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@mitmul
Last active May 7, 2016 04:17
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{
"metadata": {
"name": "",
"signature": "sha256:b881af10fbdddca562fa4788ae7e7455978c33abfd159635ab55e54e600b723f"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 1\u6b21\u5143\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\n",
"1\u6b21\u5143\u306e\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u306f\uff0c\n",
"\n",
"1. $d$\u6b21\u5143\u30d9\u30af\u30c8\u30eb${\\bf x}$\u3092$f({\\bf x}) = {\\bf w}^{\\rm T}{\\bf x} + b$\u306b\u3088\u3063\u30661\u6b21\u5143\u306b\u5199\u50cf\n",
"\n",
"2. \u305d\u308c\u3092\u30b7\u30b0\u30e2\u30a4\u30c9\u95a2\u6570\u3067$(0, 1)$\u533a\u9593\u3078\u5199\u50cf\uff1a$s({\\bf x}) \\equiv \\sigma(f({\\bf x}))$\n",
"\n",
"3. \u3053\u308c\u3092\u7528\u3044\u3066\u30e9\u30d9\u30eb$c(0\\ or\\ 1)$\u306b\u5bfe\u3059\u308b\u5c24\u5ea6\u3092\u5b9a\u7fa9\uff1a\n",
"\n",
" $p(y=c \\mid {\\bf x};{\\bf w},b) = s({\\bf x})^c(1-s({\\bf x}))^{1-c}$\n",
" \n",
" \uff08${\\bf w},b$\u306f\u78ba\u7387\u5909\u6570\u3067\u306f\u306a\u304f\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u30e2\u30c7\u30eb\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306a\u306e\u3067\uff0c$;$\u306b\u3088\u3063\u3066\u533a\u5207\u3089\u308c\u305f\u5f62\u3067\u793a\u3055\u308c\u3066\u3044\u308b\uff09\n",
"\n",
"4. \u4e0e\u3048\u3089\u308c\u305f$N$\u500b\u306e\u30c7\u30fc\u30bf\u70b9${\\bf x}_n$\u3068\u305d\u306e\u30e9\u30d9\u30eb\u5024$c_n$\u306b\u3064\u3044\u3066\uff0c\u5404\u30c7\u30fc\u30bf\u70b9\u304c\u5168\u3066\u72ec\u7acb\u3067\u3042\u308b\u3068\u306e\u4eee\u5b9a\u306e\u3082\u3068\u3067\u4ee5\u4e0b\u306e\u5c24\u5ea6\u95a2\u6570\u3092\u6700\u5927\u5316\u3059\u308b${\\bf w},b$\u3092\u6c42\u3081\u308b\n",
" $$\\mathcal{l}({\\bf w},b) = \\prod_{n=1}^N p(y \\mid {\\bf x};{\\bf w},b) = \\prod_{n=1}^N s({\\bf x}_n)^{c_n}(1-s({\\bf x}_n))^{1-c_n}$$\n",
"\n",
"\u3068\u3044\u3046\u624b\u9806\u306b\u3088\u3063\u3066${\\bf x}$\u304b\u30892\u5024\u30e9\u30d9\u30eb$c$\u3092\u4e88\u6e2c\u3059\u308b\u5199\u50cf\u3092\u5f97\u308b\uff08\u3059\u306a\u308f\u30612\u30af\u30e9\u30b9\u5206\u985e\u3092\u884c\u3046\uff09\u624b\u6cd5\u3067\u3042\u308b\uff0e\u4ee5\u4e0b\u306b\u66f8\u304f\u624b\u9806\u306e\u8a73\u7d30\u3092\u8ff0\u3079\u308b\uff0e"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\u30b7\u30b0\u30e2\u30a4\u30c9\u95a2\u6570\u306f$\\sigma(a)=\\frac{1}{1+\\exp(-a)}$\u306e\u3088\u3046\u306a\u95a2\u6570\u3067\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5f62\u3092\u3057\u3066\u3044\u308b\uff0e"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"a = np.arange(-10, 10, 0.1)\n",
"s = 1.0 / (1.0 + np.exp(-a))\n",
"plt.plot(a, s)\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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OHYOKCrj2WtNJRIKvzW0C4uPjqampaX5eU1ODy+VqccxHH31Efn4+APX19axcuZKYmBjy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\nOIhKXUTEQVTqIiIO8v/WZp60LJF0FQAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x10b03f150>"
]
}
],
"prompt_number": 92
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\u3053\u308c\u306f$(-\\infty, \\infty)$\u306e\u533a\u9593\u306e\u5b9f\u6570\u3092$(0, 1)$\u306b\u5199\u50cf\u3059\u308b\u95a2\u6570\u306a\u306e\u3067\uff0c\u3042\u308b\u30c7\u30fc\u30bf\u70b9${\\bf x}$\u3092$f({\\bf x}) = {\\bf w}^{\\rm T}{\\bf x} + b$\u306b\u3088\u3063\u30661\u6b21\u5143\u306b\u5199\u50cf\u3057\u305f\u3042\u3068\uff0c\u30b7\u30b0\u30e2\u30a4\u30c9\u95a2\u6570\u306b\u901a\u3057\u305f\u5024$\\sigma(f({\\bf x}))$\u306f\uff0c$(0,1)$\u306e\u5024\u3092\u3068\u308b\u78ba\u7387\u5024\u3067\u3042\u308b\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\uff0e\n",
"\n",
"\u4eca\uff0c\u30c7\u30fc\u30bf\u70b9${\\bf x}$\u306b\u306f\u30e9\u30d9\u30eb\u3068\u3057\u30660\u304b1\u306e\u3069\u3061\u3089\u304b\u304c\u5bfe\u5fdc\u3057\u3066\u3044\u308b\u3068\u3059\u308b\uff0e\u3053\u306e\u3068\u304d\uff0c${\\bf x}$\u306e\u30e9\u30d9\u30eb\u304c1\u3067\u3042\u308b\u78ba\u7387\u30680\u3067\u3042\u308b\u78ba\u7387\u306f\uff0c\u305d\u308c\u305e\u308c\n",
"\n",
"$$p(y=1 \\mid {\\bf x};{\\bf w},b) = \\sigma(f({\\bf x})) \\equiv s({\\bf x})$$\n",
"$$p(y=0 \\mid {\\bf x};{\\bf w},b) = 1 - \\sigma(f({\\bf x})) \\equiv 1 - s({\\bf x})$$\n",
"\n",
"\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u30e9\u30d9\u30eb\u3092$c(0\\ or\\ 1)$\u3067\u8868\u305b\u3070\uff0c\u30c7\u30fc\u30bf\u70b9${\\bf x}$\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u306e\u30e9\u30d9\u30eb\u306e\u5c24\u5ea6\u306f\n",
"\n",
"$$p(y=c \\mid {\\bf x};{\\bf w},b) = s({\\bf x})^c(1 - s({\\bf x}))^{1-c}$$\n",
"\n",
"\u3068\u307e\u3068\u3081\u3066\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u4eca\uff0c$N$\u500b\u306e\u30c7\u30fc\u30bf\u70b9\u304c\u3042\u308b\u3068\u3057\u3066\uff0c\u305d\u308c\u305e\u308c\u304c\u5168\u3066\u72ec\u7acb\u3067\u3042\u308b\u3068\u8003\u3048\u308b\u3068\uff0c\u30c7\u30fc\u30bf\u70b9\u306e\u96c6\u5408${\\bf x}_n(n=1,\\dots,N)$\u3068\u30e9\u30d9\u30eb\u306e\u96c6\u5408$c_n(n=1,\\dots,N)$\u306b\u5bfe\u3059\u308b\uff0c\u3053\u306e\u30e2\u30c7\u30eb\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3042\u308b${\\bf x},b$\u306e\u5c24\u5ea6\u306f\u5404\u30c7\u30fc\u30bf\u306e\u5c24\u5ea6\u306e\u7a4d\u3067\u8868\u305b\u308b\u306e\u3067\uff0c\n",
"\n",
"$$\\mathcal{l}({\\bf w},b) = \\prod_{n=1}^N p(y \\mid {\\bf x};{\\bf w},b) = \\prod_{n=1}^N s({\\bf x}_n)^{c_n}(1-s({\\bf x}_n))^{1-c_n}$$\n",
"\n",
"\u3068\u5b9a\u7fa9\u3067\u304d\u308b\uff0e\u3053\u306e\u6700\u5927\u5316\u3092\u8003\u3048\u308b\u306e\u3060\u304c\uff0c\u307e\u305a$(0,1)$\u533a\u9593\u306e\u5024\u306e\u7a4d\u3092\u30c7\u30fc\u30bf\u6570\u5206\u3060\u3051\u8a08\u7b97\u3057\u3088\u3046\u3068\u3059\u308b\u3068\uff0c\u6d6e\u52d5\u5c0f\u6570\u70b9\u306e\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u304c\u8d77\u3053\u308a\u3084\u3059\u3044\u305f\u3081\uff0c\u5bfe\u6570\u3092\u3068\u3063\u3066\u548c\u306e\u5f62\u3067\u8868\u3059\u3053\u3068\u306b\u3059\u308b\uff0e\u5bfe\u6570\u95a2\u6570\u306f\u5358\u8abf\u5897\u52a0\u3067\u3042\u308b\u306e\u3067\uff0c\u5bfe\u6570\u3092\u3068\u3063\u305f\u3068\u3057\u3066\u3082\u5927\u5c0f\u95a2\u4fc2\u306f\u5909\u308f\u3089\u306a\u3044\uff0e\u307e\u305f\uff0c\u5b9f\u88c5\u4e0a\u306e\u5bb9\u6613\u3055\u306e\u89b3\u70b9\u304b\u3089\uff0c\u7b26\u53f7\u3092\u53cd\u8ee2\u3059\u308b\u3053\u3068\u3067\u6700\u5927\u5316\u3067\u306f\u306a\u304f\u6700\u5c0f\u5316\u554f\u984c\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u306b\u3059\u308b\uff0e\u3059\u308b\u3068\uff0c\u76ee\u7684\u95a2\u6570\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u304d\u4e0b\u305b\u308b\uff0e\n",
"\n",
"\\begin{eqnarray}\n",
"\\def\\sx{s({\\bf x}_n)}\n",
"\\mathcal{L}({\\bf w},b) &=&\n",
"-\\sum_{n=1}^N \\ln \\left\\{\n",
" \\sx^{c_n}(1 - \\sx)^{1 - c_n}\n",
"\\right\\} \\\\\n",
"&=& -\\sum_{n=1}^N \\left\\{\n",
" c_n \\ln \\sx + (1 - c_n) \\ln (1 - \\sx)\n",
"\\right\\}\n",
"\\end{eqnarray}\n",
"\n",
"\u3053\u308c\u3092\u8ca0\u306e\u5bfe\u6570\u5c24\u5ea6\uff08negative log likelihood\uff09\u95a2\u6570\u3068\u547c\u3076\uff0e\u307e\u305f\uff0c\u30e2\u30c7\u30eb\u306e\u4e88\u6e2c\u306e\u306f\u305a\u308c\u5177\u5408\u3092\u8868\u3059\u306e\u3067\uff0c\u640d\u5931\u95a2\u6570\uff08loss function\uff09\u3068\u3082\u547c\u3070\u308c\u308b\uff0e\u3053\u308c\u3092\u6700\u5c0f\u5316\u3059\u308b\u30d1\u30e9\u30e1\u30fc\u30bf${\\bf w},b$\u306f\uff0c\u3053\u306e\u95a2\u6570\u3092\u30d1\u30e9\u30e1\u30fc\u30bf\u305d\u308c\u305e\u308c\u3067\u504f\u5fae\u5206\u3057\u30660\u3068\u304a\u3051\u3070\u6c42\u307e\u308b\u3088\u3046\u306a\u6c17\u304c\u3059\u308b\uff0e\u30b7\u30b0\u30e2\u30a4\u30c9\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u304c\n",
"\n",
"$$\\sigma(a) = \\frac{1}{1 + \\exp(-a)}$$\n",
"\n",
"$$\\frac{d \\sigma}{d a} = \\frac{\\exp(-a)}{(1 + \\exp(-a))^2} = \\frac{1}{1 + \\exp(-a)}\\frac{\\exp(-a)}{1 + \\exp(-a)} = \\sigma(a)\\frac{1 + \\exp(-a) - 1}{1 + \\exp(-a)} = \\sigma(a)\\left( 1 - \\sigma(a) \\right)$$\n",
"\n",
"\u3068\u306a\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\uff0c\u30d1\u30e9\u30e1\u30fc\u30bf${\\bf w},b$\u305d\u308c\u305e\u308c\u306b\u304a\u3051\u308b\u504f\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u3066\u307f\u308b\uff0e"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### ${\\bf w}$\u306b\u304a\u3051\u308b\u504f\u5c0e\u95a2\u6570\n",
"$$\n",
"\\frac{\\partial \\mathcal{L}}{\\partial {\\bf w}} =\n",
"-\\sum_{n=1}^N \\left\\{\n",
" c_n \\frac{\\partial \\ln\\sigma(f({\\bf x}_n))}{\\partial f({\\bf x}_n)}\\frac{\\partial f({\\bf x}_n)}{\\partial {\\bf w}} +\n",
" (1 - c_n) \\frac{\\partial \\ln(1 - \\sigma(f({\\bf x}_n)))}{\\partial f({\\bf x}_n)} \\frac{\\partial f({\\bf x}_n)}{{\\bf w}}\n",
"\\right\\}\n",
"$$\n",
"\n",
"\\begin{eqnarray}\n",
"\\def\\xn{{\\bf x}_n}\n",
"\\frac{\\partial \\mathcal{L}}{\\partial {\\bf w}} = -\\sum_{n=1}^N \\xn (c_n - \\sx)\n",
"\\end{eqnarray}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### $b$\u306b\u304a\u3051\u308b\u504f\u5c0e\u95a2\u6570\n",
"${\\bf w}$\u3068\u540c\u69d8\u306b\n",
"\n",
"\\begin{eqnarray}\n",
"\\def\\xn{{\\bf x}_n}\n",
"\\frac{\\partial \\mathcal{L}}{\\partial b} = -\\sum_{n=1}^N (c_n - \\sx)\n",
"\\end{eqnarray}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### \u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u5b66\u7fd2\n",
"\u4ee5\u4e0a\u306e2\u3064\u306e\u5c0e\u95a2\u6570\n",
"\n",
"$$ \\frac{\\partial \\mathcal{L}}{\\partial {\\bf w}} = -\\sum_{n=1}^N \\xn (c_n - \\sx)$$\n",
"$$ \\frac{\\partial \\mathcal{L}}{\\partial b} = -\\sum_{n=1}^N (c_n - \\sx)$$\n",
"\n",
"\u306f\uff0c\u30b7\u30b0\u30e2\u30a4\u30c9\u95a2\u6570$\\sx$\u3092\u542b\u3093\u3067\u3044\u308b\u305f\u3081\uff0c$=0$\u3068\u304a\u3044\u3066\u89e3\u6790\u7684\u306b${\\bf w}$\u3068$b$\u306e\u5024\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044\uff0e\u305d\u3053\u3067\uff0c\u3053\u306e\u504f\u5c0e\u95a2\u6570\u3092\u4f7f\u3063\u3066\uff0c\u52fe\u914d\u964d\u4e0b\u6cd5\uff08gradient descent\uff09\u306b\u3088\u308b\u30d1\u30e9\u30e1\u30fc\u30bf${\\bf w},b$\u306e\u66f4\u65b0\u3092\u884c\u3046\u3053\u3068\u3067\uff0c\u640d\u5931\u95a2\u6570$\\mathcal{L}({\\bf w},b)$\u306e\u6700\u5c0f\u5316\u3092\u884c\u3046\uff0e\n",
"\n",
"\u3053\u306e\u305f\u3081\u306e\u66f4\u65b0\u5f0f\u306f\u4ee5\u4e0b\u3067\u3042\u308b\uff0e\n",
"\n",
"$${\\bf w} \\leftarrow {\\bf w} - \\eta\\frac{\\partial \\mathcal{L}}{\\partial {\\bf w}}$$\n",
"\n",
"$$b \\leftarrow b - \\eta\\frac{\\partial \\mathcal{L}}{\\partial b}$$\n",
"\n",
"\u305f\u3060\u3057\uff0c$\\eta$\u306f\u5b66\u7fd2\u7387\u3068\u3088\u3070\u308c\uff0c\u4e00\u56de\u306e\u66f4\u65b0\u3067\u3069\u306e\u304f\u3089\u3044\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u5909\u5316\u3055\u305b\u308b\u304b\u3068\u3044\u3046\u5ea6\u5408\u3044\u3092\u8868\u3059\uff0e\u3053\u308c\u304c\u5927\u304d\u3044\u3068\u632f\u52d5\u3057\u306a\u304c\u3089\u6700\u9069\u89e3\u3078\u8fd1\u3065\u304f\u3053\u3068\u306b\u306a\u308a\uff0c\u5c0f\u3055\u3044\u3068\u53ce\u675f\u306b\u6642\u9593\u3092\u8981\u3059\u308b\u3053\u3068\u306b\u306a\u308b\uff0e"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### \u78ba\u7387\u7684\u52fe\u914d\u964d\u4e0b\u6cd5\uff08stochastic gradient descent: SGD\uff09\n",
"\u4e0a\u8a18\u306e\u66f4\u65b0\u5f0f\u306b\u3088\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u66f4\u65b0\u3067\u306f\uff0c\u52fe\u914d\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u6bce\u56de\uff0c\u5168\u3066\u306e\u30c7\u30fc\u30bf\u70b9\u306b\u6e21\u3063\u3066\u548c\u3092\u3068\u308b\u5fc5\u8981\u304c\u3042\u308b\uff0e\u3053\u308c\u306f\uff0c\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u304c\u5927\u304d\u3044\u306a\u5834\u5408\u306f\u975e\u5e38\u306b\u8a08\u7b97\u30b3\u30b9\u30c8\u304c\u5927\u304d\u304f\u306a\u3063\u3066\u3057\u307e\u3046\uff0e\n",
"\n",
"\u305d\u3053\u3067\uff0c\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u4e2d\u304b\u3089\u90e8\u5206\u7684\u306b\u3044\u304f\u3064\u304b\u306e\u30c7\u30fc\u30bf\u70b9\u3092\u9078\u3073\u3068\u3063\u3066\uff0c\u305d\u308c\u3089\u306b\u5bfe\u3057\u3066\u3060\u3051\u4e0a\u8a18\u306e\u548c\u3092\u8a08\u7b97\u3057\u3066\u52fe\u914d\u3068\u3057\uff0c\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u66f4\u65b0\u3059\u308b\u65b9\u6cd5\u304c\u3088\u304f\u3068\u3089\u308c\u308b\uff0e\u3053\u308c\u3092\u78ba\u7387\u7684\u52fe\u914d\u964d\u4e0b\u6cd5\uff08stochastic gradient descent: SGD\uff09\u3068\u547c\u3076\uff0e\u3069\u306e\u30c7\u30fc\u30bf\u70b9\u90e8\u5206\u96c6\u5408\u3092\u9078\u629e\u3059\u308b\u304b\u3092\u78ba\u7387\u7684\u306b\u9078\u3076\u305f\u3081\u3053\u3046\u547c\u3070\u308c\u308b\uff0e\u3053\u306e\u3068\u304d\uff0c\u4e00\u56de\u306e\u66f4\u65b0\u306b\u7528\u3044\u3089\u308c\u308b\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u90e8\u5206\u96c6\u5408\u306e\u3053\u3068\u3092\u30df\u30cb\u30d0\u30c3\u30c1\uff08minibatch\uff09\u3068\u547c\u3076\u3053\u3068\u304c\u3042\u308b\uff0e\n",
"\n",
"\u307e\u305f\uff0c\u52fe\u914d\u306e\u8a08\u7b97\u306e\u969b\uff0c\u4e0a\u5f0f\u306e\u3088\u3046\u306b\u305f\u3060\u7dcf\u548c\u3092\u3068\u308b\u306e\u3067\u306f\u306a\u304f\uff0c\u5e73\u5747\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\uff0c\u901a\u5e38\u306e\u52fe\u914d\u964d\u4e0b\u6cd5\u306e\u5834\u5408\u306f\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u5927\u304d\u3055\u306b\uff0c\u78ba\u7387\u7684\u52fe\u914d\u964d\u4e0b\u6cd5\u306e\u5834\u5408\u306f\u30df\u30cb\u30d0\u30c3\u30c1\u306e\u5927\u304d\u3055\u306b\uff0c\u52fe\u914d\u306e\u5927\u304d\u3055\u304c\u5f71\u97ff\u3055\u308c\u306a\u3044\u3088\u3046\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u3053\u306e\u3088\u3046\u306b\u3059\u308b\u3053\u3068\u3067\u5b66\u7fd2\u7387$\\eta$\u306e\u6c7a\u5b9a\u3082\u5bb9\u6613\u306b\u306a\u308b\uff0e"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### \u5b9f\u88c5\n",
"\u307e\u305a\uff0c2\u3064\u306e\u30af\u30e9\u30b9\u304b\u3089\u751f\u6210\u3055\u308c\u305f\u30c7\u30fc\u30bf\u70b9\u7fa4\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u3059\u308b\uff0e\u305d\u308c\u305e\u308c\u306e\u30c7\u30fc\u30bf\u70b9\u306f\u4e2d\u5fc3\u3092$(0,0),(5,5)$\u306b\u3082\u3064\u5206\u65631\u306e\u6b63\u898f\u5206\u5e03\u304b\u3089100\u500b\u305a\u3064\u30b5\u30f3\u30d7\u30eb\u3055\u308c\u305f\u70b9\u3067\u3042\u308b\uff0e"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"d = 2\n",
"N = 1000\n",
"x1 = np.random.randn(N, d)\n",
"x2 = np.random.randn(N, d) + np.array([5, 5])\n",
"\n",
"plt.scatter(x1[:, 0], x1[:, 1], c='r')\n",
"plt.scatter(x2[:, 0], x2[:, 1], c='b')\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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LYDOAbgACAF4GsFz1bwUQCeBeAM0B/B+Ag5C9PG0A/gPgEIAlADQArQFMAJAB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\n",
"text": [
"<matplotlib.figure.Figure at 0x10b075390>"
]
}
],
"prompt_number": 93
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\u3053\u308c\u3092\u3072\u3068\u3064\u306e\u30c7\u30fc\u30bf\u884c\u5217\u306b\u307e\u3068\u3081\uff0c\u5bfe\u5fdc\u3059\u308b\u30e9\u30d9\u30eb\u30d9\u30af\u30c8\u30eb\u3092\u4f5c\u6210\u3059\u308b\uff0e\u3053\u3053\u3067\u306f\uff0c\u30af\u30e9\u30b91\u306b\u5c5e\u3059\u308b\u30c7\u30fc\u30bf\u70b9\u306b\u306f\u30e9\u30d9\u30eb\u5024$c=0$\u3092\uff0c\u30af\u30e9\u30b92\u306b\u5c5e\u3059\u308b\u30c7\u30fc\u30bf\u70b9\u306b\u306f\u30e9\u30d9\u30eb\u5024$c=1$\u3092\u5bfe\u5fdc\u3055\u305b\u308b\uff0e"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = np.vstack((x1, x2))\n",
"\n",
"label1 = np.zeros(N)\n",
"label2 = np.ones(N)\n",
"label = np.hstack((label1, label2))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 94
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\u30b7\u30b0\u30e2\u30a4\u30c9\u95a2\u6570\u3068\uff0c\u30c7\u30fc\u30bf\u70b9\u7fa4\u884c\u5217\uff08$N \\times d$\uff09\u304b\u3089\u30af\u30e9\u30b9\u5c24\u5ea6\u3092\u7b97\u51fa\u3059\u308b\u95a2\u6570p_y_given_x(x)\u3092\u5b9a\u7fa9\u3059\u308b\uff0e"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def sigmoid(a):\n",
" return 1.0 / (1.0 + np.exp(-a))\n",
"\n",
"def p_y_given_x(x):\n",
" return sigmoid(np.dot(x, w) + b)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 95
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\u30c7\u30fc\u30bf\u70b9\u7fa4\u3068\u6b63\u89e3\u30e9\u30d9\u30eb\u30d9\u30af\u30c8\u30eb\u3092\u3068\u308a\uff0c\u52fe\u914d\u3092\u8fd4\u3059\u95a2\u6570\u3092\u5b9a\u7fa9\u3059\u308b\uff0e"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def grad(x, label):\n",
" error = label - p_y_given_x(x)\n",
" w_grad = -np.mean(x.T * error, axis=1)\n",
" b_grad = -np.mean(error)\n",
" \n",
" return w_grad, b_grad"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 96
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u9069\u5f53\u306b\u521d\u671f\u5316\u3057\u305f\u306e\u3061\uff0c\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u309210\u500b\u305a\u3064\u306e\u30df\u30cb\u30d0\u30c3\u30c1\u306b\u5206\u3051\u3066\uff0c\u78ba\u7387\u7684\u52fe\u914d\u964d\u4e0b\u6cd5\u3092\u7528\u3044\u3066\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u6700\u9069\u5316\u3059\u308b\uff0e"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"dataset = np.column_stack((x,label))\n",
"np.random.shuffle(dataset) #\u30c7\u30fc\u30bf\u70b9\u306e\u9806\u756a\u3092\u30b7\u30e3\u30c3\u30d5\u30eb\n",
"\n",
"x = dataset[:, :2]\n",
"label = dataset[:, 2]\n",
"\n",
"w = np.random.rand(d)\n",
"b = np.random.random()\n",
"\n",
"eta = 0.1\n",
"minibatch_size = 10\n",
"\n",
"errors = list()\n",
"for _ in range(10):\n",
" for index in range(0, x.shape[0], minibatch_size):\n",
" _x = x[index:index + minibatch_size]\n",
" _label = label[index:index + minibatch_size]\n",
" w_grad, b_grad = grad(_x, _label)\n",
" w -= eta * w_grad\n",
" b -= eta * b_grad\n",
" errors.append(np.mean(np.abs(label - p_y_given_x(x))))\n",
"\n",
"print np.mean(np.abs(label - p_y_given_x(x)))\n",
"plt.plot(errors)\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"0.0129718198572\n"
]
},
{
"metadata": {},
"output_type": "display_data",
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jsLAQt9vNV77ylZh+hngx0rasra3F6XRSXFxMcXExO3bsCM3TtgzP7/dz1113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\nAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x10ab8efd0>"
]
}
],
"prompt_number": 97
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\u4e0a\u306e\u30b3\u30fc\u30c9\u3067\u306f\u30df\u30cb\u30d0\u30c3\u30c1\u6700\u9069\u5316\u3092\u3055\u3089\u306b10\u56de\u7e70\u308a\u8fd4\u3057\u3066\u3044\u308b\uff0e\u7e70\u308a\u8fd4\u3057\u3054\u3068\u306b\u30a8\u30e9\u30fc\u3092\u8a18\u9332\u3057\uff0c\u6700\u5f8c\u306b\u305d\u306e\u5909\u5316\u3092\u30b0\u30e9\u30d5\u5316\u3057\u3066\u3044\u308b\uff0e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u66f4\u65b0\u3059\u308b\u305f\u3073\u306b\u8aa4\u5dee\u304c\u6e1b\u3063\u3066\u3044\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308b\uff0e"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### \u5b66\u7fd2\u3055\u308c\u305f\u30d1\u30e9\u30e1\u30fc\u30bf\u306b\u3088\u308b\u76f4\u7dda\uff1a${\\bf w}^{\\rm T}{\\bf x} + b = 0$\u306e\u56f3\u793a"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"bx = np.arange(-6, 10, 0.1)\n",
"by = -b/w[1] - w[0]/w[1]*bx\n",
"\n",
"plt.xlim([-5, 10])\n",
"plt.ylim([-5, 9])\n",
"plt.plot(bx, by)\n",
"plt.scatter(x1[:, 0], x1[:, 1], c='r')\n",
"plt.scatter(x2[:, 0], x2[:, 1], c='b')\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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i+uuv39V3nz6nWkJ91Hqe/8DnyyAlpZH1iFtY0v7ceqp5GA17Ikabz0G6z46b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\nAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x10ab9a2d0>"
]
}
],
"prompt_number": 98
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# \u591a\u6b21\u5143\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\n",
"\u4e0a\u8a18\u306e\u4f8b\u3067\u306f1\u6b21\u5143\u306e\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u3092\u8003\u3048\u305f\uff0e\u3053\u308c\u306f2\u30af\u30e9\u30b9\u5206\u985e\u554f\u984c\u3092\u8003\u3048\u308b\u306e\u306b\u5229\u7528\u3067\u304d\u308b\u3053\u3068\u304c\u5206\u304b\u3063\u305f\uff0e\u3067\u306f\uff0c$K$\u30af\u30e9\u30b9\u5206\u985e\u3092\u8003\u3048\u308b\u5834\u5408\u306f\u3069\u3046\u306a\u308b\u3060\u308d\u3046\u304b\uff0e\u3053\u306e\u5834\u5408\uff0c\u51fa\u529b\u304c$K$\u6b21\u5143\u306e\u30af\u30e9\u30b9\u6240\u5c5e\u5ea6\u78ba\u7387\uff08class-membership probability\uff09\u30d9\u30af\u30c8\u30eb\u3068\u306a\u308b\u3088\u3046\u306b\u30bd\u30d5\u30c8\u30de\u30c3\u30af\u30b9\u95a2\u6570\u3068\u3044\u3046\u306e\u3092\u7528\u3044\u308b\uff0e\u30bd\u30d5\u30c8\u30de\u30c3\u30af\u30b9\u95a2\u6570\u306f\u30b7\u30b0\u30e2\u30a4\u30c9\u95a2\u6570\u306e\u591a\u5909\u91cf\u7248\u3067\u3042\u308a\uff0c$K$\u6b21\u5143\u30d9\u30af\u30c8\u30eb${\\bf a}$\u306e$k$\u756a\u76ee\u306e\u8981\u7d20\u3092$a_k(k=1,\\dots,K)$\u3068\u66f8\u304f\u3053\u3068\u306b\u3059\u308b\u3068\uff0c\n",
"\n",
"$$\n",
"\\def\\softmax{\\boldsymbol\\pi}\n",
"\\pi(a_k) = \\frac{\\exp(a_i)}{\\sum_{j=1}^K \\exp(a_j)}$$\n",
"\n",
"\u3068\u5b9a\u7fa9\u3055\u308c\u308b\uff0e\u4ee5\u964d\uff0c\u4fbf\u5b9c\u4e0a$(\\pi(a_1),\\dots,\\pi(a_K))^{\\rm T}$\u3068\u3044\u3046\u30d9\u30af\u30c8\u30eb\u3092$\\softmax({\\bf a})$\u3068\u66f8\u304f\u3053\u3068\u306b\u3059\u308b\uff0e\n",
"\n",
"\u30bd\u30d5\u30c8\u30de\u30c3\u30af\u30b9\u95a2\u6570\u306b\u30d9\u30af\u30c8\u30eb\u3092\u5165\u529b\u3059\u308b\u3068\uff0c\u51fa\u529b\u3055\u308c\u308b\u5024\u306f\u540c\u6b21\u5143\u306e\u30d9\u30af\u30c8\u30eb\u3068\u306a\u308b\u304c\uff0c\u5404\u8981\u7d20\u306e\u5408\u8a08\u5024\u304c\u5fc5\u305a1\u3068\u306a\u308b\u3088\u3046\u306a\u30d9\u30af\u30c8\u30eb\u3068\u306a\u308b\uff0e\u3059\u306a\u308f\u3061\n",
"\n",
"$$\\sum_{k=1}^K \\pi(a_k) = 1$$\n",
"\n",
"\u304c\u5e38\u306b\u6210\u308a\u7acb\u3064\uff0e\u3088\u3063\u3066\uff0c\u51fa\u529b\u3055\u308c\u308b\u30d9\u30af\u30c8\u30eb\u306f\u96e2\u6563\u78ba\u7387\u5206\u5e03\u3067\u3042\u308b\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"K = 10\n",
"a = np.random.rand(K)\n",
"\n",
"def softmax(a):\n",
" return np.exp(a) / np.sum(np.exp(a))\n",
"\n",
"y = softmax(a)\n",
"\n",
"plt.xlim([-1, K])\n",
"plt.bar(np.arange(K), y, width=0.1)\n",
"plt.show()\n",
"\n",
"print 'summation:', np.sum(y) # \u8981\u7d20\u306e\u5408\u8a08\u5024\u51fa\u529b"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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iQuFwOGn/5ubm2dd+v19+vz+lcQHAFOFweNEsTSZp2LtcLsVisdntWCwmt9udtM3o6Khc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\n",
"text": [
"<matplotlib.figure.Figure at 0x10b06c390>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"summation: 1.0\n"
]
}
],
"prompt_number": 99
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$K$\u30af\u30e9\u30b9\u5206\u985e\u554f\u984c\u306b\u304a\u3044\u3066\uff0c$D$\u6b21\u5143\u30d9\u30af\u30c8\u30eb${\\bf x}$\u3068\uff0c\u305d\u308c\u306b\u5bfe\u5fdc\u3059\u308b\u6b63\u89e3\u30af\u30e9\u30b9$c_k$\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\uff0c\u591a\u6b21\u5143\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u30e2\u30c7\u30eb\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u624b\u9806\u3067\u8a08\u7b97\u3092\u884c\u3046\uff0e\n",
"\n",
"1. $D$\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308b\u30c7\u30fc\u30bf\u70b9${\\bf x}$\u3092$K$\u6b21\u5143\u306b\u5199\u50cf\uff1a$f({\\bf x}) = {\\bf W}^{\\rm T}{\\bf x} + {\\bf b}$\uff08${\\bf W}$\u306f$D \\times K$\u306e\u91cd\u307f\u884c\u5217\uff0c${\\bf b}$\u306f$K$\u6b21\u5143\u30d9\u30af\u30c8\u30eb\uff09\n",
"2. \u30bd\u30d5\u30c8\u30de\u30c3\u30af\u30b9\u95a2\u6570\u306b\u901a\u3057\u3066\u30af\u30e9\u30b9\u6240\u5c5e\u5ea6\u78ba\u7387\u30d9\u30af\u30c8\u30eb\u3092\u8a08\u7b97\uff1a${\\bf y} = \\softmax(f({\\bf x}))$\n",
"3. ${\\bf x}$\u304c\u6240\u5c5e\u3059\u308b\u30af\u30e9\u30b9\u304c$c_k$\u306e\u3068\u304d\uff0c\u6b63\u89e3\u30c7\u30fc\u30bf\u3068\u3057\u3066$k$\u500b\u76ee\u306e\u8981\u7d20\u3060\u3051\u304c1\u3067\u305d\u306e\u4ed6\u306e\u8981\u7d20\u304c0\u3067\u3042\u308b\u3088\u3046\u306a\u6559\u5e2b\u30d9\u30af\u30c8\u30eb${\\bf t}$\uff08\u4f8b\uff1a$(0,\\dots,1,\\dots,0)^{\\rm T}$\uff09\u304c\u7528\u610f\u3055\u308c\u3066\u3044\u308b\u3068\u3059\u308b\uff0e\u3053\u308c\u3092\u7528\u3044\u3066\uff0c\u30c7\u30fc\u30bf\u70b9\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u306e\u30d1\u30e9\u30e1\u30fc\u30bf${\\bf W},{\\bf b}$\u306e\u5c24\u5ea6\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3059\u308b\uff1a\n",
" $$p({\\bf y}={\\bf t} \\mid {\\bf x};{\\bf W},{\\bf b}) = \\prod_{k=1}^K y_k^{t_k}$$\n",
" \u3053\u306e\u3068\u304d\uff0c${\\bf t}$\u306e\u5f62\u3092\u5ff5\u982d\u306b\uff0c$y_k^{t_k}$\u306b\u7740\u76ee\u3059\u308b\u3068\uff0c\u3053\u308c\u306f$k$\u304c${\\bf x}$\u304c\u6240\u5c5e\u3057\u3066\u3044\u308b\u30af\u30e9\u30b9\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u7b49\u3057\u3044\u3068\u304d\u3060\u3051$t_k=1$\u3068\u306a\u3063\u3066$y_k$\u306b\u7b49\u3057\u304f\u306a\u308a\uff0c\u305d\u308c\u4ee5\u5916\u306e$k$\u306e\u3068\u304d\u306f$t_k=0$\u3088\u308a$y_k^0=1$\u3068\u306a\u308b\u4ed5\u7d44\u307f\u3092\u3068\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308b\uff0e\u3053\u308c\u3092\u5168\u3066\u306e\u8981\u7d20$k=1,\\dots,K$\u306b\u6e21\u3063\u3066\u639b\u3051\u3042\u308f\u305b\u3066\u3044\u308b\u306e\u3067\uff0c\u7d50\u679c\u7684\u306b\u30af\u30e9\u30b9\u6240\u5c5e\u5ea6\u78ba\u7387\u30d9\u30af\u30c8\u30eb\u306e\u8981\u7d20\u306e\u3046\u3061\uff0c\u6b63\u89e3\u30af\u30e9\u30b9\u3078\u306e\u6240\u5c5e\u5ea6\u78ba\u7387\u3060\u3051\u3092\u53d6\u308a\u51fa\u3059\u64cd\u4f5c\u306b\u7b49\u3057\u3044\uff0e\n",
"4. $N$\u500b\u306e\u30c7\u30fc\u30bf\u70b9\u304c\u305d\u308c\u305e\u308c\u72ec\u7acb\u306b\u89b3\u6e2c\u3055\u308c\u308b\u3068\u3057\u3066\uff0c\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u5168\u4f53\u306b\u6e21\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u5c24\u5ea6\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3059\u308b\uff1a\n",
" $$\\mathcal{l}({\\bf W},{\\bf b}) = p({\\bf Y}={\\bf T} \\mid {\\bf X};{\\bf W},{\\bf b}) = \\prod_{n=1}^N \\prod_{k=1}^K y_{nk}^{t_{nk}}$$\n",
" \u305f\u3060\u3057\n",
" + ${\\bf Y}$\u306f$N$\u500b\u306e\u30c7\u30fc\u30bf\u306e\u30af\u30e9\u30b9\u6240\u5c5e\u5ea6\u30d9\u30af\u30c8\u30eb\uff08\u5217\u30d9\u30af\u30c8\u30eb\uff09\u3092\u884c\u65b9\u5411\u306b\u4e26\u3079\u305f\u3082\u306e$({\\bf y}_1,\\dots,{\\bf y}_N)$\u3067\u3042\u308a\uff0c\n",
" \n",
" $${\\bf Y} = \\left(\n",
" \\begin{array}{ccc}\n",
" y_{11} & & y_{N1} \\\\\n",
" \\vdots & & \\vdots \\\\\n",
" y_{1k} & \\cdots & y_{Nk} \\\\\n",
" \\vdots & & \\vdots \\\\\n",
" y_{1K} & & y_{NK} \n",
" \\end{array}\n",
" \\right) = \\softmax({\\bf W}^{\\rm T}{\\bf X} + {\\bf B})$$\n",
" \n",
" \u3068\u3044\u3046$K \\times N$\u884c\u5217\n",
" + ${\\bf T}$\u306f$N$\u500b\u306e\u30c7\u30fc\u30bf\u306e\u6559\u5e2b\u30d9\u30af\u30c8\u30eb\uff08\u5217\u30d9\u30af\u30c8\u30eb\uff09\u3092\u884c\u65b9\u5411\u306b\u4e26\u3079\u305f\u3082\u306e$({\\bf t}_1,\\dots,{\\bf t}_N)$\u3067\u3042\u308a\uff0c\n",
" \n",
" $${\\bf T} = \\left(\n",
" \\begin{array}{ccc}\n",
" t_{11} & & t_{N1} \\\\\n",
" \\vdots & & \\vdots \\\\\n",
" t_{1k} & \\cdots & t_{Nk} \\\\\n",
" \\vdots & & \\vdots \\\\\n",
" t_{1K} & & t_{NK} \n",
" \\end{array}\n",
" \\right)$$\n",
" \n",
" \u3068\u3044\u3046$K \\times N$\u884c\u5217\n",
" \n",
" + ${\\bf X}$\u306f\u30c7\u30fc\u30bf\u884c\u5217\uff08\u30c7\u30b6\u30a4\u30f3\u884c\u5217\u3068\u3082\u547c\u3070\u308c\u308b\uff09\u3067\u3042\u308a\uff0c\u30c7\u30fc\u30bf\u30d9\u30af\u30c8\u30eb\uff08\u5217\u30d9\u30af\u30c8\u30eb\uff09\u3092\u884c\u65b9\u5411\u306b\u4e26\u3079\u305f\u3082\u306e$({\\bf x}_1,\\dots,{\\bf x}_N)$\u3067\uff0c\n",
" \n",
" $${\\bf X} = \\left(\n",
" \\begin{array}{ccc}\n",
" x_{11} & & x_{N1} \\\\\n",
" \\vdots & & \\vdots \\\\\n",
" x_{1d} & \\cdots & x_{Nd} \\\\\n",
" \\vdots & & \\vdots \\\\\n",
" x_{1D} & & x_{ND} \n",
" \\end{array}\n",
" \\right)$$\n",
" \n",
" \u3068\u3044\u3046$D \\times N$\u884c\u5217\n",
" + ${\\bf B}$\u306f\u5168\u304f\u540c\u3058$K$\u6b21\u5143\u30d0\u30a4\u30a2\u30b9\u30d9\u30af\u30c8\u30eb${\\bf b}$\u3092\u884c\u65b9\u5411\u306b$N$\u500b\u30b3\u30d4\u30fc\u3057\u305f$K \\times N$\u884c\u5217\n",
" $${\\bf B} = \\left(\n",
" \\begin{array}{ccc}\n",
" b_{1} & & b_{1} \\\\\n",
" \\vdots & & \\vdots \\\\\n",
" b_{k} & \\cdots & b_{k} \\\\\n",
" \\vdots & & \\vdots \\\\\n",
" b_{K} & & b_{K} \n",
" \\end{array}\n",
" \\right)$$\n",
" \n",
" \u3068\u3044\u3046$K \\times N$\u884c\u5217\u306b\u306a\u308b\uff0e\n",
" \n",
"5. \u4e0a\u8a18\u306e\u5c24\u5ea6\u3092\u6700\u5927\u306b\u3059\u308b\u3088\u3046\u306b${\\bf W},{\\bf b}$\u3092\u6c42\u3081\u308b\u3053\u3068\u3067\u5b66\u7fd2\u3092\u884c\u3046"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### \u52fe\u914d\u8a08\u7b97\u306e\u6e96\u5099\n",
"\u5c24\u5ea6$\\mathcal{l}({\\bf W},{\\bf b})$\u3092\u4f8b\u306b\u3088\u3063\u3066\u8ca0\u306e\u5bfe\u6570\u5c24\u5ea6\u306b\u5909\u63db\u3059\u308b\u3068\uff0c\n",
"\n",
"$$\\mathcal{L}({\\bf W},{\\bf b}) = -\\sum_{n=1}^N \\sum_{k=1}^K t_{nk} \\ln y_{nk}$$\n",
"\n",
"\u3068\u306a\u308b\uff0e\u66f4\u65b0\u5f0f\u3092\u6c42\u3081\u308b\u305f\u3081\u306b\u52fe\u914d\u3092\u7b97\u51fa\u3057\u3088\u3046\uff0e\n",
"\n",
"\u30d1\u30e9\u30e1\u30fc\u30bf${\\bf W},{\\bf b}$\u306b\u95a2\u3059\u308b\u52fe\u914d\u306f\uff0c\n",
"\n",
"$$\\frac{\\partial \\mathcal{L}}{\\partial {\\bf W}} = \\left( \\frac{\\partial \\mathcal{L}}{\\partial {\\bf w}_1},\\dots,\\frac{\\partial \\mathcal{L}}{\\partial {\\bf w}_j},\\dots,\\frac{\\partial \\mathcal{L}}{\\partial {\\bf w}_K} \\right)$$\n",
"\n",
"$$\\frac{\\partial \\mathcal{L}}{\\partial {\\bf b}} = \\left( \\frac{\\partial \\mathcal{L}}{\\partial b_1},\\dots,\\frac{\\partial \\mathcal{L}}{\\partial b_j},\\dots,\\frac{\\partial \\mathcal{L}}{\\partial b_K} \\right)$$\n",
"\n",
"\u3092\u8003\u3048\u308c\u3070\u3088\u3044\u304b\u3089\uff0c\u554f\u984c\u3068\u306a\u308b\u306e\u306f$\\frac{\\partial \\mathcal{L}}{\\partial {\\bf w}_j},\\frac{\\partial \\mathcal{L}}{\\partial b_j}$\u3067\u3042\u308b\uff0e"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### $\\frac{\\partial \\mathcal{L}}{\\partial {\\bf w}_j}$\u306e\u8a08\u7b97\n",
"\\begin{eqnarray}\n",
"\\frac{\\partial \\mathcal{L}}{\\partial {\\bf w}_j}\n",
"&=& -\\frac{\\partial}{\\partial {\\bf w}_j}\n",
" \\sum_{n=1}^N \\sum_{k=1}^K\n",
" t_{nk} \\ln y_{nk} \\\\\n",
"&=& -\\sum_{n=1}^N \\sum_{k=1}^K\n",
" t_{nk}\n",
" \\frac{\\partial \\ln y_{nk}}{\\partial y_{nk}}\n",
" \\frac{\\partial y_{nk}}{\\partial a_{nj}}\n",
" \\frac{\\partial a_{nj}}{\\partial {\\bf w}_j} \\\\\n",
"&=& -\\sum_{n=1}^N \\sum_{k=1}^K\n",
" t_{nk}\n",
" \\frac{1}{y_{nk}}\n",
" \\frac{\\partial y_{nk}}{\\partial a_{nj}}\n",
" \\frac{\\partial a_{nj}}{\\partial {\\bf w}_j}\n",
"\\end{eqnarray}\n",
"\n",
"\u3053\u3053\u3067\uff0c${\\bf a}_n = {\\bf W}^{\\rm T}{\\bf x}_n + {\\bf b}$\u3068\u304a\u304d\uff0c\u3053\u306e$k$\u500b\u76ee\u306e\u8981\u7d20\u3092$a_{nk}$\u3068\u66f8\u3044\u305f\uff0e\u307e\u305f\uff0c\n",
"\n",
"$${\\bf y}_n = \\softmax({\\bf a}_n) = (\\pi(a_{n1}),\\dots,\\pi(a_{nK}))^{\\rm T}$$\n",
"\n",
"\u3067\u3042\u308b\u304b\u3089\uff0c$y_{nk} = \\pi(a_{nk})$\u3067\u3042\u308b\uff0e\u5fae\u5206\u306e\u9023\u9396\u5f8b\u306e\u90e8\u5206\u306b\u3064\u3044\u3066\u306f\uff0c\n",
"\n",
"\\begin{eqnarray}\n",
"y_{nk} &=& \\pi(a_{nk}) \\\\\n",
"a_{nk} &=& {\\bf w}_k^{\\rm T}{\\bf x}_n + b_k\n",
"\\end{eqnarray}\n",
"\n",
"\u306b\u6ce8\u610f\u3059\u308b\uff0e\n",
"\n",
"\u3067\u306f\uff0c$\\frac{\\partial y_{nk}}{\\partial a_{nj}}$\u304a\u3088\u3073$\\frac{\\partial a_{nj}}{\\partial {\\bf w}_j}$\u306b\u3064\u3044\u3066\u500b\u5225\u306b\u8003\u3048\u3066\u3044\u304f\uff0e"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### $\\frac{\\partial y_{nk}}{\\partial a_{nj}}$\u306e\u8a08\u7b97\n",
"\u3053\u3053\u3067\u6dfb\u5b57\u306e\u90fd\u5408\u4e0a$\\frac{\\partial y_{nk}}{\\partial a_{nj}}$\u3092\u4e00\u65e6$\\frac{\\partial y_{nk}}{\\partial a_{ni}}$\u3068\u66f8\u304f\u3068\uff0c\n",
"\n",
"+ $i = k$\u306e\u3068\u304d\n",
" \\begin{eqnarray}\n",
" \\frac{\\partial y_{nk}}{\\partial a_{ni}} = \\frac{\\partial \\pi(a_{nk})}{\\partial a_{ni}}\n",
" &=& \\frac{\\exp(a_{nk})}{\\sum_{j=1}^K \\exp(a_{nj})} - \\frac{\\exp(a_{nk})^2}{\\left( \\sum_{j=1}^K \\exp(a_{nj}) \\right)^2} \\\\\n",
" &=& \\pi(a_{nk})(1 - \\pi(a_{nk}))\n",
" \\end{eqnarray}\n",
" \n",
"+ $i \\neq k$\u306e\u3068\u304d\n",
" \\begin{eqnarray}\n",
" \\frac{\\partial y_{nk}}{\\partial a_{ni}} = \\frac{\\partial \\pi(a_{nk})}{\\partial a_{ni}}\n",
" &=& -\\frac{\\exp(a_{ni})\\exp(a_{nk})}{\\left( \\sum_{j=1}^K \\exp(a_{nj}) \\right)^2} \\\\\n",
" &=& -\\pi(a_{ni})\\pi(a_{nk}) \\\\\n",
" &=& \\pi(a_{nk})(0 - \\pi(a_{ni})) \\\\\n",
" \\end{eqnarray}\n",
" \n",
"\u3068\u306a\u308b\u306e\u3067\uff0c\u518d\u3073\u6dfb\u5b57$i$\u3092$j$\u306b\u7f6e\u304d\u63db\u3048\u308b\u3068\uff0c\n",
"\n",
"$$\\frac{\\partial y_{nk}}{\\partial a_{nj}} = y_{nk}({\\bf I}_{jk} - y_{nj})$$\n",
"\n",
"\u3068\u66f8\u3051\u308b\uff0e\u3053\u3053\u3067${\\bf I}_{jk}$\u306f$K \\times K$\u5358\u4f4d\u884c\u5217${\\bf I}$\u306e$(j,k)$\u8981\u7d20\u3067\u3042\u308b\uff0e\u3053\u308c\u306f$j=k$\u306e\u3068\u304d1\u3067\u3042\u308a\uff0c\u305d\u308c\u4ee5\u5916\u306e\u5834\u5408\u306f0\u3092\u3068\u308b\uff0e"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### $\\frac{\\partial a_{nj}}{\\partial {\\bf w}_j}$\u306e\u8a08\u7b97\n",
"\n",
"$$\\frac{\\partial a_{nj}}{\\partial {\\bf w}_j} = \\frac{\\partial}{\\partial {\\bf w}_j}({\\bf w}_j^{\\rm T}{\\bf x}_n + b_j) = {\\bf x}_n$$\n",
"\n",
"\u3067\u3042\u308b\uff0e"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### ${\\bf w}_j$\u306b\u95a2\u3059\u308b\u52fe\u914d\n",
"\u4e0a\u8a18\u306e\u7d50\u679c\u3092\u7528\u3044\u308b\u3068\uff0c\n",
"\n",
"$$\\frac{\\partial \\mathcal{L}}{\\partial {\\bf w}_j}\n",
"= -\\sum_{n=1}^N \\sum_{k=1}^K t_{nk} {\\bf x}_n ({\\bf I}_{jk} - y_{nj})\n",
"= -\\sum_{n=1}^N {\\bf x}_n \\left\\{ \\sum_{k=1}^K t_{nk}{\\bf I}_{kj} - \\sum_{k=1}^K t_{nk}y_{nj} \\right\\}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\u3068\u306a\u308b\uff0e\u3053\u3053\u3067\uff0c${\\bf I}_{kj}$\u306f\uff0c$j=k$\u306e\u3068\u304d\u3060\u30511\u3067\uff0c\u305d\u308c\u4ee5\u5916\u306e\u3068\u304d\u306f0\u3060\u304b\u3089\uff0c$\\sum_{k=1}^K t_{nk}{\\bf I}_{kj} = t_{nj}$\u3068\u66f8\u3051\u308b\uff0e\u307e\u305f\uff0c$\\sum_{k=1}^N t_{nk}y_{nj}$\u306b\u304a\u3051\u308b$y_{nj}$\u306f\uff0c\u3053\u306e\u548c\u3092\u3068\u308b\u9593\u306f\u4e0d\u5909\u3067\u3042\u308a\uff0c\u307e\u305f\u3053\u306e\u3068\u304d$t_{nk}$\u306f$k=1,\\dots,K$\u306e\u3044\u305a\u308c\u304b1\u3064\u3067\u3060\u30511\u3092\u3068\u308a\uff0c\u305d\u308c\u4ee5\u5916\u306e\u3068\u304d\u306f0\u3067\u3042\u308b\u6559\u5e2b\u4fe1\u53f7\u3060\u304b\u3089\uff0c$\\sum_{k=1}^N t_{nk}y_{nj} = y_{nj}$\u3068\u3057\u3066\u554f\u984c\u306a\u3044\uff0e"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\u3059\u308b\u3068\uff0c\u7d50\u5c40\n",
"\n",
"$$\\frac{\\partial \\mathcal{L}}{\\partial {\\bf w}_j} = \\sum_{n=1}^N (y_{nj} - t_{nj}){\\bf x}_n$$\n",
"\n",
"\u3068\u3044\u3046\u30b7\u30f3\u30d7\u30eb\u306a\u5f62\u306b\u5909\u5f62\u3067\u304d\u308b\uff0e"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### $b_j$\u306b\u95a2\u3059\u308b\u52fe\u914d\n",
"$b_j$\u3067\u504f\u5fae\u5206\u3059\u308b\u3053\u3068\u3067\u5909\u5316\u3059\u308b\u306e\u306f\uff0c\u9023\u9396\u5f8b\u306e\u6700\u5f8c\u304c$\\frac{\\partial a_{nj}}{\\partial b_j} = 1$\u306b\u306a\u308b\u3060\u3051\u306a\u306e\u3067\uff0c\n",
"\n",
"$$\\frac{\\partial \\mathcal{L}}{\\partial b_j} = \\sum_{n=1}^N (y_{nj} - t_{nj})$$\n",
"\n",
"\n",
"\u3067\u3042\u308b\uff0e"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### \u66f4\u65b0\u5f0f\n",
"\u4e0a\u8a18\u306e\u52fe\u914d\u3092\u7528\u3044\u3066\u66f4\u65b0\u5f0f\u3092\u5b9a\u7fa9\u3059\u308b\uff0e\n",
"\n",
"$${\\bf w}_j \\leftarrow {\\bf w}_j - \\eta \\frac{\\partial \\mathcal{L}}{\\partial {\\bf w}_j} = {\\bf w}_j - \\eta \\sum_{n=1}^N (y_{nj} - t_{nj}){\\bf x}_n$$\n",
"\n",
"$$b_j \\leftarrow b_j - \\eta \\frac{\\partial \\mathcal{L}}{\\partial b_j} = b_j - \\eta \\sum_{n=1}^N (y_{nj} - t_{nj})$$\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### \u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u6271\u3044\u306b\u3064\u3044\u3066\n",
"1\u6b21\u5143\uff0f\u591a\u6b21\u5143\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u53cc\u65b9\u306b\u304a\u3044\u3066\u30e2\u30c7\u30eb\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3042\u308b\u91cd\u307f\u3068\u30d0\u30a4\u30a2\u30b9\u3092${\\bf w}, b(or\\ {\\bf b})$\u306e\u3088\u3046\u306b\u5225\u3005\u306b\u6271\u3063\u3066\u3044\u305f\u304c\uff0c\u3053\u308c\u306f\u30c7\u30fc\u30bf\u70b9\u30d9\u30af\u30c8\u30eb\u3092$\\tilde{\\bf x} = (1, x_0, \\dots, x_D)$\u306e\u3088\u3046\u306b\u6700\u521d\u306e\u6b21\u5143\u304c\u3064\u306d\u306b1\u3068\u306a\u308b\u62e1\u5f35\u30d9\u30af\u30c8\u30eb\u3068\u3057\u3066\u6271\u3044\uff0c\u91cd\u307f\u3092$\\tilde{\\bf w} = (w_0, w_1, \\dots, w_K)$\u306e\u3088\u3046\u306b\u3057\u3066\u30d0\u30a4\u30a2\u30b9\u30921\u3064\u3081\u306e\u6b21\u5143\u306b\u8ffd\u52a0\u3057\u3066\u6271\u3048\u3070\uff0c$\\tilde{\\bf w}^{\\rm T}\\tilde{\\bf x}$\u3068\u3057\u3066\u3053\u308c\u307e\u3067\u306e${\\bf w}^{\\rm T}{\\bf x} + b$\u3092\u6271\u3048\u308b\uff0e\u591a\u6b21\u5143\u306e\u5834\u5408\u3082\u540c\u69d8\u3067\uff0c$\\tilde{\\bf W}^{\\rm T}\\tilde{\\bf x}$\u3068\u6271\u3048\u308b\u3088\u3046\u306b\u306a\u308b\uff0e\u3059\u308b\u3068\u3053\u308c\u307e\u3067\u306e\u66f4\u65b0\u5f0f\u306e\u5c0e\u51fa\u306a\u3069\u306b\u304a\u3051\u308b\u30d0\u30a4\u30a2\u30b9\u306e\u8003\u616e\u306f\uff08\u6570\u5f0f\u4e0a\uff09\u5fc5\u8981\u304c\u306a\u304f\u306a\u308b\uff0e\u81ea\u52d5\u7684\u306b\u91cd\u307f\u306e\u4e2d\u306e\u8981\u7d20\u306e\u3072\u3068\u3064\u3068\u3057\u3066\u6271\u308f\u308c\u308b\u3088\u3046\u306b\u306a\u308b\u304b\u3089\u3067\u3042\u308b\uff0e"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### \u5b9f\u88c5\n",
"\u307e\u305a\u306f\u30c7\u30fc\u30bf\u70b9\u3068\u30e9\u30d9\u30eb\u306e\u30bb\u30c3\u30c8\u3092\u7528\u610f\u3059\u308b\uff0e"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"D = 2\n",
"N = 1500\n",
"K = 3\n",
"\n",
"# \u30c7\u30fc\u30bf\u70b9\u3092\u7528\u610f\n",
"mean1 = [-2, 2] # \u30af\u30e9\u30b91\u306e\u5e73\u5747\n",
"mean2 = [0, 0] # \u30af\u30e9\u30b92\u306e\u5e73\u5747\n",
"mean3 = [2, -2] # \u30af\u30e9\u30b93\u306e\u5e73\u5747\n",
"cov = [[1.0,0.8], [0.8,1.0]] # \u5171\u5206\u6563\u884c\u5217\uff08\u5168\u30af\u30e9\u30b9\u5171\u901a\uff09\n",
"\n",
"x1 = np.random.multivariate_normal(mean1, cov, N / 3)\n",
"x2 = np.random.multivariate_normal(mean2, cov, N / 3)\n",
"x3 = np.random.multivariate_normal(mean3, cov, N / 3)\n",
"x = np.vstack((x1, x2, x3))\n",
"\n",
"# \u6559\u5e2b\u30d9\u30af\u30c8\u30eb\u3092\u7528\u610f\n",
"label1 = np.zeros((N / 3, 3), dtype=np.int32) + np.array([1, 0, 0])\n",
"label2 = np.zeros((N / 3, 3), dtype=np.int32) + np.array([0, 1, 0])\n",
"label3 = np.zeros((N / 3, 3), dtype=np.int32) + np.array([0, 0, 1])\n",
"label = np.vstack((label1, label2, label3))\n",
"\n",
"# \u56f3\u793a\n",
"plt.xlim((-6, 6))\n",
"plt.ylim((-6, 6))\n",
"plt.scatter(x1[:, 0], x1[:, 1], c='r')\n",
"plt.scatter(x2[:, 0], x2[:, 1], c='g')\n",
"plt.scatter(x3[:, 0], x3[:, 1], c='b')\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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HEqiBFeyo/T0MqpOZqXNHjNDmzZsVj8f1/vvva9asWWpRs6b6WtHOsseErVAXnfskUCQQ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/AAAg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\ncd68eTxx4sQl5xUb2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"text": [
"<matplotlib.figure.Figure at 0x10d08de90>"
]
}
],
"prompt_number": 100
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\u4e0a\u3067\u5b9a\u7fa9\u3057\u305f\u30bd\u30d5\u30c8\u30de\u30c3\u30af\u30b9\u95a2\u6570\u306f\u8907\u6570\u306e\u591a\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306b\u5bfe\u3057\u3066\u30d9\u30af\u30c8\u30eb\u3054\u3068\u306bsoftmax\u3092\u8a08\u7b97\u3059\u308b\u4ed5\u69d8\u306b\u306a\u3063\u3066\u3044\u306a\u3044\u306e\u3067\uff0c\u8907\u6570\u30d9\u30af\u30c8\u30eb\u3092\u884c\u5217\u3068\u3057\u3066\u6e21\u3057\u305f\u5834\u5408\u306b\u3082\u6b63\u3057\u304f\u30d9\u30af\u30c8\u30eb\u3054\u3068\u306bsoftmax\u304c\u9069\u7528\u3055\u308c\u305f\u3082\u306e\u3092\u8fd4\u3059\u95a2\u6570\u3068\u3057\u3066\u518d\u5b9a\u7fa9\u3059\u308b\uff0e\n",
"\n",
"\u6b21\u306b\uff0c$\\softmax({\\bf W}^{\\rm T}{\\bf X} + {\\bf b})$\u3092\u8a08\u7b97\u3059\u308b\u95a2\u6570p_y_given_x(x)\u3092\u7528\u610f\u3059\u308b\uff0e\u3053\u308c\u306f\u4e0e\u3048\u3089\u308c\u305f\u30c7\u30fc\u30bf\u70b9\u304c\u5217\u65b9\u5411\u306b\u4e26\u3093\u3060$N \\times D$\u6b21\u5143\u306e\u884c\u5217\u3092\u4e0e\u3048\u308b\u3068\uff0c\u884c\u3054\u3068\uff08\u30c7\u30fc\u30bf\u70b9\u3054\u3068\uff09\u306b\u5404\u30af\u30e9\u30b9\u3078\u306e\u6240\u5c5e\u5ea6\u78ba\u7387\u30d9\u30af\u30c8\u30eb\u3092\u8a08\u7b97\u3057\uff0c\u3053\u308c\u3092\u5217\u65b9\u5411\u3078\u4e26\u3079\u305f$N \\times K$\u884c\u5217\u3092\u8fd4\u3059\u95a2\u6570\u3067\u3042\u308b\uff0e\n",
"\n",
"grad\u95a2\u6570\u306f\u4e0a\u3067\u5b9a\u7fa9\u3057\u305f\u52fe\u914d\u3092\u6c42\u3081\u308b\u95a2\u6570\u3067\u3042\u308b\uff0e\u5b9a\u7fa9\u3067\u306f\u7dcf\u548c\u3092\u3068\u3063\u3066\u3044\u305f\u304c\uff0c\u3053\u3053\u3067\u306f\u5e73\u5747\u3092\u3068\u308b\u3053\u3068\u306b\u3059\u308b\uff0e"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"dataset = np.column_stack((x, label))\n",
"np.random.shuffle(dataset) #\u30c7\u30fc\u30bf\u70b9\u306e\u9806\u756a\u3092\u30b7\u30e3\u30c3\u30d5\u30eb\n",
"\n",
"x = dataset[:, :2]\n",
"label = dataset[:, 2:]\n",
"\n",
"def softmax(x):\n",
" return (np.exp(x).T / np.sum(np.exp(x), axis=1)).T\n",
"\n",
"def p_y_given_x(x):\n",
" return softmax(np.dot(x, w.T) + b)\n",
"\n",
"def grad(x, label):\n",
" error = p_y_given_x(x) - label\n",
" w_grad = np.zeros_like(w)\n",
" b_grad = np.zeros_like(b)\n",
" \n",
" for j in range(w.shape[0]):\n",
" w_grad[j] = np.mean(error[:, j] * x.T, axis=1)\n",
" b_grad[j] = np.mean(error[:, j])\n",
" \n",
" return w_grad, b_grad, np.mean(np.abs(error), axis=0)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 101
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\u5b9f\u969b\u306e\u5b66\u7fd2\u3092\u884c\u3046\u524d\u306b\uff0c\u5b66\u7fd2\u7387$\\eta$\u3068\u30df\u30cb\u30d0\u30c3\u30c1\u30b5\u30a4\u30ba\u3092\u8a2d\u5b9a\u3059\u308b\uff0e\u5b66\u7fd2\u30eb\u30fc\u30d7\u3067\u306f\u30df\u30cb\u30d0\u30c3\u30c1\u3054\u3068\u306b\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u5168\u4f53\u3092\u5b66\u7fd2\u3059\u308b\u3053\u3068\u3092100\u56de\u7e70\u308a\u8fd4\u3057\u3066\u3044\u308b\uff0e\u7d50\u679c\u3068\u3057\u3066\u5404\u30af\u30e9\u30b9\u3078\u6240\u5c5e\u5ea6\u78ba\u7387\u306e\u8aa4\u5dee\u306e\u5e73\u5747\u306e\u63a8\u79fb\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u3066\u3044\u308b\uff0e"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"w = np.random.rand(K, D)\n",
"b = np.random.rand(K)\n",
"\n",
"eta = 0.1\n",
"minibatch_size = 500\n",
"\n",
"# import numpy.linalg as LA\n",
"\n",
"errors = []\n",
"for _ in range(100):\n",
" for index in range(0, N, minibatch_size):\n",
" _x = x[index: index+minibatch_size]\n",
" _label = label[index: index+minibatch_size]\n",
" w_grad, b_grad, error = grad(_x, _label)\n",
" w -= eta * w_grad\n",
" b -= eta * b_grad\n",
"\n",
" errors.append(error)\n",
"errors = np.asarray(errors)\n",
"\n",
"plt.plot(errors[:, 0])\n",
"plt.plot(errors[:, 1])\n",
"plt.plot(errors[:, 2])\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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SMsbY+0dlAV5DTwMZasZIvvzwlb5nZ2AHLXUttLZvDQsdC8Rnx2NX5C602dQGGQUZb6m0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\nPzDlJKXPvFEmAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x10b04ced0>"
]
}
],
"prompt_number": 102
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\u3055\u3089\u306b\uff0c\u8b58\u5225\u5883\u754c\u3092\u4ee5\u4e0b\u306b\u56f3\u793a\u3059\u308b\uff0e"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"bx = np.arange(-10, 10, 0.1)\n",
"by0 = -(w[0, 0] - w[1, 0]) / (w[0, 1] - w[1, 1]) * bx - (b[0] - b[1]) / (w[0, 1] - w[1, 1])\n",
"by1 = -(w[1, 0] - w[2, 0]) / (w[1, 1] - w[2, 1]) * bx - (b[1] - b[2]) / (w[1, 1] - w[2, 1])\n",
"\n",
"plt.plot(bx, by0)\n",
"plt.plot(bx, by1)\n",
"\n",
"plt.xlim((-6, 6))\n",
"plt.ylim((-6, 6))\n",
"plt.scatter(x1[:, 0], x1[:, 1], c='r')\n",
"plt.scatter(x2[:, 0], x2[:, 1], c='g')\n",
"plt.scatter(x3[:, 0], x3[:, 1], c='b')\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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0aLU0SS+4M0QZ+m6IPO4VAD0tFrZo2DDdq14KUY7eDCKHezxEW1gFItXQCfCI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\nLdVYeB4hywX81KlTrF+/PkNDQ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"text": [
"<matplotlib.figure.Figure at 0x10ab9a390>"
]
}
],
"prompt_number": 103
}
],
"metadata": {}
}
]
}
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