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20210130_線形モデルのベイズ推定.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 線形モデルのベイズ推定\n",
"\n",
"[Gaussian Processes for Machine Learning](http://www.gaussianprocess.org/gpml/chapters/)の2.1節のFigure 2.1 を目測で再現したもの。"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"計画行列\n",
" [[1.0, -5.0], [1.0, 2.0], [1.0, 5.0]]\n",
"正解の値\n",
" [-5.5, 0.5, 4.5]\n",
"事後分布の分散共分散行列\n",
" [[ 0.25462963 -0.00925926]\n",
" [-0.00925926 0.01851852]]\n",
"事後分布の平均\n",
" [-0.59953704 0.94907407]\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x576 with 7 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import multivariate_normal\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib import cm\n",
"from pylab import rcParams\n",
"rcParams['font.size'] = 14\n",
"rcParams['font.family']='Ume Hy Gothic O5'\n",
"\n",
"sigma_n_2 = 1.0 # モデルのノイズ\n",
"\n",
"X = [[1.0, -5.0], [1.0, 2.0], [1.0, 5.0]] # 計画行列(1つ目の成分は切片用で常に1)\n",
"Y = [-5.5, 0.5, 4.5] # 正解の値\n",
"print('計画行列\\n', X)\n",
"print('正解の値\\n', Y)\n",
"\n",
"# 事後分布の分散共分散行列\n",
"A_inv = np.linalg.inv(np.matrix(X).T * np.matrix(X) / sigma_n_2 + np.eye(2))\n",
"# 事後分布の平均\n",
"w_hat = (1.0 / sigma_n_2) * A_inv * np.matrix(X).T * np.matrix(Y).T\n",
"w_hat = np.asarray(w_hat.flatten())[0]\n",
"print('事後分布の分散共分散行列\\n', A_inv)\n",
"print('事後分布の平均\\n', w_hat)\n",
"\n",
"# 予測値、予測値の±2シグマ\n",
"list_x = np.linspace(-6, 6, 61)\n",
"list_y_hat = [w_hat[0] + w_hat[1] * x_ for x_ in list_x]\n",
"list_var_hat = [(np.matrix([1, x_]) * A_inv * np.matrix([1, x_]).T)[0, 0] for x_ in list_x]\n",
"list_y_ub = [y_ + 2.0 * np.sqrt(var_) for y_, var_ in zip(list_y_hat, list_var_hat)]\n",
"list_y_lb = [y_ - 2.0 * np.sqrt(var_) for y_, var_ in zip(list_y_hat, list_var_hat)]\n",
"\n",
"# パラメータ空間のある点での事前分布、尤度、事後分布\n",
"def prior(pos):\n",
" return multivariate_normal([0.0, 0.0], np.eye(2)).pdf(pos)\n",
"def likelihood(pos):\n",
" mu = (np.matrix(X) * np.matrix(pos).T).flatten()\n",
" return multivariate_normal(np.asarray(mu)[0], sigma_n_2 * np.eye(3)).pdf(Y)\n",
"def posterior(pos):\n",
" return likelihood(pos) * prior(pos)\n",
"\n",
"# パラメータ空間のメッシュの各点の密度を返す\n",
"def get_densities(grid, func):\n",
" pdf = []\n",
" for i in range(grid.shape[0]):\n",
" pdf_ = []\n",
" for j in range(grid.shape[1]):\n",
" pdf_.append(func(grid[i, j, :]))\n",
" pdf.append(pdf_)\n",
" return pdf\n",
"\n",
"# メッシュ\n",
"x, y = np.meshgrid(np.linspace(-2, 2, 41), np.linspace(-2, 2, 41))\n",
"grid = np.dstack((x, y))\n",
"\n",
"# グラフ描画\n",
"fig, axes = plt.subplots(2, 2, figsize=(10, 8))\n",
"\n",
"axes[0, 0].set_title('パラメータの事前分布(標準正規分布)')\n",
"p = axes[0, 0].contourf(x, y, get_densities(grid, prior), cmap=cm.Purples)\n",
"fig.colorbar(p, ax=axes[0, 0])\n",
"\n",
"axes[0, 1].set_title('訓練データ')\n",
"axes[0, 1].scatter(np.array(X)[:,1], Y, color=\"black\")\n",
"axes[0, 1].plot(list_x, list_y_hat, color=\"black\", linewidth=1)\n",
"axes[0, 1].plot(list_x, list_y_ub, color=\"black\", linewidth=1, linestyle='dotted')\n",
"axes[0, 1].plot(list_x, list_y_lb, color=\"black\", linewidth=1, linestyle='dotted')\n",
"axes[0, 1].grid(linewidth=1, linestyle='dotted')\n",
"axes[0, 1].set_axisbelow(True)\n",
"\n",
"axes[1, 0].set_title('パラメータの尤度')\n",
"p = axes[1, 0].contourf(x, y, get_densities(grid, likelihood), cmap=cm.Purples)\n",
"fig.colorbar(p, ax=axes[1, 0])\n",
"\n",
"axes[1, 1].set_title('パラメータの事後分布(正規化なし)')\n",
"p = axes[1, 1].contourf(x, y, get_densities(grid, posterior), cmap=cm.Purples)\n",
"fig.colorbar(p, ax=axes[1, 1])\n",
"\n",
"fig.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": "3.6.8"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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