqzxYOmilla7I65/ot1W1nnZQ1WZJUj2FbOBiypBEYcCRpdtknSxNpUsLLwkKzxydJqp8hS43hHXOSpGni3YUaWasFR46s31036Pyg571jTpI0TZzJ0kj6zTq1WsVS36uvwoUXvr4/1PJy0d38/PmihUH3bJV3zEmSpokzWRpJv1mnY8eK40738mPH1n+n1YLbby8CWGc7me7nO20NttIvqmkGzeJJkmaHM1nqa7Mi9FFmnVZW1reSgfVmnvv2rb/+JBeUW1MmSermTJZ66gSG3/3d4nHjzEy/Wad9+4plwIjicd++9d/pdDmPWD/XaeY5DawpkyR1cyZLPfUKDL26lvc69+ijvWfAOsHs2LFiBuvcuemqvbKmTJLUzWak6qnqpa9J6Ye1VdP695IkrbPju0orExgMG5KkaWXH9xk1znAzahG6BeCSJJUofI+IqyLi0Yh4MiK+GxEfbZ+/JCK+ERE/aD++aXzD1WYGFatvFwvAJUkqd3fhOeB3MvNngRuB2yPi7cAdwInMvA440T7WNthquFlehptuKh7HqVMAPjdnAbgkaXaNvFyYmc8Dz7d//oeIeBK4ArgZWGxf9gCwAny81Cg1lK3c3ba8DB/5SPHz179ePC4tjWccnbsIrcmSJM2ysRS+R8Q1wF8A1wPPZObFXc+9lJmvWzKMiCVgCeDqq6/+N08//XTpcWj4mqybbloPVwC/9Evwta+N9lqSJM2SbSt8j4ifBo4DBzPz76O70+QmMnMZWIbi7sKy41Bh2GL1vXtfG7L27n3t8xavS5JUTqmQFREXUgSsz2fml9unX4iIyzPz+Yi4HHix7CD1ehtnmbY669RZGjx+vAhYG5cKh2lGKkmS+hs5ZEUxZXUf8GRm/mHXU48A+4FPtR8fLjVCvc7GWaajR+Hgwa3POi0t9a/Dsnu5JEnllJnJehfwG8C3I+Jb7XOfoAhXX4qI24BngA+VG6I22jjLdPx477sKy9RTWbwuSVI5Ze4u/N9AvwKsPaO+rgbbOMu0dy889tj68e7d46mnGrUZqSRJsuP7ROo1y3TDDevH1lNJklQ/Q9aE2jjLtPHYeipJkuplyJpC1lNJklQ/Q9aUsp5KkqR6ldm7UBVoteDIkfo2d5YkSePhTFaD9Ouy7vY2kiRNHkNWDfqFpl53BYLb20iSNIkMWdtssz0Be3VZtx2DJEmTyZC1zTYLTf3uCrQdgyRJk8eQtc0G7QnYq/+V7RgkSZo8hqwKbFaoPkposh2DJEmTx5A1ZpvVXHUYmiRJmn72yRqzfncISpKk2WLIGrNOzdXcnIXqkiTNMpcLx2yYmiubi0qSNP0MWRXYrOZqmJotSZI0+Vwu3GbWbEmSNBsMWdvMmi1JkmaDy4UV6lV7ZXNRSZJmgyGrIp3aq7NnYccOuPtuWFoqnrNPliRJ08/lwoqsrBQBa20Nzp2DAweK4CVJkmaDIauEVguOHOkdnhYXixmsjvPnLXKXJGmWuFw4okGtGBYWiiXCAweKgLVrl0XukiTNEkPWiHq1YthYZ7W0BDfcYJG7JEmzyJA1ot27i+XAzM1bMVjkLknSbLImawStFhw8WMxi7dgBR48apCRJ0msZskbQWSpcWytmss6cqXtEkiSpaQxZI7BruyRJGsSarBHYtV2SJA1iyBqRBe2SJGkzLhdKkiRVwJAlSZJUAUPWBpttlSNJkjQsa7K6DNoqR5IkaVjOZHXptVWOJEnSKAxZXex/JUmSxsXlQoplwk7PK/tfSZKkcZj5kNWrDuvQobpHJUmSJt3MLxdahyVJkqow8yFrUB2WLR0kSdIoZn65cLN9CG3pIEmSRjUTIau7sL1XSOq3D2GvpURDliRJGsbUh6wys1GdpcTO79rSQZIkDauSmqyIeG9EfD8inoqIO6p4j2GVKWzvLCUePuxSoSRJ2pqxz2RFxBxwN/DvgVPANyPikcz83rjfaxhlZ6P6LSVKkiRtporlwp8DnsrMHwJExIPAzUAtIWuzwnZJkqSqVBGyrgCe7To+BfzbCt5naM5GSZKk7VZFTVb0OJevuyhiKSJWI2L19OnTFQxDkiSpPlWErFPAVV3HVwLPbbwoM5czcz4z5y+77LIKhiFJklSfKkLWN4HrIuLaiNgJfBh4pIL3kSRJaqyx12Rl5rmIOAB8DZgDPpeZ3x33+0iSJDVZJc1IM/OrwFereG1JkqRJMPMbREuSJFXBkCVJklQBQ5YkSVIFDFmSJEkViMzX9Qnd/kFEnAaerujlLwX+rqLXVjl+Ns3lZ9Nsfj7N5WfTXOP8bP5FZg5s8tmIkFWliFjNzPm6x6HX87NpLj+bZvPzaS4/m+aq47NxuVCSJKkChixJkqQKzELIWq57AOrLz6a5/Gyazc+nufxsmmvbP5upr8mSJEmqwyzMZEmSJG07Q5YkSVIFpjZkRcR7I+L7EfFURNxR93hmWURcFRGPRsSTEfHdiPho+/wlEfGNiPhB+/FNdY91lkXEXEQ8ERFfaR9fGxGPtz+fL0bEzrrHOIsi4uKIeCgi/m/7O7Tgd6cZIuK32/+mfScivhARb/B7U5+I+FxEvBgR3+k61/O7EoU/bmeEv4qId1YxpqkMWRExB9wNvA94O/BrEfH2ekc1084Bv5OZPwvcCNze/jzuAE5k5nXAifax6vNR4Mmu408Dn2l/Pi8Bt9UyKv0R8GeZ+S+Bf0XxGfndqVlEXAH8FjCfmdcDc8CH8XtTpz8B3rvhXL/vyvuA69p/loB7qhjQVIYs4OeApzLzh5n5CvAgcHPNY5pZmfl8Zv5l++d/oPiPxBUUn8kD7cseAD5QzwgVEVcCvwLc2z4O4N3AQ+1L/HxqEBE/A/wCcB9AZr6SmS/jd6cpLgB+KiIuAC4CnsfvTW0y8y+A/7fhdL/vys3AsSz8H+DiiLh83GOa1pB1BfBs1/Gp9jnVLCKuAd4BPA68JTOfhyKIAW+ub2Qz7yjwMWCtfbwbeDkzz7WP/Q7V463AaeD+9lLuvRHxRvzu1C4z/wb4A+AZinD1Y+Akfm+apt93ZVtywrSGrOhxzl4VNYuInwaOAwcz8+/rHo8KEfF+4MXMPNl9uselfoe23wXAO4F7MvMdwD/i0mAjtGt7bgauBf458EaKJaiN/N4007b8GzetIesUcFXX8ZXAczWNRUBEXEgRsD6fmV9un36hMz3bfnyxrvHNuHcBvxoRP6JYWn83xczWxe1lEPA7VJdTwKnMfLx9/BBF6PK7U7/3AH+dmacz81Xgy8DP4/emafp9V7YlJ0xryPomcF37Lo+dFMWIj9Q8ppnVru+5D3gyM/+w66lHgP3tn/cDD2/32ASZeSgzr8zMayi+K3+emb8OPAp8sH2Zn08NMvNvgWcj4m3tU3uA7+F3pwmeAW6MiIva/8Z1Phu/N83S77vyCLCvfZfhjcCPO8uK4zS1Hd8j4pcp/m98DvhcZv73moc0syLi3wGPAd9mvebnExR1WV8Crqb4B+tDmbmxaFHbKCIWgf+ame+PiLdSzGxdAjwB/OfMPFvn+GZRRPxrihsSdgI/BG6h+B9kvzs1i4j/BvxHijuonwB+k6Kux+9NDSLiC8AicCnwAvB7wP+kx3elHYzvorgb8Z+AWzJzdexjmtaQJUmSVKdpXS6UJEmqlSFLkiSpAoYsSZKkChiyJEmSKmDIkiRJqoAhS5IkqQKGLEmSpAr8f4ubqkTDPkF9AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x2251479da58>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m = 100\n",
"\n",
"np.random.seed(42)\n",
"x_values = 100 * np.random.rand(m,1)\n",
"x_values = np.sort(x_values, axis=0)\n",
"y = 7 * np.sin(0.12 * x_values) + x_values + 2 * np.random.randn(m, 1)\n",
"plt.figure(figsize=(10, 5))\n",
"plt.plot(x_values, y, \"b.\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"X = np.c_[np.ones([m, 1]), x_values]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# k 值对权重的影响"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x2251479df60>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(12,8))\n",
"\n",
"ks = [100, 5, 1]\n",
"for index in range(len(ks)):\n",
" \n",
" ws = []\n",
" for i in range(m):\n",
" wi = np.exp(- np.sum(np.square(X[i] - X[m//2])) / (2 * ks[index]**2))\n",
" ws.append(wi)\n",
" \n",
" plt.subplot(len(ks), 1, index+1)\n",
" plt.plot(x_values, ws)\n",
" plt.title(\"k={}\".format(ks[index]))\n",
" \n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 预测"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[48.041602]\n"
]
}
],
"source": [
"def calculate_theta(x_test, k):\n",
" # 构造矩阵 W\n",
" W = np.eye(m, m)\n",
" for i in range(m):\n",
" W[i,i] = np.exp(- np.sum(np.square(X[i] - x_test)) / (2 * k**2))\n",
"\n",
" # 应用局部加权线性回归,求解 theta\n",
" theta = np.linalg.inv(X.T.dot(W).dot(X)).dot(X.T).dot(W).dot(y)\n",
" \n",
" return theta\n",
"\n",
"def predict(x_test, k):\n",
" theta = calculate_theta(x_test, k)\n",
" y_pred = theta[0] + x_test * theta[1]\n",
" return y_pred\n",
"\n",
"print(predict(50, 5))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 过拟合与欠拟合"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x22514801dd8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"test_count = 50\n",
"x_test_values = np.linspace(0, 100, test_count)\n",
"\n",
"def lwlr(x_test_values, k):\n",
" \n",
" left_values = x_test_values - m / test_count / 2\n",
" right_values = x_test_values + m / test_count / 2\n",
" X_tests = np.c_[np.ones(test_count), x_test_values.reshape(-1, 1)]\n",
" \n",
" x_plots = []\n",
" y_plots = []\n",
"\n",
" for t, l, r in zip(X_tests, left_values, right_values):\n",
" \n",
" theta = calculate_theta(t, k)\n",
"\n",
" x_test_points = np.array([[l], [r]])\n",
" X_test = np.c_[np.ones([2, 1]), x_test_points]\n",
" y_test_points = X_test.dot(theta)\n",
"\n",
" x_plots.extend(x_test_points)\n",
" y_plots.extend(y_test_points)\n",
" \n",
" plt.plot(x_values, y, \"b.\")\n",
" plt.plot(x_plots, y_plots, 'r-', linewidth=2)\n",
" plt.title(\"k={}\".format(k))\n",
"\n",
"plt.figure(figsize=(12, 8))\n",
"ks = [100, 5, 1]\n",
"for index in range(len(ks)):\n",
" plt.subplot(len(ks), 1, index+1)\n",
" lwlr(x_test_values, ks[index])\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
},
"toc": {
"base_numbering": 1,
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 2
}

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