{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPython 3.5.5\n", "IPython 6.2.1\n", "\n", "numpy 1.14.1\n", "scipy 1.0.0\n", "sklearn 0.19.1\n", "pandas 0.22.0\n", "matplotlib 2.2.2\n" ] } ], "source": [ "%load_ext watermark\n", "%watermark -v -p numpy,scipy,sklearn,pandas,matplotlib" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**4장 – 모델 훈련**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "_이 노트북은 4장에 있는 모든 샘플 코드와 연습문제 해답을 가지고 있습니다._" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 설정" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "파이썬 2와 3을 모두 지원합니다. 공통 모듈을 임포트하고 맷플롯립 그림이 노트북 안에 포함되도록 설정하고 생성한 그림을 저장하기 위한 함수를 준비합니다:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# 파이썬 2와 파이썬 3 지원\n", "from __future__ import division, print_function, unicode_literals\n", "\n", "# 공통\n", "import numpy as np\n", "import os\n", "\n", "# 일관된 출력을 위해 유사난수 초기화\n", "np.random.seed(42)\n", "\n", "# 맷플롯립 설정\n", "%matplotlib inline\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "plt.rcParams['axes.labelsize'] = 14\n", "plt.rcParams['xtick.labelsize'] = 12\n", "plt.rcParams['ytick.labelsize'] = 12\n", "\n", "# 한글출력\n", "matplotlib.rc('font', family='NanumBarunGothic')\n", "\n", "# 그림을 저장할 폴드\n", "PROJECT_ROOT_DIR = \".\"\n", "CHAPTER_ID = \"training_linear_models\"\n", "\n", "def save_fig(fig_id, tight_layout=True):\n", " path = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID, fig_id + \".png\")\n", " if tight_layout:\n", " plt.tight_layout()\n", " plt.savefig(path, format='png', dpi=300)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 정규 방정식을 사용한 선형 회귀" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "X = 2 * np.random.rand(100, 1)\n", "y = 4 + 3 * X + np.random.randn(100, 1)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(X, y, \"b.\")\n", "plt.xlabel(\"$x_1$\", fontsize=18)\n", "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", "plt.axis([0, 2, 0, 15])\n", "save_fig(\"generated_data_plot\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "X_b = np.c_[np.ones((100, 1)), X] # 모든 샘플에 x0 = 1을 추가합니다.\n", "theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[4.21509616],\n", " [2.77011339]])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta_best" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[4.21509616],\n", " [9.75532293]])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_new = np.array([[0], [2]])\n", "X_new_b = np.c_[np.ones((2, 1)), X_new] # 모든 샘플에 x0 = 1을 추가합니다.\n", "y_predict = X_new_b.dot(theta_best)\n", "y_predict" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(X_new, y_predict, \"r-\", linewidth=2, label=\"예측\")\n", "plt.plot(X, y, \"b.\")\n", "plt.xlabel(\"$x_1$\", fontsize=18)\n", "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", "plt.legend(loc=\"upper left\", fontsize=14)\n", "plt.axis([0, 2, 0, 15])\n", "save_fig(\"linear_model_predictions\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([4.21509616]), array([[2.77011339]]))" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.linear_model import LinearRegression\n", "lin_reg = LinearRegression()\n", "lin_reg.fit(X, y)\n", "lin_reg.intercept_, lin_reg.coef_" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[4.21509616],\n", " [9.75532293]])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lin_reg.predict(X_new)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`LinearRegression` 클래스는 scipy.linalg.lstsq() 함수(\"least squares\"의 약자)를 사용하므로 직접 호출할 수 있습니다:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[4.21509616],\n", " [2.77011339]])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta_best_svd, residuals, rank, s = np.linalg.lstsq(X_b, y, rcond=1e-6)\n", "theta_best_svd" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "이 함수는 $\\mathbf{X}^+\\mathbf{y}$을 계산합니다. $\\mathbf{X}^{+}$는 $\\mathbf{X}$의 _유사역행렬_(pseudoinverse)입니다(Moore–Penrose 유사역행렬입니다). `np.linalg.pinv()`을 사용해서 유사역행렬을 직접 계산할 수 있습니다:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[4.21509616],\n", " [2.77011339]])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.pinv(X_b).dot(y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 경사 하강법을 사용한 선형 회귀" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "eta = 0.1\n", "n_iterations = 1000\n", "m = 100\n", "theta = np.random.randn(2,1)\n", "\n", "for iteration in range(n_iterations):\n", " gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)\n", " theta = theta - eta * gradients" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[4.21509616],\n", " [2.77011339]])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[4.21509616],\n", " [9.75532293]])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_new_b.dot(theta)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "theta_path_bgd = []\n", "\n", "def plot_gradient_descent(theta, eta, theta_path=None):\n", " m = len(X_b)\n", " plt.plot(X, y, \"b.\")\n", " n_iterations = 1000\n", " for iteration in range(n_iterations):\n", " if iteration < 10:\n", " y_predict = X_new_b.dot(theta)\n", " style = \"b-\" if iteration > 0 else \"r--\"\n", " plt.plot(X_new, y_predict, style)\n", " gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)\n", " theta = theta - eta * gradients\n", " if theta_path is not None:\n", " theta_path.append(theta)\n", " plt.xlabel(\"$x_1$\", fontsize=18)\n", " plt.axis([0, 2, 0, 15])\n", " plt.title(r\"$\\eta = {}$\".format(eta), fontsize=16)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(42)\n", "theta = np.random.randn(2,1) # random initialization\n", "\n", "plt.figure(figsize=(10,4))\n", "plt.subplot(131); plot_gradient_descent(theta, eta=0.02)\n", "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", "plt.subplot(132); plot_gradient_descent(theta, eta=0.1, theta_path=theta_path_bgd)\n", "plt.subplot(133); plot_gradient_descent(theta, eta=0.5)\n", "\n", "save_fig(\"gradient_descent_plot\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 확률적 경사 하강법" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "theta_path_sgd = []\n", "m = len(X_b)\n", "np.random.seed(42)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_epochs = 50\n", "t0, t1 = 5, 50 # 학습 스케줄 하이퍼파라미터 learning schedule hyperparameters\n", "\n", "def learning_schedule(t):\n", " return t0 / (t + t1)\n", "\n", "theta = np.random.randn(2,1) # 무작위 초기화\n", "\n", "for epoch in range(n_epochs):\n", " for i in range(m):\n", " if epoch == 0 and i < 20: # 책에는 빠짐\n", " y_predict = X_new_b.dot(theta) # 책에는 빠짐\n", " style = \"b-\" if i > 0 else \"r--\" # 책에는 빠짐\n", " plt.plot(X_new, y_predict, style) # 책에는 빠짐\n", " random_index = np.random.randint(m)\n", " xi = X_b[random_index:random_index+1]\n", " yi = y[random_index:random_index+1]\n", " gradients = 2 * xi.T.dot(xi.dot(theta) - yi)\n", " eta = learning_schedule(epoch * m + i)\n", " theta = theta - eta * gradients\n", " theta_path_sgd.append(theta) # 책에는 빠짐\n", "\n", "plt.plot(X, y, \"b.\") # 책에는 빠짐\n", "plt.xlabel(\"$x_1$\", fontsize=18) # 책에는 빠짐\n", "plt.ylabel(\"$y$\", rotation=0, fontsize=18) # 책에는 빠짐\n", "plt.axis([0, 2, 0, 15]) # 책에는 빠짐\n", "save_fig(\"sgd_plot\") # 책에는 빠짐\n", "plt.show() # 책에는 빠짐" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[4.21076011],\n", " [2.74856079]])" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "SGDRegressor(alpha=0.0001, average=False, epsilon=0.1, eta0=0.1,\n", " fit_intercept=True, l1_ratio=0.15, learning_rate='invscaling',\n", " loss='squared_loss', max_iter=50, n_iter=None, penalty=None,\n", " power_t=0.25, random_state=42, shuffle=True, tol=None, verbose=0,\n", " warm_start=False)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.linear_model import SGDRegressor\n", "sgd_reg = SGDRegressor(max_iter=50, penalty=None, eta0=0.1, random_state=42)\n", "sgd_reg.fit(X, y.ravel())" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([4.16782089]), array([2.72603052]))" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sgd_reg.intercept_, sgd_reg.coef_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 미니배치 경사 하강법" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "theta_path_mgd = []\n", "\n", "n_iterations = 50\n", "minibatch_size = 20\n", "\n", "np.random.seed(42)\n", "theta = np.random.randn(2,1) # 무작위 초기화\n", "\n", "t0, t1 = 200, 1000\n", "def learning_schedule(t):\n", " return t0 / (t + t1)\n", "\n", "t = 0\n", "for epoch in range(n_iterations):\n", " shuffled_indices = np.random.permutation(m)\n", " X_b_shuffled = X_b[shuffled_indices]\n", " y_shuffled = y[shuffled_indices]\n", " for i in range(0, m, minibatch_size):\n", " t += 1\n", " xi = X_b_shuffled[i:i+minibatch_size]\n", " yi = y_shuffled[i:i+minibatch_size]\n", " gradients = 2/minibatch_size * xi.T.dot(xi.dot(theta) - yi)\n", " eta = learning_schedule(t)\n", " theta = theta - eta * gradients\n", " theta_path_mgd.append(theta)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[4.25214635],\n", " [2.7896408 ]])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "theta_path_bgd = np.array(theta_path_bgd)\n", "theta_path_sgd = np.array(theta_path_sgd)\n", "theta_path_mgd = np.array(theta_path_mgd)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(7,4))\n", "plt.plot(theta_path_sgd[:, 0], theta_path_sgd[:, 1], \"r-s\", linewidth=1, label=\"SGD\")\n", "plt.plot(theta_path_mgd[:, 0], theta_path_mgd[:, 1], \"g-+\", linewidth=2, label=\"미니배치\")\n", "plt.plot(theta_path_bgd[:, 0], theta_path_bgd[:, 1], \"b-o\", linewidth=3, label=\"배치\")\n", "plt.legend(loc=\"upper left\", fontsize=16)\n", "plt.xlabel(r\"$\\theta_0$\", fontsize=20)\n", "plt.ylabel(r\"$\\theta_1$ \", fontsize=20, rotation=0)\n", "plt.axis([2.5, 4.5, 2.3, 3.9])\n", "save_fig(\"gradient_descent_paths_plot\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 다항 회귀" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import numpy.random as rnd\n", "\n", "np.random.seed(42)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "m = 100\n", "X = 6 * np.random.rand(m, 1) - 3\n", "y = 0.5 * X**2 + X + 2 + np.random.randn(m, 1)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(X, y, \"b.\")\n", "plt.xlabel(\"$x_1$\", fontsize=18)\n", "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", "plt.axis([-3, 3, 0, 10])\n", "save_fig(\"quadratic_data_plot\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-0.75275929])" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n", "X_poly = poly_features.fit_transform(X)\n", "X[0]" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-0.75275929, 0.56664654])" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_poly[0]" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([1.78134581]), array([[0.93366893, 0.56456263]]))" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lin_reg = LinearRegression()\n", "lin_reg.fit(X_poly, y)\n", "lin_reg.intercept_, lin_reg.coef_" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X_new=np.linspace(-3, 3, 100).reshape(100, 1)\n", "X_new_poly = poly_features.transform(X_new)\n", "y_new = lin_reg.predict(X_new_poly)\n", "plt.plot(X, y, \"b.\")\n", "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"예측\")\n", "plt.xlabel(\"$x_1$\", fontsize=18)\n", "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", "plt.legend(loc=\"upper left\", fontsize=14)\n", "plt.axis([-3, 3, 0, 10])\n", "save_fig(\"quadratic_predictions_plot\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.preprocessing import StandardScaler\n", "from sklearn.pipeline import Pipeline\n", "\n", "for style, width, degree in ((\"g-\", 1, 300), (\"b--\", 2, 2), (\"r-+\", 2, 1)):\n", " polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n", " std_scaler = StandardScaler()\n", " lin_reg = LinearRegression()\n", " polynomial_regression = Pipeline([\n", " (\"poly_features\", polybig_features),\n", " (\"std_scaler\", std_scaler),\n", " (\"lin_reg\", lin_reg),\n", " ])\n", " polynomial_regression.fit(X, y)\n", " y_newbig = polynomial_regression.predict(X_new)\n", " plt.plot(X_new, y_newbig, style, label=str(degree), linewidth=width)\n", "\n", "plt.plot(X, y, \"b.\", linewidth=3)\n", "plt.legend(loc=\"upper left\")\n", "plt.xlabel(\"$x_1$\", fontsize=18)\n", "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", "plt.axis([-3, 3, 0, 10])\n", "save_fig(\"high_degree_polynomials_plot\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "from sklearn.metrics import mean_squared_error\n", "from sklearn.model_selection import train_test_split\n", "\n", "def plot_learning_curves(model, X, y):\n", " X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=10)\n", " train_errors, val_errors = [], []\n", " for m in range(1, len(X_train)):\n", " model.fit(X_train[:m], y_train[:m])\n", " y_train_predict = model.predict(X_train[:m])\n", " y_val_predict = model.predict(X_val)\n", " train_errors.append(mean_squared_error(y_train[:m], y_train_predict))\n", " val_errors.append(mean_squared_error(y_val, y_val_predict))\n", "\n", " plt.plot(np.sqrt(train_errors), \"r-+\", linewidth=2, label=\"훈련\")\n", " plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"검증\")\n", " plt.legend(loc=\"upper right\", fontsize=14) # 책에는 빠짐\n", " plt.xlabel(\"훈련 세트 크기\", fontsize=14) # 책에는 빠짐\n", " plt.ylabel(\"RMSE\", fontsize=14) # 책에는 빠짐" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lin_reg = LinearRegression()\n", "plot_learning_curves(lin_reg, X, y)\n", "plt.axis([0, 80, 0, 3]) # 책에는 빠짐\n", "save_fig(\"underfitting_learning_curves_plot\") # 책에는 빠짐\n", "plt.show() # 책에는 빠짐" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.pipeline import Pipeline\n", "\n", "polynomial_regression = Pipeline([\n", " (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n", " (\"lin_reg\", LinearRegression()),\n", " ])\n", "\n", "plot_learning_curves(polynomial_regression, X, y)\n", "plt.axis([0, 80, 0, 3]) # 책에는 빠짐\n", "save_fig(\"learning_curves_plot\") # 책에는 빠짐\n", "plt.show() # 책에는 빠짐" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 규제가 있는 모델" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.linear_model import Ridge\n", "\n", "np.random.seed(42)\n", "m = 20\n", "X = 3 * np.random.rand(m, 1)\n", "y = 1 + 0.5 * X + np.random.randn(m, 1) / 1.5\n", "X_new = np.linspace(0, 3, 100).reshape(100, 1)\n", "\n", "def plot_model(model_class, polynomial, alphas, **model_kargs):\n", " for alpha, style in zip(alphas, (\"b-\", \"g--\", \"r:\")):\n", " model = model_class(alpha, **model_kargs) if alpha > 0 else LinearRegression()\n", " if polynomial:\n", " model = Pipeline([\n", " (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n", " (\"std_scaler\", StandardScaler()),\n", " (\"regul_reg\", model),\n", " ])\n", " model.fit(X, y)\n", " y_new_regul = model.predict(X_new)\n", " lw = 2 if alpha > 0 else 1\n", " plt.plot(X_new, y_new_regul, style, linewidth=lw, label=r\"$\\alpha = {}$\".format(alpha))\n", " plt.plot(X, y, \"b.\", linewidth=3)\n", " plt.legend(loc=\"upper left\", fontsize=15)\n", " plt.xlabel(\"$x_1$\", fontsize=18)\n", " plt.axis([0, 3, 0, 4])\n", "\n", "plt.figure(figsize=(8,4))\n", "plt.subplot(121)\n", "plot_model(Ridge, polynomial=False, alphas=(0, 10, 100), random_state=42)\n", "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", "plt.subplot(122)\n", "plot_model(Ridge, polynomial=True, alphas=(0, 10**-5, 1), random_state=42)\n", "\n", "save_fig(\"ridge_regression_plot\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[1.55071465]])" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.linear_model import Ridge\n", "ridge_reg = Ridge(alpha=1, solver=\"cholesky\", random_state=42)\n", "ridge_reg.fit(X, y)\n", "ridge_reg.predict([[1.5]])" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1.13500145])" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sgd_reg = SGDRegressor(max_iter=5, penalty=\"l2\", random_state=42)\n", "sgd_reg.fit(X, y.ravel())\n", "sgd_reg.predict([[1.5]])" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[1.5507201]])" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ridge_reg = Ridge(alpha=1, solver=\"sag\", random_state=42)\n", "ridge_reg.fit(X, y)\n", "ridge_reg.predict([[1.5]])" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.linear_model import Lasso\n", "\n", "plt.figure(figsize=(8,4))\n", "plt.subplot(121)\n", "plot_model(Lasso, polynomial=False, alphas=(0, 0.1, 1), random_state=42)\n", "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", "plt.subplot(122)\n", "plot_model(Lasso, polynomial=True, alphas=(0, 10**-7, 1), tol=1, random_state=42)\n", "\n", "save_fig(\"lasso_regression_plot\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1.53788174])" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.linear_model import Lasso\n", "lasso_reg = Lasso(alpha=0.1)\n", "lasso_reg.fit(X, y)\n", "lasso_reg.predict([[1.5]])" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1.54333232])" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.linear_model import ElasticNet\n", "elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5, random_state=42)\n", "elastic_net.fit(X, y)\n", "elastic_net.predict([[1.5]])" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(42)\n", "m = 100\n", "X = 6 * np.random.rand(m, 1) - 3\n", "y = 2 + X + 0.5 * X**2 + np.random.randn(m, 1)\n", "\n", "X_train, X_val, y_train, y_val = train_test_split(X[:50], y[:50].ravel(), test_size=0.5, random_state=10)\n", "\n", "poly_scaler = Pipeline([\n", " (\"poly_features\", PolynomialFeatures(degree=90, include_bias=False)),\n", " (\"std_scaler\", StandardScaler()),\n", " ])\n", "\n", "X_train_poly_scaled = poly_scaler.fit_transform(X_train)\n", "X_val_poly_scaled = poly_scaler.transform(X_val)\n", "\n", "sgd_reg = SGDRegressor(max_iter=1,\n", " penalty=None,\n", " eta0=0.0005,\n", " warm_start=True,\n", " learning_rate=\"constant\",\n", " random_state=42)\n", "\n", "n_epochs = 500\n", "train_errors, val_errors = [], []\n", "for epoch in range(n_epochs):\n", " sgd_reg.fit(X_train_poly_scaled, y_train)\n", " y_train_predict = sgd_reg.predict(X_train_poly_scaled)\n", " y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n", " train_errors.append(mean_squared_error(y_train, y_train_predict))\n", " val_errors.append(mean_squared_error(y_val, y_val_predict))\n", "\n", "best_epoch = np.argmin(val_errors)\n", "best_val_rmse = np.sqrt(val_errors[best_epoch])\n", "\n", "plt.annotate('최선의 모델',\n", " xy=(best_epoch, best_val_rmse),\n", " xytext=(best_epoch, best_val_rmse + 1),\n", " ha=\"center\",\n", " arrowprops=dict(facecolor='black', shrink=0.05),\n", " fontsize=16,\n", " )\n", "\n", "best_val_rmse -= 0.03 # just to make the graph look better\n", "plt.plot([0, n_epochs], [best_val_rmse, best_val_rmse], \"k:\", linewidth=2)\n", "plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"검증 세트\")\n", "plt.plot(np.sqrt(train_errors), \"r--\", linewidth=2, label=\"훈련 세트\")\n", "plt.legend(loc=\"upper right\", fontsize=14)\n", "plt.xlabel(\"에포크\", fontsize=14)\n", "plt.ylabel(\"RMSE\", fontsize=14)\n", "save_fig(\"early_stopping_plot\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "from sklearn.base import clone\n", "sgd_reg = SGDRegressor(max_iter=1, warm_start=True, penalty=None,\n", " learning_rate=\"constant\", eta0=0.0005, random_state=42)\n", "\n", "minimum_val_error = float(\"inf\")\n", "best_epoch = None\n", "best_model = None\n", "for epoch in range(1000):\n", " sgd_reg.fit(X_train_poly_scaled, y_train) # 이어서 학습합니다\n", " y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n", " val_error = mean_squared_error(y_val, y_val_predict)\n", " if val_error < minimum_val_error:\n", " minimum_val_error = val_error\n", " best_epoch = epoch\n", " best_model = clone(sgd_reg)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(239, SGDRegressor(alpha=0.0001, average=False, epsilon=0.1, eta0=0.0005,\n", " fit_intercept=True, l1_ratio=0.15, learning_rate='constant',\n", " loss='squared_loss', max_iter=1, n_iter=None, penalty=None,\n", " power_t=0.25, random_state=42, shuffle=True, tol=None, verbose=0,\n", " warm_start=True))" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "best_epoch, best_model" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "t1a, t1b, t2a, t2b = -1, 3, -1.5, 1.5\n", "\n", "# 편향은 무시\n", "t1s = np.linspace(t1a, t1b, 500)\n", "t2s = np.linspace(t2a, t2b, 500)\n", "t1, t2 = np.meshgrid(t1s, t2s)\n", "T = np.c_[t1.ravel(), t2.ravel()]\n", "Xr = np.array([[-1, 1], [-0.3, -1], [1, 0.1]])\n", "yr = 2 * Xr[:, :1] + 0.5 * Xr[:, 1:]\n", "\n", "J = (1/len(Xr) * np.sum((T.dot(Xr.T) - yr.T)**2, axis=1)).reshape(t1.shape)\n", "\n", "N1 = np.linalg.norm(T, ord=1, axis=1).reshape(t1.shape)\n", "N2 = np.linalg.norm(T, ord=2, axis=1).reshape(t1.shape)\n", "\n", "t_min_idx = np.unravel_index(np.argmin(J), J.shape)\n", "t1_min, t2_min = t1[t_min_idx], t2[t_min_idx]\n", "\n", "t_init = np.array([[0.25], [-1]])" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def bgd_path(theta, X, y, l1, l2, core = 1, eta = 0.1, n_iterations = 50):\n", " path = [theta]\n", " for iteration in range(n_iterations):\n", " gradients = core * 2/len(X) * X.T.dot(X.dot(theta) - y) + l1 * np.sign(theta) + 2 * l2 * theta\n", "\n", " theta = theta - eta * gradients\n", " path.append(theta)\n", " return np.array(path)\n", "\n", "plt.figure(figsize=(12, 8))\n", "for i, N, l1, l2, title in ((0, N1, 0.5, 0, \"Lasso\"), (1, N2, 0, 0.1, \"Ridge\")):\n", " JR = J + l1 * N1 + l2 * N2**2\n", " \n", " tr_min_idx = np.unravel_index(np.argmin(JR), JR.shape)\n", " t1r_min, t2r_min = t1[tr_min_idx], t2[tr_min_idx]\n", "\n", " levelsJ=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(J) - np.min(J)) + np.min(J)\n", " levelsJR=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(JR) - np.min(JR)) + np.min(JR)\n", " levelsN=np.linspace(0, np.max(N), 10)\n", " \n", " path_J = bgd_path(t_init, Xr, yr, l1=0, l2=0)\n", " path_JR = bgd_path(t_init, Xr, yr, l1, l2)\n", " path_N = bgd_path(t_init, Xr, yr, np.sign(l1)/3, np.sign(l2), core=0)\n", "\n", " plt.subplot(221 + i * 2)\n", " plt.grid(True)\n", " plt.axhline(y=0, color='k')\n", " plt.axvline(x=0, color='k')\n", " plt.contourf(t1, t2, J, levels=levelsJ, alpha=0.9)\n", " plt.contour(t1, t2, N, levels=levelsN)\n", " plt.plot(path_J[:, 0], path_J[:, 1], \"w-o\")\n", " plt.plot(path_N[:, 0], path_N[:, 1], \"y-^\")\n", " plt.plot(t1_min, t2_min, \"rs\")\n", " plt.title(r\"$\\ell_{}$ penalty\".format(i + 1), fontsize=16)\n", " plt.axis([t1a, t1b, t2a, t2b])\n", " plt.ylabel(r\"$\\theta_2$\", fontsize=20, rotation=0, labelpad=15)\n", " if i == 1: plt.xlabel(r\"$\\theta_1$\", fontsize=20)\n", "\n", " plt.subplot(222 + i * 2)\n", " plt.grid(True)\n", " plt.axhline(y=0, color='k')\n", " plt.axvline(x=0, color='k')\n", " plt.contourf(t1, t2, JR, levels=levelsJR, alpha=0.9)\n", " plt.plot(path_JR[:, 0], path_JR[:, 1], \"w-o\")\n", " plt.plot(t1r_min, t2r_min, \"rs\")\n", " plt.title(title, fontsize=16)\n", " plt.axis([t1a, t1b, t2a, t2b])\n", " if i == 1: plt.xlabel(r\"$\\theta_1$\", fontsize=20)\n", "\n", "save_fig(\"lasso_vs_ridge_plot\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 로지스틱 회귀" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(-10, 10, 100)\n", "sig = 1 / (1 + np.exp(-t))\n", "plt.figure(figsize=(9, 3))\n", "plt.plot([-10, 10], [0, 0], \"k-\")\n", "plt.plot([-10, 10], [0.5, 0.5], \"k:\")\n", "plt.plot([-10, 10], [1, 1], \"k:\")\n", "plt.plot([0, 0], [-1.1, 1.1], \"k-\")\n", "plt.plot(t, sig, \"b-\", linewidth=2, label=r\"$\\sigma(t) = \\frac{1}{1 + e^{-t}}$\")\n", "plt.xlabel(\"t\")\n", "plt.legend(loc=\"upper left\", fontsize=20)\n", "plt.axis([-10, 10, -0.1, 1.1])\n", "save_fig(\"logistic_function_plot\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['data', 'feature_names', 'target', 'DESCR', 'target_names']" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn import datasets\n", "iris = datasets.load_iris()\n", "list(iris.keys())" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iris Plants Database\n", "====================\n", "\n", "Notes\n", "-----\n", "Data Set Characteristics:\n", " :Number of Instances: 150 (50 in each of three classes)\n", " :Number of Attributes: 4 numeric, predictive attributes and the class\n", " :Attribute Information:\n", " - sepal length in cm\n", " - sepal width in cm\n", " - petal length in cm\n", " - petal width in cm\n", " - class:\n", " - Iris-Setosa\n", " - Iris-Versicolour\n", " - Iris-Virginica\n", " :Summary Statistics:\n", "\n", " ============== ==== ==== ======= ===== ====================\n", " Min Max Mean SD Class Correlation\n", " ============== ==== ==== ======= ===== ====================\n", " sepal length: 4.3 7.9 5.84 0.83 0.7826\n", " sepal width: 2.0 4.4 3.05 0.43 -0.4194\n", " petal length: 1.0 6.9 3.76 1.76 0.9490 (high!)\n", " petal width: 0.1 2.5 1.20 0.76 0.9565 (high!)\n", " ============== ==== ==== ======= ===== ====================\n", "\n", " :Missing Attribute Values: None\n", " :Class Distribution: 33.3% for each of 3 classes.\n", " :Creator: R.A. Fisher\n", " :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n", " :Date: July, 1988\n", "\n", "This is a copy of UCI ML iris datasets.\n", "http://archive.ics.uci.edu/ml/datasets/Iris\n", "\n", "The famous Iris database, first used by Sir R.A Fisher\n", "\n", "This is perhaps the best known database to be found in the\n", "pattern recognition literature. Fisher's paper is a classic in the field and\n", "is referenced frequently to this day. (See Duda & Hart, for example.) The\n", "data set contains 3 classes of 50 instances each, where each class refers to a\n", "type of iris plant. One class is linearly separable from the other 2; the\n", "latter are NOT linearly separable from each other.\n", "\n", "References\n", "----------\n", " - Fisher,R.A. \"The use of multiple measurements in taxonomic problems\"\n", " Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n", " Mathematical Statistics\" (John Wiley, NY, 1950).\n", " - Duda,R.O., & Hart,P.E. (1973) Pattern Classification and Scene Analysis.\n", " (Q327.D83) John Wiley & Sons. ISBN 0-471-22361-1. See page 218.\n", " - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n", " Structure and Classification Rule for Recognition in Partially Exposed\n", " Environments\". IEEE Transactions on Pattern Analysis and Machine\n", " Intelligence, Vol. PAMI-2, No. 1, 67-71.\n", " - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\". IEEE Transactions\n", " on Information Theory, May 1972, 431-433.\n", " - See also: 1988 MLC Proceedings, 54-64. Cheeseman et al\"s AUTOCLASS II\n", " conceptual clustering system finds 3 classes in the data.\n", " - Many, many more ...\n", "\n" ] } ], "source": [ "print(iris.DESCR)" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "X = iris[\"data\"][:, 3:] # 꽃잎 넓이\n", "y = (iris[\"target\"] == 2).astype(np.int) # Iris-Virginica이면 1 아니면 0" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n", " intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n", " penalty='l2', random_state=42, solver='liblinear', tol=0.0001,\n", " verbose=0, warm_start=False)" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.linear_model import LogisticRegression\n", "log_reg = LogisticRegression(random_state=42)\n", "log_reg.fit(X, y)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n", "y_proba = log_reg.predict_proba(X_new)\n", "decision_boundary = X_new[y_proba[:, 1] >= 0.5][0]\n", "\n", "plt.figure(figsize=(8, 3))\n", "plt.plot(X[y==0], y[y==0], \"bs\")\n", "plt.plot(X[y==1], y[y==1], \"g^\")\n", "plt.plot([decision_boundary, decision_boundary], [-1, 2], \"k:\", linewidth=2)\n", "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris-Virginica\")\n", "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2, label=\"Not Iris-Virginica\")\n", "plt.text(decision_boundary+0.02, 0.15, \"결정 경계\", fontsize=14, color=\"k\", ha=\"center\")\n", "plt.arrow(decision_boundary, 0.08, -0.3, 0, head_width=0.05, head_length=0.1, fc='b', ec='b')\n", "plt.arrow(decision_boundary, 0.92, 0.3, 0, head_width=0.05, head_length=0.1, fc='g', ec='g')\n", "plt.xlabel(\"꽃잎의 폭 (cm)\", fontsize=14)\n", "plt.ylabel(\"확률\", fontsize=14)\n", "plt.legend(loc=\"center left\", fontsize=14)\n", "plt.axis([0, 3, -0.02, 1.02])\n", "save_fig(\"logistic_regression_plot\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1.61561562])" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "decision_boundary" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1, 0])" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "log_reg.predict([[1.7], [1.5]])" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.linear_model import LogisticRegression\n", "\n", "X = iris[\"data\"][:, (2, 3)] # petal length, petal width\n", "y = (iris[\"target\"] == 2).astype(np.int)\n", "\n", "log_reg = LogisticRegression(C=10**10, random_state=42)\n", "log_reg.fit(X, y)\n", "\n", "x0, x1 = np.meshgrid(\n", " np.linspace(2.9, 7, 500).reshape(-1, 1),\n", " np.linspace(0.8, 2.7, 200).reshape(-1, 1),\n", " )\n", "X_new = np.c_[x0.ravel(), x1.ravel()]\n", "\n", "y_proba = log_reg.predict_proba(X_new)\n", "\n", "plt.figure(figsize=(10, 4))\n", "plt.plot(X[y==0, 0], X[y==0, 1], \"bs\")\n", "plt.plot(X[y==1, 0], X[y==1, 1], \"g^\")\n", "\n", "zz = y_proba[:, 1].reshape(x0.shape)\n", "contour = plt.contour(x0, x1, zz, cmap=plt.cm.brg)\n", "\n", "\n", "left_right = np.array([2.9, 7])\n", "boundary = -(log_reg.coef_[0][0] * left_right + log_reg.intercept_[0]) / log_reg.coef_[0][1]\n", "\n", "plt.clabel(contour, inline=1, fontsize=12)\n", "plt.plot(left_right, boundary, \"k--\", linewidth=3)\n", "plt.text(3.5, 1.5, \"Iris-Virginica 아님\", fontsize=14, color=\"b\", ha=\"center\")\n", "plt.text(6.5, 2.3, \"Iris-Virginica\", fontsize=14, color=\"g\", ha=\"center\")\n", "plt.xlabel(\"꽃잎의 길이\", fontsize=14)\n", "plt.ylabel(\"꽃잎의 폭\", fontsize=14)\n", "plt.axis([2.9, 7, 0.8, 2.7])\n", "save_fig(\"logistic_regression_contour_plot\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "LogisticRegression(C=10, class_weight=None, dual=False, fit_intercept=True,\n", " intercept_scaling=1, max_iter=100, multi_class='multinomial',\n", " n_jobs=1, penalty='l2', random_state=42, solver='lbfgs',\n", " tol=0.0001, verbose=0, warm_start=False)" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = iris[\"data\"][:, (2, 3)] # 꽃잎 길이, 꽃잎 넓이\n", "y = iris[\"target\"]\n", "\n", "softmax_reg = LogisticRegression(multi_class=\"multinomial\",solver=\"lbfgs\", C=10, random_state=42)\n", "softmax_reg.fit(X, y)" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x0, x1 = np.meshgrid(\n", " np.linspace(0, 8, 500).reshape(-1, 1),\n", " np.linspace(0, 3.5, 200).reshape(-1, 1),\n", " )\n", "X_new = np.c_[x0.ravel(), x1.ravel()]\n", "\n", "\n", "y_proba = softmax_reg.predict_proba(X_new)\n", "y_predict = softmax_reg.predict(X_new)\n", "\n", "zz1 = y_proba[:, 1].reshape(x0.shape)\n", "zz = y_predict.reshape(x0.shape)\n", "\n", "plt.figure(figsize=(10, 4))\n", "plt.plot(X[y==2, 0], X[y==2, 1], \"g^\", label=\"Iris-Virginica\")\n", "plt.plot(X[y==1, 0], X[y==1, 1], \"bs\", label=\"Iris-Versicolor\")\n", "plt.plot(X[y==0, 0], X[y==0, 1], \"yo\", label=\"Iris-Setosa\")\n", "\n", "from matplotlib.colors import ListedColormap\n", "custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n", "\n", "plt.contourf(x0, x1, zz, cmap=custom_cmap)\n", "contour = plt.contour(x0, x1, zz1, cmap=plt.cm.brg)\n", "plt.clabel(contour, inline=1, fontsize=12)\n", "plt.xlabel(\"꽃잎의 길이\", fontsize=14)\n", "plt.ylabel(\"꽃잎의 폭\", fontsize=14)\n", "plt.legend(loc=\"center left\", fontsize=14)\n", "plt.axis([0, 7, 0, 3.5])\n", "save_fig(\"softmax_regression_contour_plot\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([2])" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "softmax_reg.predict([[5, 2]])" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[6.33134078e-07, 5.75276067e-02, 9.42471760e-01]])" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "softmax_reg.predict_proba([[5, 2]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 연습문제 해답" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. to 11." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "부록 A를 참고하세요." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 12. 조기 종료를 사용한 배치 경사 하강법으로 소프트맥스 회귀 구현하기\n", "(사이킷런을 사용하지 않고)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "먼저 데이터를 로드합니다. 앞서 사용했던 Iris 데이터셋을 재사용하겠습니다." ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [], "source": [ "X = iris[\"data\"][:, (2, 3)] # 꽃잎 길이, 꽃잎 넓이\n", "y = iris[\"target\"]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "모든 샘플에 편향을 추가합니다 ($x_0 = 1$):" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [], "source": [ "X_with_bias = np.c_[np.ones([len(X), 1]), X]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "결과를 일정하게 유지하기 위해 랜덤 시드를 지정합니다:" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [], "source": [ "np.random.seed(2042)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "데이터셋을 훈련 세트, 검증 세트, 테스트 세트로 나누는 가장 쉬운 방법은 사이킷런의 `train_test_split()` 함수를 사용하는 것입니다. 이 연습문제의 목적은 직접 만들어 보면서 알고리즘을 이해하는 것이므로 가능한 한가지 방법은 다음과 같습니다:" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [], "source": [ "test_ratio = 0.2\n", "validation_ratio = 0.2\n", "total_size = len(X_with_bias)\n", "\n", "test_size = int(total_size * test_ratio)\n", "validation_size = int(total_size * validation_ratio)\n", "train_size = total_size - test_size - validation_size\n", "\n", "rnd_indices = np.random.permutation(total_size)\n", "\n", "X_train = X_with_bias[rnd_indices[:train_size]]\n", "y_train = y[rnd_indices[:train_size]]\n", "X_valid = X_with_bias[rnd_indices[train_size:-test_size]]\n", "y_valid = y[rnd_indices[train_size:-test_size]]\n", "X_test = X_with_bias[rnd_indices[-test_size:]]\n", "y_test = y[rnd_indices[-test_size:]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "타깃은 클래스 인덱스(0, 1 그리고 2)이지만 소프트맥스 회귀 모델을 훈련시키기 위해 필요한 것은 타깃 클래스의 확률입니다. 각 샘플에서 확률이 1인 타깃 클래스를 제외한 다른 클래스의 확률은 0입니다(다른 말로하면 주어진 샘플에 대한 클래스 확률이 원-핫 벡터입니다). 클래스 인덱스를 원-핫 벡터로 바꾸는 간단한 함수를 작성하겠습니다:" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [], "source": [ "def to_one_hot(y):\n", " n_classes = y.max() + 1\n", " m = len(y)\n", " Y_one_hot = np.zeros((m, n_classes))\n", " Y_one_hot[np.arange(m), y] = 1\n", " return Y_one_hot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "10개 샘플만 넣어 이 함수를 테스트해 보죠:" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0, 1, 2, 1, 1, 0, 1, 1, 1, 0])" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y_train[:10]" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[1., 0., 0.],\n", " [0., 1., 0.],\n", " [0., 0., 1.],\n", " [0., 1., 0.],\n", " [0., 1., 0.],\n", " [1., 0., 0.],\n", " [0., 1., 0.],\n", " [0., 1., 0.],\n", " [0., 1., 0.],\n", " [1., 0., 0.]])" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "to_one_hot(y_train[:10])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "잘 되네요, 이제 훈련 세트와 테스트 세트의 타깃 클래스 확률을 담은 행렬을 만들겠습니다:" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [], "source": [ "Y_train_one_hot = to_one_hot(y_train)\n", "Y_valid_one_hot = to_one_hot(y_valid)\n", "Y_test_one_hot = to_one_hot(y_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "이제 소프트맥스 함수를 만듭니다. 다음 공식을 참고하세요:\n", "\n", "$\\sigma\\left(\\mathbf{s}(\\mathbf{x})\\right)_k = \\dfrac{\\exp\\left(s_k(\\mathbf{x})\\right)}{\\sum\\limits_{j=1}^{K}{\\exp\\left(s_j(\\mathbf{x})\\right)}}$" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [], "source": [ "def softmax(logits):\n", " exps = np.exp(logits)\n", " exp_sums = np.sum(exps, axis=1, keepdims=True)\n", " return exps / exp_sums" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "훈련을 위한 준비를 거의 마쳤습니다. 입력과 출력의 개수를 정의합니다:" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [], "source": [ "n_inputs = X_train.shape[1] # == 3 (특성 2와 편향)\n", "n_outputs = len(np.unique(y_train)) # == 3 (3개의 붓꽃 클래스)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "이제 좀 복잡한 훈련 파트입니다! 이론적으로는 간단합니다. 그냥 수학 공식을 파이썬 코드로 바꾸기만 하면 됩니다. 하지만 실제로는 꽤 까다로운 면이 있습니다. 특히, 항과 인덱스가 뒤섞이기 쉽습니다. 제대로 작동할 것처럼 코드를 작성했더라도 실제 제대로 계산하지 못합니다. 확실하지 않을 때는 각 항의 크기를 기록하고 이에 상응하는 코드가 같은 크기를 만드는지 확인합니다. 각 항을 독립적으로 평가해서 출력해 보는 것도 좋습니다. 사실 사이킷런에 이미 잘 구현되어 있기 때문에 이렇게 할 필요는 없습니다. 직접 만들어 보면 어떻게 작동하는지 이해하는데 도움이 됩니다.\n", "\n", "구현할 공식은 비용함수입니다:\n", "\n", "$J(\\mathbf{\\Theta}) =\n", "- \\dfrac{1}{m}\\sum\\limits_{i=1}^{m}\\sum\\limits_{k=1}^{K}{y_k^{(i)}\\log\\left(\\hat{p}_k^{(i)}\\right)}$\n", "\n", "그리고 그래디언트 공식입니다:\n", "\n", "$\\nabla_{\\mathbf{\\theta}^{(k)}} \\, J(\\mathbf{\\Theta}) = \\dfrac{1}{m} \\sum\\limits_{i=1}^{m}{ \\left ( \\hat{p}^{(i)}_k - y_k^{(i)} \\right ) \\mathbf{x}^{(i)}}$\n", "\n", "$\\hat{p}_k^{(i)} = 0$이면 $\\log\\left(\\hat{p}_k^{(i)}\\right)$를 계산할 수 없습니다. `nan` 값을 피하기 위해 $\\log\\left(\\hat{p}_k^{(i)}\\right)$에 아주 작은 값 $\\epsilon$을 추가하겠습니다." ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 5.446183864821945\n", "500 0.8351003035768683\n", "1000 0.6876961554414913\n", "1500 0.6010299835452123\n", "2000 0.5442782811959168\n", "2500 0.5037262742244606\n", "3000 0.4728357293908467\n", "3500 0.4481872508179334\n", "4000 0.4278347262806173\n", "4500 0.4105891022823527\n", "5000 0.3956803257488941\n" ] } ], "source": [ "eta = 0.01\n", "n_iterations = 5001\n", "m = len(X_train)\n", "epsilon = 1e-7\n", "\n", "Theta = np.random.randn(n_inputs, n_outputs)\n", "\n", "for iteration in range(n_iterations):\n", " logits = X_train.dot(Theta)\n", " Y_proba = softmax(logits)\n", " loss = -np.mean(np.sum(Y_train_one_hot * np.log(Y_proba + epsilon), axis=1))\n", " error = Y_proba - Y_train_one_hot\n", " if iteration % 500 == 0:\n", " print(iteration, loss)\n", " gradients = 1/m * X_train.T.dot(error)\n", " Theta = Theta - eta * gradients" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "바로 이겁니다! 소프트맥스 모델을 훈련시켰습니다. 모델 파라미터를 확인해 보겠습니다:" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 3.3172417 , -0.6476445 , -2.99855999],\n", " [-1.16505434, 0.11283387, 0.10251113],\n", " [-0.72087779, -0.083875 , 1.48587045]])" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Theta" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "검증 세트에 대한 예측과 정확도를 확인해 보겠습니다:" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9666666666666667" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "logits = X_valid.dot(Theta)\n", "Y_proba = softmax(logits)\n", "y_predict = np.argmax(Y_proba, axis=1)\n", "\n", "accuracy_score = np.mean(y_predict == y_valid)\n", "accuracy_score" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "와우, 이 모델이 매우 잘 작동하는 것 같습니다. 연습을 위해서 $\\ell_2$ 규제를 조금 추가해 보겠습니다. 다음 코드는 위와 거의 동일하지만 손실에 $\\ell_2$ 페널티가 추가되었고 그래디언트에도 항이 추가되었습니다(`Theta`의 첫 번째 원소는 편향이므로 규제하지 않습니다). 학습률 `eta`도 증가시켜 보겠습니다." ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 6.629574947908294\n", "500 0.5341631554372782\n", "1000 0.5037712748637473\n", "1500 0.4948056455575166\n", "2000 0.4914081948411196\n", "2500 0.4900085074445458\n", "3000 0.4894074289613261\n", "3500 0.4891431024691195\n", "4000 0.4890251654906585\n", "4500 0.48897205809605315\n", "5000 0.4889480004791562\n" ] } ], "source": [ "eta = 0.1\n", "n_iterations = 5001\n", "m = len(X_train)\n", "epsilon = 1e-7\n", "alpha = 0.1 # 규제 하이퍼파라미터\n", "\n", "Theta = np.random.randn(n_inputs, n_outputs)\n", "\n", "for iteration in range(n_iterations):\n", " logits = X_train.dot(Theta)\n", " Y_proba = softmax(logits)\n", " xentropy_loss = -np.mean(np.sum(Y_train_one_hot * np.log(Y_proba + epsilon), axis=1))\n", " l2_loss = 1/2 * np.sum(np.square(Theta[1:]))\n", " loss = xentropy_loss + alpha * l2_loss\n", " error = Y_proba - Y_train_one_hot\n", " if iteration % 500 == 0:\n", " print(iteration, loss)\n", " gradients = 1/m * X_train.T.dot(error) + np.r_[np.zeros([1, n_outputs]), alpha * Theta[1:]]\n", " Theta = Theta - eta * gradients" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "추가된 $\\ell_2$ 페널티 때문에 이전보다 손실이 조금 커보이지만 더 잘 작동하는 모델이 되었을까요? 확인해 보죠:" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "logits = X_valid.dot(Theta)\n", "Y_proba = softmax(logits)\n", "y_predict = np.argmax(Y_proba, axis=1)\n", "\n", "accuracy_score = np.mean(y_predict == y_valid)\n", "accuracy_score" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "와우, 완벽한 정확도네요! 운이 좋은 검증 세트일지 모르지만 잘 된 것은 맞습니다." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "이제 조기 종료를 추가해 보죠. 이렇게 하려면 매 반복에서 검증 세트에 대한 손실을 계산해서 오차가 증가하기 시작할 때 멈춰야 합니다." ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 4.70940845273367\n", "500 0.5740996073458013\n", "1000 0.5436382813658035\n", "1500 0.5356387684314269\n", "2000 0.5332563789170384\n", "2500 0.5326544271776569\n", "2765 0.5326058224570446\n", "2766 0.5326058230506046 early stopping!\n" ] } ], "source": [ "eta = 0.1 \n", "n_iterations = 5001\n", "m = len(X_train)\n", "epsilon = 1e-7\n", "alpha = 0.1 # 규제 하이퍼파라미터\n", "best_loss = np.infty\n", "\n", "Theta = np.random.randn(n_inputs, n_outputs)\n", "\n", "for iteration in range(n_iterations):\n", " logits = X_train.dot(Theta)\n", " Y_proba = softmax(logits)\n", " xentropy_loss = -np.mean(np.sum(Y_train_one_hot * np.log(Y_proba + epsilon), axis=1))\n", " l2_loss = 1/2 * np.sum(np.square(Theta[1:]))\n", " loss = xentropy_loss + alpha * l2_loss\n", " error = Y_proba - Y_train_one_hot\n", " gradients = 1/m * X_train.T.dot(error) + np.r_[np.zeros([1, n_outputs]), alpha * Theta[1:]]\n", " Theta = Theta - eta * gradients\n", "\n", " logits = X_valid.dot(Theta)\n", " Y_proba = softmax(logits)\n", " xentropy_loss = -np.mean(np.sum(Y_valid_one_hot * np.log(Y_proba + epsilon), axis=1))\n", " l2_loss = 1/2 * np.sum(np.square(Theta[1:]))\n", " loss = xentropy_loss + alpha * l2_loss\n", " if iteration % 500 == 0:\n", " print(iteration, loss)\n", " if loss < best_loss:\n", " best_loss = loss\n", " else:\n", " print(iteration - 1, best_loss)\n", " print(iteration, loss, \"early stopping!\")\n", " break" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "logits = X_valid.dot(Theta)\n", "Y_proba = softmax(logits)\n", "y_predict = np.argmax(Y_proba, axis=1)\n", "\n", "accuracy_score = np.mean(y_predict == y_valid)\n", "accuracy_score" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "그래도 완벽하고 더 빠릅니다." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "이제 전체 데이터셋에 대한 모델의 예측을 그래프로 나타내 보겠습니다:" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x0, x1 = np.meshgrid(\n", " np.linspace(0, 8, 500).reshape(-1, 1),\n", " np.linspace(0, 3.5, 200).reshape(-1, 1),\n", " )\n", "X_new = np.c_[x0.ravel(), x1.ravel()]\n", "X_new_with_bias = np.c_[np.ones([len(X_new), 1]), X_new]\n", "\n", "logits = X_new_with_bias.dot(Theta)\n", "Y_proba = softmax(logits)\n", "y_predict = np.argmax(Y_proba, axis=1)\n", "\n", "zz1 = Y_proba[:, 1].reshape(x0.shape)\n", "zz = y_predict.reshape(x0.shape)\n", "\n", "plt.figure(figsize=(10, 4))\n", "plt.plot(X[y==2, 0], X[y==2, 1], \"g^\", label=\"Iris-Virginica\")\n", "plt.plot(X[y==1, 0], X[y==1, 1], \"bs\", label=\"Iris-Versicolor\")\n", "plt.plot(X[y==0, 0], X[y==0, 1], \"yo\", label=\"Iris-Setosa\")\n", "\n", "from matplotlib.colors import ListedColormap\n", "custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n", "\n", "plt.contourf(x0, x1, zz, cmap=custom_cmap)\n", "contour = plt.contour(x0, x1, zz1, cmap=plt.cm.brg)\n", "plt.clabel(contour, inline=1, fontsize=12)\n", "plt.xlabel(\"꽃잎 길이\", fontsize=14)\n", "plt.ylabel(\"꽃잎 폭\", fontsize=14)\n", "plt.legend(loc=\"upper left\", fontsize=14)\n", "plt.axis([0, 7, 0, 3.5])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "이제 테스트 세트에 대한 모델의 최종 정확도를 측정해 보겠습니다:" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9333333333333333" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "logits = X_test.dot(Theta)\n", "Y_proba = softmax(logits)\n", "y_predict = np.argmax(Y_proba, axis=1)\n", "\n", "accuracy_score = np.mean(y_predict == y_test)\n", "accuracy_score" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "완벽했던 최종 모델의 성능이 조금 떨어졌습니다. 이런 차이는 데이터셋이 작기 때문일 것입니다. 훈련 세트와 검증 세트, 테스트 세트를 어떻게 샘플링했는지에 따라 매우 다른 결과를 얻을 수 있습니다. 몇 번 랜덤 시드를 바꾸고 이 코드를 다시 실행해 보면 결과가 달라지는 것을 확인할 수 있습니다." ] } ], "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": "3.5.5" }, "nav_menu": {}, "toc": { "navigate_menu": true, "number_sections": true, "sideBar": true, "threshold": 6, "toc_cell": false, "toc_section_display": "block", "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 1 }