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@CookieBox26
Last active April 17, 2019 11:39
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"参考文献: 渡辺澄夫(2012). ベイズ統計の理論と方法. コロナ社. 207ページ\n",
"\n",
"## 下の図について\n",
"\n",
"下の4図で、x から y を予測した回帰直線は赤い実線(どの図でもほぼ $y = -x$ のはず)だが、 \n",
"y から x を予測した回帰直線は青い実線である(逆関数 $x = -y$ からはずれている)。\n",
" \n",
"つまり、x が赤い点線の値のときの y の期待値は赤い点の y 座標だが、 \n",
"y が赤い点の y 座標のときの、つまり、y が青い点線の値のときの x の期待値は \n",
"青い点の x 座標である(赤い点の x 座標とは一致しない)。 \n",
" \n",
"下の方の図ほど青い点は赤い点から離れていく。\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/html": [
"<h2>分散共分散行列が 0.5 * [[1, -1], [-1, 1.1]] のとき</h2>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"x から y を予測したときの傾きは -1.0039932854371592\n",
"y から x を予測したときの傾きは -0.9031533769666772\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"<h2>分散共分散行列が 0.5 * [[1, -1], [-1, 2]] のとき(テキストと同じ)</h2>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"x から y を予測したときの傾きは -0.9976396610648335\n",
"y から x を予測したときの傾きは -0.49671596845194893\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"<h2>分散共分散行列が 0.5 * [[1, -1], [-1, 5]] のとき</h2>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"x から y を予測したときの傾きは -1.021153603474749\n",
"y から x を予測したときの傾きは -0.20048167863398375\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"<h2>分散共分散行列が 0.5 * [[1, -1], [-1, 20]] のとき</h2>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"x から y を予測したときの傾きは -0.9834603133277302\n",
"y から x を予測したときの傾きは -0.048815839086047697\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from IPython.core.display import display, HTML\n",
"import numpy as np\n",
"from matplotlib import pyplot as plt\n",
"import seaborn as sns\n",
"from pylab import rcParams\n",
"rcParams['figure.figsize'] = 6, 6\n",
"\n",
"def my_plot(mu, sigma):\n",
" # 描画範囲\n",
" xl = [-6, 6] #[-4.0 * np.sqrt(sigma[1][1]), 4.0 * np.sqrt(sigma[1][1])]\n",
" yl = [-6, 6] #[-4.0 * np.sqrt(sigma[1][1]), 4.0 * np.sqrt(sigma[1][1])]\n",
" \n",
" # 2次元正規乱数を1万個生成\n",
" values = np.random.multivariate_normal(mu, sigma, 10000)\n",
" # 周辺ヒストグラム付き散布図のプロット\n",
" #g = sns.jointplot(values[:,0], values[:,1], xlim=xl, ylim=yl, color='gray')\n",
" #plt.show()\n",
"\n",
" # 回帰\n",
" fit0 = np.polyfit(values[:,0], values[:,1], 1)\n",
" print('x から y を予測したときの傾きは {}'.format(fit0[0]))\n",
" fit1 = np.polyfit(values[:,1], values[:,0], 1)\n",
" print('y から x を予測したときの傾きは {}'.format(fit1[0]))\n",
"\n",
" # 回帰のプロット\n",
" plt.scatter(values[:,0], values[:,1], c='gray')\n",
"\n",
" plt.plot(xl, np.poly1d(fit0)(xl), c='red') # x から y を予測した回帰直線(赤線)\n",
" plt.plot([-1, -1], yl, c='red', linestyle='dashed') # x = -1 断面(赤点線)\n",
" plt.scatter(-1, np.poly1d(fit0)(-1), c='red', marker='o', s=100) # x = -1 における y の期待値(赤い点)\n",
"\n",
" plt.plot(np.poly1d(fit1)(yl), yl, c='blue') # y から x を予測した回帰直線(青線)\n",
" plt.plot(xl, [1, 1], c='blue', linestyle='dashed') # y = 1 断面(青点線)\n",
" plt.scatter(np.poly1d(fit1)(1), 1, c='blue', marker='o', s=100) # y = 1 における x の期待値(青い点)\n",
"\n",
" plt.xlim(xl)\n",
" plt.ylim(yl)\n",
" plt.show()\n",
"\n",
"display(HTML('<h2>分散共分散行列が 0.5 * [[1, -1], [-1, 1.1]] のとき</h2>'))\n",
"mu = [0, 0]\n",
"sigma = 0.5 * np.array([[1, -1], [-1, 1.1]])\n",
"my_plot(mu, sigma)\n",
" \n",
"display(HTML('<h2>分散共分散行列が 0.5 * [[1, -1], [-1, 2]] のとき(テキストと同じ)</h2>'))\n",
"mu = [0, 0]\n",
"sigma = 0.5 * np.array([[1, -1], [-1, 2]])\n",
"my_plot(mu, sigma)\n",
"\n",
"display(HTML('<h2>分散共分散行列が 0.5 * [[1, -1], [-1, 5]] のとき</h2>'))\n",
"mu = [0, 0]\n",
"sigma = 0.5 * np.array([[1, -1], [-1, 5]])\n",
"my_plot(mu, sigma)\n",
"\n",
"display(HTML('<h2>分散共分散行列が 0.5 * [[1, -1], [-1, 20]] のとき</h2>'))\n",
"mu = [0, 0]\n",
"sigma = 0.5 * np.array([[1, -1], [-1, 20]])\n",
"my_plot(mu, sigma)"
]
},
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"### 上の図で考えた分布\n",
"分散共分散行列が以下($s > 1$)で平均が $(0, 0)$ の2変量正規分布を考えた(テキスト 207 ページの例はこれの $s=2$ に相当する)。$x$ の周辺分布は $s$ によらないが、$y$ の周辺分布は分散が $s/2$ なので $s$ が大きくなるほど広がる。 \n",
"$$\n",
"\\Sigma = \\frac{1}{2}\n",
"\\begin{pmatrix}\n",
"1 & -1 \\\\\n",
"-1 & s\n",
"\\end{pmatrix} \\, , \\quad \\Sigma^{-1} = \\frac{2}{s-1}\n",
"\\begin{pmatrix}\n",
"s & 1 \\\\\n",
"1 & 1\n",
"\\end{pmatrix}\\, , \\quad |\\Sigma | = \\frac{s-1}{4} \\, , \\quad \\frac{1}{2\\pi \\sqrt{|\\Sigma |}} = \\frac{1}{\\pi \\sqrt{s-1}}\n",
"$$\n",
"同時分布: $p(x, y) = \\bigl(1 / (\\pi \\sqrt{s-1}) \\bigr) \\exp \\bigl( (-sx^2 - 2xy - y^2) / (s-1) \\bigr) $ \n",
" $p(x, y) = \\bigl(1 / (\\pi \\sqrt{s-1}) \\bigr) \\exp \\bigl( (- (y+x)^2 -(s-1) x^2) / (s-1) \\bigr) $ \n",
" $p(x, y) = \\bigl(1 / (\\pi \\sqrt{s-1}) \\bigr) \\exp \\bigl( (- s(x+y/s)^2 - (s-1)y^2/s ) / (s-1) \\bigr) $ \n",
"$x$ の周辺分布: $p(x) = \\bigl(1 / \\sqrt{\\pi} \\bigr) \\exp \\bigl(- x^2 \\bigr) $ \n",
"$y$ の周辺分布: $p(y) = \\bigl(1 / \\sqrt{\\pi s} \\bigr) \\exp \\bigl(- y^2 /s \\bigr) $ \n",
"$x$ を与えた下での条件付確率分布: $p(y | x) = \\bigl( 1 / \\sqrt{\\pi(s-1)} \\bigr) \\exp \\bigl(- ( y + x)^2 / (s-1) \\bigr) $ \n",
"$y$ を与えた下での条件付確率分布: $p(x | y) = \\bigl( \\sqrt{ s / \\pi(s-1)} \\bigr) \\exp \\bigl(- s ( x + y/s)^2 / (s-1) \\bigr) $ \n",
" \n",
"$s$ の値にかかわらず、 $x$ から $y$ を予測したときの回帰関数は $y = -x$ である。 \n",
"他方、 $y$ から $x$ を予測したときの回帰関数は $x = -y /s$ である。 \n",
" \n",
"$s$ の値にかかわらず、$x = x_0$ でこの2変量分布を切った断面では $y = -x_0$ のところが一番高い。 \n",
"他方、$y = -x_0$ でこの2変量分布を切った断面では $x = -x_0$ のところよりも $x = -x_0 / s$ のところの方がもっと高い。\n",
" \n",
"点 $(x_0, -x_0)$ はその点で $x$ 軸に垂直に切るならその断面のうち一番確率密度が大きい点だが、 \n",
"その点で $y$ 軸に垂直に切るならその断面のうち一番確率密度が大きい点ではない。 \n",
" \n",
"### なぜ青い線は赤い線からずれるかの説明1\n",
"どんな $x_0$ でも、$x = x_0$ でこの2変量分布を切った断面は $y = -x_0$ のところが一番高い山である。 \n",
"ただ、$x_0$ の絶対値が大きくなるほど山の大きさ自体が小さくなっていく(周辺分布 $p(x_0) = \\bigl(1 / \\sqrt{\\pi} \\bigr) \\exp \\bigl(- x_0^2 \\bigr) $ より)。 \n",
" \n",
"もし仮に $x_0$ の絶対値が大きくなっても $x = x_0$ 断面の山の大きさが小さくなっていかず、ずっと一定なら、 \n",
"点 $(x_0, -x_0)$ は $y = -x_0$ で分布を切った断面においても一番高い点になるはずである。 \n",
"(この2変量分布は直線 $y = -x$ 上でずっと一定の最大値をとるはずだから。) \n",
" \n",
"しかし、実際には $x_0$ の絶対値が大きくなるほど山の大きさ自体が小さくなっていくので、そうならない。 \n",
"もし「原点から左斜め上に歩いていって $y$ 軸に垂直に切った断面の頂点をたどりたい」というときに、$x$ 軸に垂直な断面で切ったときの山の頂点の軌跡である $y = -x_0$ 上を歩いていくと(赤い実線をたどると)、 「左側にいくほど山の大きさ自体が小さくなる」効果が大きいために $y$ 軸に垂直な断面で切ったときの山の頂点をたどることはできない。 \n",
"そのため、 $y$ 軸に垂直な断面で切ったときの山の頂点をたどりたいなら、この効果を避けるため、赤い実線をたどるときよりも左側に行くことを抑えながら歩かないといけない → 青い実線をたどることになる。\n",
"\n",
"### なぜ青い線は赤い線からずれるかの説明2\n",
"\n",
"$s$ が大きくなるほど青い点は赤い点から離れていく(青い点の x 座標が -1 から 0 に近づいていく)。 \n",
" \n",
"いま、($y$ 座標は無視して)「赤い点線の左側になる確率(赤い点線の左側にある点数)」と「赤い点線の右側になる確率(赤い点線の右側にある点数)」は $s$ の値によらない($x$ の周辺分布は $s$ の値によらない)。 \n",
"赤い点線は $x$ の周辺分布の平均 $0$ より左側の $x=-1$ に引かれているので、赤い点線の右側になる確率の方が大きい。 \n",
" \n",
"青い点線のごく周辺だけに注目すると、$s$ が 1 に近いときは、赤い点線の左側の点数と右側の点数が近い(一番上の図の状態)。ので、青い点線のごく周辺だけ切り取ったときに左右の点数の釣り合いが取れる位置(青い点)は赤い点線に近い。\n",
"\n",
"ただ、$s$ が大きくなるほど $y$ 方向の分散が大きくなってくる。すると、青い点線のごく周辺では、\n",
"- 赤い点線の左側では青い点線の上の方からどんどん点が引越してくる。\n",
"- 赤い点線の右側では青い点線の下の方がらどんどん点が引越してくる。\n",
"\n",
"ということが起きるが(出ていく点もあるのでだいぶ不正確な表現)、元々赤い点線の右側の点数の方が多いために、後者の勢いの方が強く、青い点線のごく周辺だけ切り取ったときに左右の点数の釣り合いが取れる位置(青い点)は右側にずれる。 "
]
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