{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# ベイズ線形回帰の可視化例 (PRML sec. 3.3)\n", "\n", "
\n", " このページのオリジナルのipynbファイル\n", " [トップページへ戻る]\n", "
\n", "\n", "公開されている実装例\n", "\n", "https://qiita.com/ctgk/items/555802600638f41b40c5\n", "\n", "をもとに、目的変数の分布が、予測値(回帰式による値)の周りでガウシアンとなっているような場合のベイズ回帰を行い、予測値と確率分布の偏差を描画するプログラムを紹介する。\n", "\n", "改変は最小限であるので、基底の数やサンプル数を変えて試してみてほしい。\n", "\n", "(PRML 3.3節参照)\n", "\n", "トレーニングデータからガウシアン予測分布を算出する式は、[前項](BayesApproach.html)の(4)~(7)式で与えられる。(以下に再掲)\n", "\n", "$$\n", "p(t|x, {\\bf x},{\\bf t}) = \\mathcal{N}(t| m(x), s^2(x)) \\tag{5}\n", "$$\n", "\n", "$$\n", "m(x) = {\\bf m}_N^T \\phi (x) = \\beta \\phi (x)^T {\\bf S} \\sum_{n=1}^N \\phi (x_n) t_n \\tag{6}\n", "$$\n", "$$\n", "s^2(x) = \\beta^{-1} + \\phi (x)^T {\\bf S}\\phi (x) \\tag{7}\n", "$$\n", "\n", "$\\alpha$, $\\beta$はモデルに外から与えるパラメータである。$\\alpha$は、なにもデータが得られてない段階の${\\bf w}$の確率の分散、$\\beta$は目的変数の分散(これは観測者にとってはわからない)を表す。\n", "\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "code_folding": [] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# Polynomial basis\n", "class PolynomialFeatures(object):\n", " \"\"\"\n", " 基底関数を多項式(次数:degree)とし、計画行列を作成する\n", " transform: 引数: トレーニング用の説明変数データを与える\n", " 返り値: 計画行列\n", " \n", " \"\"\"\n", " def __init__(self, degree):\n", " self.degree = degree\n", "\n", " def transform(self, x):\n", " features = [x ** i for i in range(self.degree + 1)]\n", " return np.array(features).transpose()\n", "\n", "# Gaussian basis\n", "class GaussianFeatures():\n", " \"\"\"\n", " 基底関数をガウシアンとして計画行列を作成する\n", " 範囲 [0,1.01] をdegree等分して、それらをガウシアンの中心(平均)とする\n", " mu: 平均 S: 標準偏差\n", " \n", " transform: 引数: トレーニング用の説明変数データ\n", " 返り値: 計画行列\n", " \n", " \"\"\"\n", " def __init__(self, degree):\n", " self.degree = degree\n", " self.mu = np.linspace(0, 1.01, degree)\n", " self.S = (self.mu[1] - self.mu[0])*2.0 # muの刻み幅よりは大きくしたい\n", "\n", " def gaussian_basis_func(self, x, i):\n", " return np.exp(-(x - self.mu[i])**2 / (2 * self.S**2))\n", "\n", " def transform(self, x):\n", " features = [[self.gaussian_basis_func(x1, i) for i in range(self.degree)] for x1 in x]\n", " return np.array(features)\n", "\n", "\n", "class BayesianRegression(object):\n", " \"\"\"\n", " ベイズ回帰 (PRML3.3節に述べられているアルゴリズム)\n", " fit: トレーニング(X:説明変数データ, t:目的変数データ)\n", " 前項の(4)式により事後分布の分散と平均を計算\n", " predict: 予測 (X: 説明変数データ, 返り値: 予測値と標準偏差)\n", " fitにより求めた、平均値と分散より、予測値(平均値)と標準偏差(誤差範囲)を計算\n", " \"\"\"\n", " def __init__(self, alpha=0.1, beta=0.25):\n", " self.alpha = alpha\n", " self.beta = beta\n", "\n", " def fit(self, X, t):\n", " # 上記(4)式\n", " self.w_var = np.linalg.inv(\n", " self.alpha * np.identity(np.size(X, 1))\n", " + self.beta * X.T.dot(X)) \n", " # (6)式のm_Nの計算\n", " self.w_mean = self.beta * self.w_var.dot(X.T.dot(t))\n", "\n", " def predict(self, X):\n", " y = X.dot(self.w_mean) # (6)式の計算\n", " y_var = 1 / self.beta + np.sum(X.dot(self.w_var) * X, axis=1) # (7)式の計算\n", " y_std = np.sqrt(y_var)\n", " return y, y_std\n", "\n", "\n", "def create_toy_data(func, low=0, high=1, size=10, sigma=1.):\n", " \"\"\"\n", " サンプルデータ作成用の関数\n", " [low, high]の範囲をsize等分し、説明変数とする\n", " 説明変数の値をfunc関数で計算し、\n", " それにガウシアンノイズを乗せて目的変数の値を計算し、返す\n", " \"\"\"\n", " x = np.random.uniform(low, high, size)\n", " t = func(x) + np.random.normal(scale=sigma, size=size)\n", " return x, t\n", "\n", "def main(x, t, features = None, ax = None, title=\"\"): # メインルーチン\n", " \"\"\"\n", " 引数で与えられた基底(オブジェクト)でのベイズ回帰分布を求め、\n", " テスト用説明変数(下記x_test)に対する予測値と誤差範囲を描画する\n", "  ・feature=Noneならば、ガウシアン基底とする\n", " ・featureオブジェクトクラスは事前に作っておく\n", " (PolynomialFeature、GaussianFeatureは上で用意)\n", " \"\"\"\n", "\n", " if ax == None:\n", " fig = plt.figure(figsize=(6, 4))\n", " ax = fig.add_subplot(1,1,1)\n", " \n", " ax.scatter(x, t, s=50, marker='o', alpha=0.5, label=\"observation\")\n", " \n", " # features = PolynomialFeatures(degree=num_basis) # 多項式基底\n", " if features == None:\n", " features = GaussianFeatures(degree=num_basis) # ガウシアン基底\n", " X = features.transform(x) # 計画行列をつくる\n", " \n", " regression = BayesianRegression(alpha=1e-3, beta=2) # 回帰クラスオブジェクト生成\n", " regression.fit(X, t) # 回帰\n", "\n", " x_test = np.linspace(0, 1, 100)\n", " X_test = features.transform(x_test)\n", " y, y_std = regression.predict(X_test)\n", "\n", " ax.plot(x_test, func(x_test), color='blue', label=\"sin($2\\pi x$)\")\n", " ax.plot(x_test, y, color='red', label=\"predict_mean\")\n", " ax.fill_between(x_test, y - y_std, y + y_std,\n", " color='pink', alpha=0.5, label=\"predict_std\")\n", " ax.legend()\n", " ax.set_title(\"Predictive distribution \" + title)\n", " ax.set_xlabel(\"x\")\n", " ax.set_ylabel(\"t\")\n", " #plt.show()\n", "\n", "\n", "if __name__ == '__main__':\n", "\n", " def func(x):\n", " return np.sin(2 * np.pi * x)\n", " # サンプルデータ作成\n", " num_data = 100\n", " x, t = create_toy_data(func, low=0, high=1, size=num_data, sigma=0.5)\n", "\n", " # 描画準備\n", " fig, ax = plt.subplots(1, 2, figsize=(12, 5))\n", " \n", " # ベイズ回帰\n", " num_basis=10\n", " poly_features = PolynomialFeatures(degree=num_basis) # 多項式基底\n", " main(x, t, features=poly_features, ax=ax[0], title=\"(polynomial basis)\")\n", " \n", " gauss_features =GaussianFeatures(degree=num_basis) # ガウシアン基底\n", " main(x, t, features=gauss_features, ax=ax[1], title=\"(Gaussian basis)\")\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 4 supplement\n", "\n", "121行目からのfunc()がサンプルデータ作成のベースとなる関数である。この関数やデータ数(num_data)、付加ランダム項の分散(sigma)などを変えてテストしてみよう。\n", "\n", "説明変数(x軸)の密度が一様ではない「偏ったデータ」を生成し試してみよう。\n", "\n", "[偏ったデータを作るプログラム例](various_data4fitting.html)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "学習データが周期関数($\\sin$)なので、べき多項式へのフィッティングでは範囲の右端では無理が生じていることがわかる。ガウシアンの方がその点ではまさる。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 参考:基底関数の図 (PRML Fig. 3.1)\n", "\n", "多項式\n", "\n", "ガウシアン\n", "\n", "シグモイド\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.16" }, "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": 4 }