{ "cells": [ { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "簡単な具体例について考えることにする。" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## 例1" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "意見は有限でなく、$[0,1]$の間の値を一様な確率で取るとする。このとき、そうして得られた確率変数$x$に関して、\n", "確率密度関数$f(x)$は\n", "\n", "$$f(x) = 1\\ \\ \\ (0\\le x \\le 1)\\ \\ \\ \\text{otherwise}\\ \\ 0$$\n", "\n", "である。累積分布関数$F(x)$は\n", "\n", "$$F(x) = x\\ \\ \\ (0\\le x \\le 1)$$\n", "\n", "となる。" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "subslide" } }, "source": [ "$i$が$k$番目に発言したあと、$j$が$k+1$番目に発言する確率が、発言者の人数を$n$人として、沈黙を含めない時、\n", "\n", "$$p_{i}(k,j) = p(n) = \\frac{1}{n}$$\n", "\n", "のように、誰が発言する確率も等しい場合を考えることとする。" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "subslide" } }, "source": [ "$j$が発言するとき、その発言$x^{j}$は確率変数であり、その期待値と分散は\n", "\n", "$$ E(x^{j}) = \\frac{1}{2}$$\n", "$$ V(x^{j}) = \\frac{1}{12}$$\n", "である。\n" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "以上の議論とは関係なく、誰が発言しようと、その発言が一様な確率で$[0,1]$の間の値を取るとすると、この問題は結局ある閾値$r(0 \n" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "subslide" } }, "source": [ "一様な確率で$[0,1]$の間の数が選ばれるとき、その確率変数が$[\\max(0,x-r), \\min(x+r,1)]$の範囲に入っている確率は、確率密度関数を用いて、\n", "\n", "\n", "\\begin{align}\n", "p(\\max(0, x-r), \\min(x+r, 1)) &= \\int ^{\\min(x+r,1)}_{\\max(0, x-r)} 1 dx \\\\\n", "&= \\left[ x\\right]^{\\min(x+r,1)}_{\\max(0, x-r)}\\\\\n", "\\end{align}\n", "\n", "よって\n", "\n", "$$p(x,r)= \\left\\{ \\begin{array}{ll}x+r & 0\\le x< \\min(r,1-r) \\\\\n", "p(r) = \\min(2r, 1) & \\min(r, 1-r)\\le x \\le \\max(1-r, r) \\\\\n", "1 - x+r & \\max(1-r, r) < x \\le 1\n", "\\end{array}\\right.$$\n", "\n", "を得る。これはグラフにすると下図のようになる。\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "from IPython.html.widgets import interactive\n", "from IPython.display import display\n", "import numpy as np\n", "\n", "def plot_p(r=0.1):\n", " plt.figure(figsize=(10,8))\n", " x = np.array([0, min(r, 1-r), max(1-r,r), 1])\n", " y = np.array([r, min(2*r, 1), min(2*r, 1), r])\n", " plt.plot(x,y)\n", " _x = [-0.1,1.1]\n", " _y = [1,1]\n", " plt.plot(_x, _y, '--d')\n", " plt.xlabel(r'$x$')\n", " plt.ylabel(r'$p(x)$')\n", " plt.title(r'graph of $x$ - $p(x)$ when $r=%1.2f$' % r)\n", " plt.xlim(0,1)\n", " plt.ylim(0, 1.2)\n", " plt.show()\n", "\n", "w = interactive(plot_p, r=(0.01, 1., 0.01))\n", "display(w)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "これまで考えてきたように、会議の合意が得られたとする指標を、ある発言がなされた時に、それまでの発言のうちのいくつかに関連があることが条件であった。このリンクの結び方を、単純にその間の長さが一定値より小さければつなぐことにすると、これまでの考察をそのまま使うことができて、\n", "\n", "$k+1$番目の発言$x_{k}$がなされた時、$k$番目までの発言のうち$y$個の発言が領域$[\\max(0,x-r), \\min(x+r,1)]$の中に存在する確率は、\n", "\n", "$$_{k}C_{y}[p(r)]^{y}[p(r)]^{k-y}$$\n", "\n", "で表せる。" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_type": "subslide" }, "slideshow": { "slide_type": "subslide" } }, "source": [ "これは、\n", "\n", "$$P[X=y] =\\ _{k}C_{y}[p(r)]^{y}[1-p(r)]^{k-y}$$\n", "\n", "のように書けば明らかなように、確率変数$X$に対するパラメータ$k,p$の二項分布$B(k,p)$を表している。ここで注意すべき点は、$p(x_{k}, r)$は$x_{k}$によって変わるものであったから、$x$に対して期待値を取ったものを考えなければならないことである。$p(r)$はそのようにして得られた期待値であることを意味している。\n", "\n", "\n", "この時、確率変数$X$に対する期待値と分散は、\n", "\n", "$$E(X) = kp(r)$$\n", "\n", "$$V(X) = kp(r)(1-p(r))$$\n", "\n", "$X$の最頻値は、$(k+1)p$以下の最大の整数。ただし、$m = (k+1)p$において$m$が整数である場合、$m − 1$と$m$の双方が最頻値となる。" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "-" } }, "source": [ "また、時刻$k$が大きい時には二項分布は正規分布に近似できるので、期待値は中央値とほぼ等しくなる。" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "subslide" } }, "source": [ "以上から、リンクの張り方に関する閾値$y$の選び方として\n", "\n", "$$y = kp(x_{k+1}, r),$$\n", "$$\\ ^{\\forall} k\\ \\text{which satisfy}\\ kp(x_{k+1}, r) > 5\\\\\n", "\\text{and}\\ kp(x_{k+1}, r)(1-p(x_{k+1},r)) > 5$$\n", "\n", "というのが考えられる。このようにすれば、この条件を満たすどんな時刻$k$においても、またどのような閾値$r$を設定したとしても、時刻$k+1$で選ばれた$x_{k+1}$の$r$によって定まる領域において、$y$個以上の他の点を見出す確率を$1/2$とできる。" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "subslide" } }, "source": [ "すなわち、時刻の依存性はないため、$x_{k+1}$のまわりの領域に$y$個以上の他の点が存在する場合を1、存在しない場合を0とすれば、これらの起こる確率は、それぞれ$1/2$であるから、$k$回目に試行が終了する確率は$p=1/2$の[幾何分布](http://ja.wikipedia.org/wiki/%E5%B9%BE%E4%BD%95%E5%88%86%E5%B8%83)に従う:" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "subslide" } }, "source": [ "$$P[X=k] = \\left( \\frac{1}{2} \\right)^{k}$$\n", "\n", "このときの期待値と分散は\n", "\n", "$$E(X) = \\frac{1}{p} = 2$$\n", "$$V(X) = \\frac{1-p}{p^{2}} = 2$$\n", "\n", "すなわち、これまでのような場合を考えたとすると、平均として2回で試行が終了し、ほとんどの試行は1~3回で終了することになる。しかし、これは先程述べたような二項分布の正規分布への近似ができない領域であることに注意が必要である。したがって、実際には$y$の選び方をうまく選ぶことによって(たとえば試行が終了する回数の期待値が、二項分布を正規分布に近似できるような$k$となるように$p$を決めるような$y$)、実際に$k$の期待値はこの確率分布のものと等しくなるだろう。" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "以上の試行はあくまで閾値$y$を$y=kp(r)$とした場合のものであったが、実際の会議の場面を想定するなら、人数が多くなるほど結論に必要な時間は増大すると見るべきで、したがって今のような完全にランダムな発言の場合において$y$の選び方は、少なくとも今の選び方よりも大きい値となるようにしなければならない。" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_number": 15, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "fragment" } }, "source": [ "また、二項分布$B(k,p)$のことを思い出せば、$y$の選び方をうまくとれば、任意の時刻$k$と閾値$r$について$p$の値が固定されるように$y$の値を決めることができ、その時の試行回数は先ほどの幾何分布に従う。" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 15, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "最後にこの例の条件と結果を整理する。\n", "\n", "条件:\n", "\n", "- 沈黙なし\n", "- 発言者は等確率で選ぶ\n", "- 発言は[0,1]の一様乱数\n", "\n", "結果:\n", "\n", "- 発言がなされたときにリンクが張られる数は二項分布$B(k,p(x_{k+1},r))$に従う\n", "- $y$を$k,r$にしたがって変化する適当な関数におけば、リンクの個数が$y$個を超えるのに必要な時間は幾何分布に従う\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "source": [ "## 単純に試したもの" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": true, "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "import scipy.misc as sc\n", "\n", "k = np.arange(2, 100)\n", "\n", "def prob(r, y):\n", " # p(x,r) = p(r) = 2*rとする\n", " # 時系列に対して確率を求める\n", " p = []\n", " for _k in k:\n", " _p = 0.\n", " _y = int(y)\n", " while _y < _k+1:\n", " _p += sc.comb(_k, _y, exact=True)*((2*r)**_y)*((1-2*r)**(_k-_y))\n", " _y += 1\n", " p.append(_p)\n", " return p" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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l4JREx6tpkCHVM27A2k+wtl7oulLD669/80HbjZfU6rufG97/mFZreznrIf51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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y = np.arange(1, 30)\n", "r = 0.1\n", "for _y in y:\n", " p = prob(r, int(_y))\n", " plt.plot(k, np.array(p), label=r\"$y=%1.1f$\" % _y)\n", "plt.xlabel(r'$k$')\n", "plt.ylabel(r'$p_{y}(r=%1.1f,k)$' % r)\n", "\n", "plt.show()\n", " " ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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AT7X2s306Bo3BaoKN3WJe06dPBXV1R6VHoPaMZMVXy9jvFMQKbARCYIXAqgZr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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r = np.linspace(0.01, 0.49, 10)\n", "y = 10\n", "for _r in r:\n", " p = prob(_r, y)\n", " plt.plot(k, np.array(p), label=r\"$r=%1.1f$\" % _r)\n", "plt.xlabel(r'$k$')\n", "plt.ylabel(r'$p_{r}(y=%d, k)$' % y)\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(array([75, 76, 77, 79, 82, 83, 84, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96,\n", " 97]),)\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y = 19\n", "r = 0.1\n", "p = prob(r, y)\n", "a = np.array(p)<0\n", "print np.where(a)\n", "plt.plot(k, p)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.186723864824\n" ] } ], "source": [ "_p = 0.\n", "_y = 19\n", "_k = 77\n", "r = 0.1\n", "while _y < _k+1:\n", " _p += sc.comb(_k, _y, exact=True)*((2*r)**_y)*((1-2*r)**(_k-_y))\n", " _y += 1\n", "print _p" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "text/plain": [ "6" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import itertools\n", "a = itertools.combinations('ABCD', 2)\n", "len(list(a))" ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "text/plain": [ "array(5.0774988410545005e+17)" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import scipy.misc as sc\n", "sc.comb(77, 19)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 15, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "skip" } }, "source": [ "組み合わせの大きさは膨大になりすぎ、小さい数に対して何十乗の計算を行っているために、誤差は無視できないほど大きくなる。大体$k=60$を超えると、信頼できる結果は得られそうにない。" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 0 }