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hands-on/04_training_linear_models.ipynb
2018-01-31 13:53:11 +09:00

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Chapter 4 Training Linear Models**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"_This notebook contains all the sample code and solutions to the exercises in chapter 4._"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Setup"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, let's make sure this notebook works well in both python 2 and 3, import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# To support both python 2 and python 3\n",
"from __future__ import division, print_function, unicode_literals\n",
"\n",
"# Common imports\n",
"import numpy as np\n",
"import os\n",
"\n",
"# to make this notebook's output stable across runs\n",
"np.random.seed(42)\n",
"\n",
"# To plot pretty figures\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",
"# Where to save the figures\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",
" print(\"Saving figure\", fig_id)\n",
" if tight_layout:\n",
" plt.tight_layout()\n",
" plt.savefig(path, format='png', dpi=300)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Linear regression using the Normal Equation"
]
},
{
"cell_type": "code",
"execution_count": 2,
"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": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure generated_data_plot\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f137c6c8b00>"
]
},
"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": 4,
"metadata": {},
"outputs": [],
"source": [
"X_b = np.c_[np.ones((100, 1)), X] # add x0 = 1 to each instance\n",
"theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[4.21509616],\n",
" [2.77011339]])"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"theta_best"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[4.21509616],\n",
" [9.75532293]])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X_new = np.array([[0], [2]])\n",
"X_new_b = np.c_[np.ones((2, 1)), X_new] # add x0 = 1 to each instance\n",
"y_predict = X_new_b.dot(theta_best)\n",
"y_predict"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f13600d2da0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(X_new, y_predict, \"r-\")\n",
"plt.plot(X, y, \"b.\")\n",
"plt.axis([0, 2, 0, 15])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The figure in the book actually corresponds to the following code, with a legend and axis labels:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure linear_model_predictions\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f135565d400>"
]
},
"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": [
"# Linear regression using batch gradient descent"
]
},
{
"cell_type": "code",
"execution_count": 11,
"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": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[4.21509616],\n",
" [2.77011339]])"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"theta"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[4.21509616],\n",
" [9.75532293]])"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X_new_b.dot(theta)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure gradient_descent_plot\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f13440f6eb8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"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)\n",
"\n",
"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": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure gradient_descent_plot\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f13440820b8>"
]
},
"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": [
"# Stochastic Gradient Descent"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"theta_path_sgd = []\n",
"m = len(X_b)\n",
"np.random.seed(42)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure sgd_plot\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f133d0732b0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n_epochs = 50\n",
"t0, t1 = 5, 50 # learning schedule hyperparameters\n",
"\n",
"def learning_schedule(t):\n",
" return t0 / (t + t1)\n",
"\n",
"theta = np.random.randn(2,1) # random initialization\n",
"\n",
"for epoch in range(n_epochs):\n",
" for i in range(m):\n",
" if epoch == 0 and i < 20: # not shown in the book\n",
" y_predict = X_new_b.dot(theta) # not shown\n",
" style = \"b-\" if i > 0 else \"r--\" # not shown\n",
" plt.plot(X_new, y_predict, style) # not shown\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) # not shown\n",
"\n",
"plt.plot(X, y, \"b.\") # not shown\n",
"plt.xlabel(\"$x_1$\", fontsize=18) # not shown\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18) # not shown\n",
"plt.axis([0, 2, 0, 15]) # not shown\n",
"save_fig(\"sgd_plot\") # not shown\n",
"plt.show() # not shown"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[4.21076011],\n",
" [2.74856079]])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"theta"
]
},
{
"cell_type": "code",
"execution_count": 19,
"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": 19,
"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": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(array([4.16782089]), array([2.72603052]))"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sgd_reg.intercept_, sgd_reg.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Mini-batch gradient descent"
]
},
{
"cell_type": "code",
"execution_count": 21,
"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) # random initialization\n",
"\n",
"t0, t1 = 10, 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 * 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": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[4.25214635],\n",
" [2.7896408 ]])"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"theta"
]
},
{
"cell_type": "code",
"execution_count": 23,
"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": 24,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure gradient_descent_paths_plot\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f133c1acb70>"
]
},
"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": [
"# Polynomial regression"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import numpy.random as rnd\n",
"\n",
"np.random.seed(42)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"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": 27,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure quadratic_data_plot\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAF69JREFUeJzt3X+MZWddx/HPZ7cswmaxVFvQwihguyWFhqRDYajKYpHKiqjZlIBoSZBOFVBIKNGtrFRK3IrYFn80dfmR7BL5YWxhBRUpq2sszKadltAScZGCNMWq0NJSoLDt9usf546dnd5759x7z3nOc855v5LNzd65c89zf8z5nOd5vuc5jggBAJCbDU03AACAYQgoAECWCCgAQJYIKABAlggoAECWCCgAQJYIKABAlioNKNuPsn2R7Qdsv3zV/c+3fbPtW2wv235uldsFAHTPcRU/3wWSQtKhlTtsHy/pWkkviYgl29sk7bf9lIj4bsXbBwB0RKU9qIi4KiL+RNLRVXefK+lwRCwNHnNQ0p2Szqly2wCAbqm6BzXMUyXdtua+2wb3P4LtRUmLkrR58+YzTzvttHpbBwCo3He+Ix0+LEVItrR1q7R5c/Gzm2666RsRceJ6z5EioKxje1SS9KBG9N4iYo+kPZI0Pz8fy8vL9bYOAFC53bulXbuko0elDRuk88+Xdu4sfmb7q2WeI0UV3x2S5tbcNze4HwDQQdu2SZs2SRs3Frfbtk3+HCl6UPslXW77mRFxq+2zJJ0m6boE2wYANGBhQTpwQDp4sAinhYXJn6P2gIqIe22fJ+l9tkPF8N72iLin7m0DAJqzsDBdMK2oJaAiYtua//+zpGfXsS0AQDexkgQAIEsEFAAgSwQUACBLBBQAIEsEFAAgSwQUACBLBBQAIEsEFAAgSwQUACBLBBQAIEsEFAAgSwQUAGAmS0vF9Z+Wlqp93hSX2wAAdNTSknTOOdKRI8V1nw4cmG0F89XoQQEApnbwYBFOR48WtwcPVvfcBBQAYGpVXDl3FIb4AABTq+LKuaMQUACAmcx65dxRGOIDAGSJgAIAZImAAgBkiYACAGSJgAIAZImAAgBkiYACAGSJgAIAZImAAgBkiYACAGSJgAKAzNV1vaXcsRYfAGSszust5Y4eFABkrM7rLeWOgAKAjNV5vaWymhpiZIgPADJW1fWWlpbKP8fqx0rNDTESUACQuVmvtzTJPNbax77qVY8cYkwVUAzxAUDHTTKPtfaxUnNDjPSgAKDjVuaxVnpF40Jm7WPPP7/4t29fosau4ohIsyH7zZJ+TdL9kh4j6UMR8Yfjfmd+fj6Wl5dTNA8AOm3aOaiFhepL3W3fFBHz6z0uSQ/K9k9JeqOkMyLiLtsnSLrZ9o0RcV2KNgBAl60XQJPMY6197LAhwhTzUKmG+L4+uH28pLskPU7F/Nf/JNo+AHRW3SfzTjJEWKUkARUR/257UdKNtr8u6SRJr46IW9Y+dvC4RUmam5tL0TwAaLW6ezhVlbpPKtUQ36mSrpb0sxGxbPsnJH3c9n9FxKHVj42IPZL2SMUcVIr2AUCbpejhzFrqPo1UQ3wvlXR9RCxLUkR8yfZHJP2KpENjfxMAMNa0PZxJCidSPM9aqQLqi5LeYPtHIuJO24+TdK6k9ybaPgB02qQ9nKrmreqc/0pyom5E/K2kKyR9wvYhSddL+kcVw34AgMSqWoS2zsVsk52oGxGXS7o81fYAAKNVNW9V5/wXK0kAQA9VVZlXZ4VfspUkpsFKEgDQPWVXkmCxWABAlggoAECWCCgAQJYIKABAlggoAECWCCgAQJYIKABAlggoAECWCCgAQJYIKABAlggoAECWCCgAQJYIKABAlggoAECWCCgAQJYIKABAlggoAMBUlpak3buL2zpwyXcASGhpqZ7Lo6e2tCSdc4505Ii0aVNx2feqXw8BBQCJpNipp3LwYPE6jh4tbg8erP61MMQHAIkM26nXoe6hN6noAW7aJG3cWNxu21b9NuhBAUAiKzv1lR5UHTv1VL20hYXiuescriSgACCRFDv1FENvKxYW6h2iJKAAIKG6d+opemmpEFAA0CEpemmpEFAA0DF199JSoYoPAJAlAgoAkCUCCgCQJQIKAJAlAgoAkCUCCgCQJQIKAFogxfp6ueE8KADIXJdWQZ9E0h6U7TfZ/rztG20v235syu0DQBulWgU9N8l6ULb/QNKjJT0rIh60fbyk76XaPoBuyvkCgFW1rUvr600iSUANwuhcSR+T9Gnb35N0WUT8w5DHLkpalKS5ubkUzQPQUjkPfVXZti6trzeJVEN8Z0o6XdIdEfEcSW+U9AHbT1v7wIjYExHzETF/4oknJmoegDbKeeir6rYtLEg7d/YnnKR0AXWSpP+MiL2SFBGflXRA0s8l2j6ADkpxVddp5dy2tkg1B/W/kr615r6HJB1NtH0AHZTz0FfObWsLR0T9G7E3SfqqpPMi4nrbWyV9WtJZEfHlUb83Pz8fy8vLtbcPAJCO7ZsiYn69xyXpQUXEEdvbJb3H9gYVvadXjQsnAEC/JSszH8w7nZlqewCQUs7l7m1VqkjC9tW2w/aPDvnZVttHbL+r+uYBQP5WSsp37Spu+7QcUZ3KVvGtvN1nDfnZFSoKIC6pokEA0DY5l7u3WdmAOjS4PSagbP+8pBdL+v2I+GaVDQOAtlhdUn7ccdLtt9OLqkKpgIqIw5Lu1qqAsv0oSZdL+rykv6yldQAwg1QrgK+UlF9wgRQhvfvd44f6+rgy+TQmKZI4JOls246iNv0Nkk6V9MKI4HwmAFlJvQzSwkIxtHf06LFDfWu3mfPyTLmZZCWJQ5J+UNJW2ydJ2iXpoxFxoJaWAcAMmpgXKrN6BPNV5U3Sg1pdKPHTKlYmf1PlLQKACjSxAniZ1SP6ujL5NEqvJGF7i6R7JF0v6Scl/XFE/G6NbWMlCQAzyfXcpFzblUrZlSQmWurI9q2SniHpvyWdGhH3Td/E9RFQANA9ZQNq0tXMbxjc7qw7nAAA/VY6oAZl5dskLUvaW1eDAACQJiuSuEjSUyS9MlIsgQ4A6LWxAWX7BBWXaj9D0pslXR4Rh8b9DgAAVVivB3WupA+ouODgFZJqrdoDAGDF2ICKiA9K+mCitmSv76WhAJBSsutBtR3LkwBAWpOWmfcWy5MAQFoEVEll1tgCAFSHIb6SyqyxBQCoDgE1gYUFggn9RIFQgfchLQIKwFgUCBV4H9JjDgrAWG0tEKr6qrVtfR/ajB4UgLHaeP2iOno7bXwf2o6AAjBWGwuEhvV21mv3evNLbXwf2o6AArCuthUITdrbKdvjatv70HYEFIDOWent7NtX7vHjelxU7jWHgALQWXv3FoGzd+/4eahRPS4q95pFFR+ATpqk6m6lx3XppceGEJV7zepdD4ruOtAPk85DDZtfonKvWb0KKLrrQH/MWnW3cjB75ZXSXXdxUNuETgXUer2jaUpPAeSpzGjItFV3HMzmobUBtfbLWeYLRXcd6Ia6A4SD2Ty0MqCGfTnLfKE40Q7ohroDhIPZPLQyoIZ9Oct+odp8oh0FHkCh7gDhYDYPrQyoYV/Orn+hGBMHHtb1v3cUkgeU7dMl/aukP42IS6Z5jlFfzjb3jtbDmDhwrDr/3jkgzEPSgLJ9vKS/kPTBsr8zaliry2E0DGPiQDocEOYhWUDZ3iBpr6SLJb1ozOMWJS1K0hOe8DSOYgYY0gDS4YAwDyl7UG+XdF1EfMb2yICKiD2S9kjSk540HxzFPKxvvUagKRwQ5iFJQNneIWkuIi6e5Pe2bJHuvpujGADpcUDYvFQ9qBdLerrtQ4P/P0kqCiYi4rxRv7R5M0cxANBXSQIqIl6z+v+2Lxncf8l6v8tRDICmcO5hs1p5HhQA1I1S8+Y1ElDTnv8EAKlQat48LlgItNzSkrR7d3GL6qyUmm/cSJFWUxjiA1qMYaj6UGrePAIKaLGmh6HqLCIo89x1FzFQpNWsVgfULF9OqnPQBU2ueFBn763Mc9N77L7WBtQsX06+2OiKJoeh6uy9lXnupnuPqF9riySGfTnXGjV5XOZ3gbZYWJB27ky/c66ziKDMc1PE0H2t7UGtN7QxrpfEQpDA7OrsvZV5booYuq+1AbXel3Nc958vNlCNOosIyjw3RQzd1tqAksZ/OdfrJc36xabIAgDq1eqAGqfOXhJFFugjDsqQWmcDSqqv+z9q+JA/YHQVB2VoQqcDqi7Dhg/5A0aXUdKNJrS2zHxWs6xftjJ8eOmlDwcRpevTYR25dqCkG03oZQ+qit7O2uFDStcnR6+zPah8RRN6GVDDeju33ipdc420Y4e0uDj5c/IHPDmGjdqFkm6k1suAWtvbuece6eKLi5998pPF7bQhxR/waGuLSOh1VosiHXRNLwNqbW/nkkuO/fk110wXUHVr8w5o1HAevc5qMFyKLuplQEnH9nZ27Hi457Ty/9y0fQc0ajiPXmc1GC5FF/U2oFZb6S3NMgdVt7bvgBjOqxfvL7rIEdF0G0aan5+P5eXlppuRhbb3oKR2D1G2Ae8v2sL2TRExv+7jCKj2YAcEoAvKBhRDfC3CfA2APuntShIAgLwRUAD+X6qlp1jiCmUwxAdAUrpCnC4U/CANelCJcMSI3KVa8JiFlVEWPagExh0x5lyZl3PbUL1U51JxzhbKIqASGHeBw1yHOnJuG+pR1dJT6x3YsMQVyiKgEhh1xDjr6hB19nDavnIFpjPrqQxlD2w4ZQJlEFAVGxYao44YZxnqWG9HMGt4pRqG6fIwYpdf2ygc2KBKBFSFxoXGsCPGWYY6xu0IqrogY93DMF0eRuzyaxuH+SVUiYCq0DRHj9MOdYzbEVR1FFv3MEyXj7a7/NrGYX4JVSKgKlTl0eMsE81tOYptSzun0eXXth7ml1CVTi8W28QcQBXbrGJ4qC3zH21p5zS6/NqAWWS3WKztCyW9VtIDkjZJujoirqpre03NAVRx9FjF8FBbjmLb0s5pVPnaCDv0UZKAsr1R0imSzo6Ib9s+WdKXbO+PiK/Vsc02zwEMGx5iB5XWsPe7qc+gqYMtvnNoWpKAioijki5addddko5I2ljXNts8B7B2fknqZ0VYU4YFgtTcZ9DEwVZfqxCRl6aKJK6U9OGIuH3tD2wvSlqUpLm5uak30PZqotXDQ7t3t7c32Eaj1opr6jNo4mCrzSMQ6I7kAWX77ZJOlrRj2M8jYo+kPVJRJDHLttowv1FmGKXNvcE2GvV+N/UZNHGwxXcOOUgaULbfKelpknZExJGU287RJMvCtLk3WKUU8yKj3u8mP4OV7a305urePt855CBVkcQGSVdJeryk8yLiwRTbzd0kwyg59gZTT6KnnBcZtfJHU59BE3NCOX7n0C+prge1XdKFkp4q6Xrbhwb/Xpho+1laGUbZuLF9wygrO8xdu4rbFNe5GjU31Ad9fu3or1RVfB+X5BTbapM2D6M0MYne53mRaV87peJoM5Y6qsAsO4G2DqM0ERbjAr3rO+JpDmYoFUfbEVAz6utOoOwOs+rgGBboffkMJj2YoVQcbUdAzajPO4G1O8y1YZQqOPr8GYzT5yFRdAMBNUZbzlHKYXhrWBilCo4cPoMctXmOE5AIqJHaco5SLsNbw8IoVXA0/RnkrK1znIBEQI3UlnOUchneGhZGKYODHTHQPQTUCG0ZNsqlnaPCiOAAMK1OX7BwVjnM7ZTRlnYCgFT+goUEFForRTA3Gf4ceKCrsruiLrohl51miuKQJgtQmi5+yeVzRr8RUCit6Z3maimKQ5osQGly2zl9zui3VIvFogNyWrA0xUK7dW9jaam4GOWwhXabXEg4p88Z/UYPCqXlUjEopSlhr3Mb6/VSmjy3K6fPGf1GQKG03E6ITVHCXtc2ygzhNVWin9vnjP4ioDARzmuqRu69FD5n5ICAAhpALwVYHwEFNIReCjAeVXwAgCwRUKjVuFJq8P4A4zDEh9rkcMJnzisi5PD+jJLz+4b+IKBQm6YvBZJzAEjl35/UYZH7+4b+YIgPtWlyNQQp/xURyrw/K2Gxa1dxm2IoMPf3Df1BDwq1abqUug3nGq33/jTRC839fUN/cLkNdFrb51KaGm5r+/uGvHE9qAz1/Y++769/Wrxv6BquB5WZuo6E27LzYuJ9epzQi76iSCKROiaem5hAnxYT7wAmRUAlUkdFW5t2+k1X9AFoH4b4Eqmjoq1N1VZNV/TVqS3DrEDbUCTRcl3ZObb1dTC3BkyOIome6MIE+iQ7+dyCrOnVMoAuI6DQuEmW/Mmtt9KmYVagbQgoNK7sTj7H3kqX59aAphFQaFzZnXyuvZUuDLMCOSKgUJlZ5ofK7OTprQD9kiygbD9f0hWDbR6R9PqIOJRq+6hXqvkheitAfyQ5Udf28ZKulfS6iDhD0kWS9tt+bIrto35tOmkYQDukWkniXEmHI2JJkiLioKQ7JZ2TaPuoGStFAKhaqiG+p0q6bc19tw3uP4btRUmLg/9+3/bna25bjn5Y0jeabsTktmyWHrfl/vu/dd/znnffd6Z8kpa+9pn19XVLvPY+vvatZR6UKqAs6eia+x7UkB5cROyRtEeSbC+XOdu4a/r6uqX+vva+vm6J197H12671BJBqYb47pA0t+a+ucH9AAA8QqqA2i/pDNvPlCTbZ0k6TdJ1ibYPAGiZJEN8EXGv7fMkvc92qBje2x4R96zzq3vqb12W+vq6pf6+9r6+bonX3kelXnfWq5kDAPqLCxYCALJEQAEAskRAAQCylGVA2T7B9j7bt9o+ZPsztrc13a662d5i+49sf8H2DbZvHKxh2AuDz/39tsP2E5tuTwq2n2/7Ztu32F62/dym25SK7UfZvsj2A7Zf3nR7UrJ9oe3PDT7zW2y/tuk2pWD70sHrvmHwvf/NcY/PdTXzEyVdGxHnS5Lt7ZL2SvqxRltVv60qVtg4PSIesr1D0rslndpss5J5m6S/lvSrTTckhVVrVL4kIpYGB2H7bT8lIr7bbOuSuEBSSOrVotG2N0o6RdLZEfFt2ydL+pLt/RHxtYabV7dvSpqPiAdsnyjpK7Y/ERFfGfbgLAMqIg5LOixJtjeo+DC/2GijEoiIZUmrz7C+U5l+RnWIiNdLku2mm5LKI9aotL2yRuXHGm1ZAhFxlSTZ/oWm25JSRBxVsWD2irtUXOFhYzMtSiciLl/13x+X9G1Jd496fNY7v0G3/10qPsBzG25OUrY3S/ozSbuabgtqU3qNSnTalZI+HBG3N92QFGyfIunvJf2QpJdFxL2jHpvlHNSKiPiQpCdKukzSP9l+dMNNSsL2YyR9RNLfRMRfNd0e1Kb0GpXoJttvl3SypNc33ZZUIuI/IuIUFSMF+2yfPuqx2f8hRGGfpBNUDPV1mu0tKo4uPhURu5tuD2rFGpU9Zvudkk6XtCMijjTdntQi4rOSliS9YNRjsgwo279s+8xV/3+BpIckfbm5VtXP9uNVrE/40Yh4R9PtQe1Yo7KHbG+wfbWkJ0s6ry/hZPuZtl/mwSTzoDjkOTp23v0Yuc5B/Zuky2w/WcWQx4OSXtqDyqbfk/QMSa+w/YpV92+PiJETiWinGdaoRLttl3Shih3z9auKgt4SEZ9qrFX1+6qk35D0O7YfkLRJ0q6IGFnFyVp8AIAsZTnEBwAAAQUAyBIBBQDIEgEFAMgSAQUAyBIBBQDIEgEFAMgSAQUAyBIBBQDIEgEFAMgSAQUAyBIBBSRi+zG277B9+9prm9l+j+2jg4t0AhABBSQTEfdLequKyyy8duV+27sl/bqk3xpcpBOAWM0cSMr2Rkmfk3SSiku7v0bSFZLeGhFva7JtQG4IKCAx2y+R9DFJByT9jKQ/j4jfbrZVQH4Y4gMSi4iPS7pZ0jmSPizpDWsfY/t1tm+w/T3bBxM3EchCrlfUBTrL9sskPWvw3/ti+DDGnZIuk/RsSQup2gbkhIACErL9Iknvl/QRSQ9IerXtKyLiC6sfFxHXDh4/l76VQB4Y4gMSsf0cSddK+rSkV0p6i6SHJO1usl1ArggoIAHbT5f0d5K+KOmXIuL7EXGbpPdK+kXbZzfaQCBDBBRQs8Ew3Scl3SvpxRHxrVU/fpuk+yW9o4m2ATljDgqoWUTcruLk3GE/u1PSY9O2CGgHAgrIkO3jVPx9Hidpg+0fkPRQRBxptmVAOgQUkKe3qFgWacX9kv5F0rZGWgM0gJUkAABZokgCAJAlAgoAkCUCCgCQJQIKAJAlAgoAkCUCCgCQJQIKAJCl/wNUV+CJcVxGkAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f133c1f44e0>"
]
},
"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": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-0.75275929])"
]
},
"execution_count": 28,
"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": 29,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-0.75275929, 0.56664654])"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X_poly[0]"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(array([1.78134581]), array([[0.93366893, 0.56456263]]))"
]
},
"execution_count": 30,
"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": 31,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure quadratic_predictions_plot\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f133d086668>"
]
},
"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": 32,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure high_degree_polynomials_plot\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f135561e668>"
]
},
"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": 33,
"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_predict, y_train[:m]))\n",
" val_errors.append(mean_squared_error(y_val_predict, y_val))\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) # not shown in the book\n",
" plt.xlabel(\"훈련 세트 크기\", fontsize=14) # not shown\n",
" plt.ylabel(\"RMSE\", fontsize=14) # not shown"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure underfitting_learning_curves_plot\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f135559ee10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lin_reg = LinearRegression()\n",
"plot_learning_curves(lin_reg, X, y)\n",
"plt.axis([0, 80, 0, 3]) # not shown in the book\n",
"save_fig(\"underfitting_learning_curves_plot\") # not shown\n",
"plt.show() # not shown"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure learning_curves_plot\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f13600b9e10>"
]
},
"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]) # not shown\n",
"save_fig(\"learning_curves_plot\") # not shown\n",
"plt.show() # not shown"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Regularized models"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure ridge_regression_plot\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f133d0c27b8>"
]
},
"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": 37,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1.55071465]])"
]
},
"execution_count": 37,
"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": 38,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([1.13500145])"
]
},
"execution_count": 38,
"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": 39,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1.5507201]])"
]
},
"execution_count": 39,
"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": 40,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure lasso_regression_plot\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f13555ac128>"
]
},
"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": 41,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([1.53788174])"
]
},
"execution_count": 41,
"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": 42,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([1.54333232])"
]
},
"execution_count": 42,
"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": 43,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure early_stopping_plot\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1344043780>"
]
},
"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_predict, y_train))\n",
" val_errors.append(mean_squared_error(y_val_predict, y_val))\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": 44,
"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) # continues where it left off\n",
" y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
" val_error = mean_squared_error(y_val_predict, y_val)\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": 45,
"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": 45,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"best_epoch, best_model"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [],
"source": [
"t1a, t1b, t2a, t2b = -1, 3, -1.5, 1.5\n",
"\n",
"# ignoring bias term\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": 48,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/haesun/anaconda3/envs/handson-ml/lib/python3.5/site-packages/matplotlib/cbook/deprecation.py:106: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance. In a future version, a new instance will always be created and returned. Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.\n",
" warnings.warn(message, mplDeprecation, stacklevel=1)\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure lasso_vs_ridge_plot\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1355ecd6a0>"
]
},
"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",
"\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",
"\n",
"for subplot in (221, 223):\n",
" plt.subplot(subplot)\n",
" plt.ylabel(r\"$\\theta_2$\", fontsize=20, rotation=0)\n",
"\n",
"for subplot in (223, 224):\n",
" plt.subplot(subplot)\n",
" plt.xlabel(r\"$\\theta_1$\", fontsize=20)\n",
"\n",
"save_fig(\"lasso_vs_ridge_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Logistic regression"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure logistic_function_plot\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f133dedd198>"
]
},
"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": 50,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"['target', 'feature_names', 'DESCR', 'target_names', 'data']"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn import datasets\n",
"iris = datasets.load_iris()\n",
"list(iris.keys())"
]
},
{
"cell_type": "code",
"execution_count": 51,
"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": 52,
"metadata": {},
"outputs": [],
"source": [
"X = iris[\"data\"][:, 3:] # petal width\n",
"y = (iris[\"target\"] == 2).astype(np.int) # 1 if Iris-Virginica, else 0"
]
},
{
"cell_type": "code",
"execution_count": 53,
"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": 53,
"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": 54,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f133c26c780>]"
]
},
"execution_count": 54,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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Bu66/i7kD52qC91Ga5JXHaNrUTrGsVQt++slOsYzVKzpuF/57OLfNuY3ElETGNx/PtF7T8Pf720xn5SM0ySuPUq+eTfQNG8LWrfbCrCZ695m9bTaD5g4iKTWJR1o9wlvd39I58D5Oz67yODVqwMqV0KgRbNtmSxerK/fJL58wPHw4KSaFp9o9xcs3v4xcWLtR+Sy98Ko8UtWqdmz+yy+1iqU7zNo2izsi7sBgeL7T8zzd/mmnQ1IFRHvyymNVrQr33Zf+PDoatNRR7s3bMY+RX47EYJjUaZIm+EJGk7zyCtHR0LGjnXVz4oTT0XiPhTsXMnT+UFJMCk+3e5qn2j/ldEiqgGmSV16haFFbDmHrVujRQ0shuGLp7qUMmDuA5NRkJraeyHOdnnM6JOUATfLKK1SpAsuXQ0iIvWGqb19b4Exlb+WelfSd05fElEQeaPEA/+v6P73IWkhpkldeo2ZNm+grV4YVK2DIEEhKcjoqz7Ph4AZ6ze7FueRzjAkdwxu3vKEJvhDTJK+8Sv36sGwZlCtnSx+MHg2pqU5H5Tn+iP2D7p9152zSWUY0HcHUW6dqgi/kNMkrr9OkCXzzja1t07ixLYmg4MDpA3Sb2Y3jCcfpUb8H03tP1xudlM6TV96pZUv44w+oXt3pSDxDXEIc3WZ2I/pUNK1rtGbuwLkE+Ac4HZbyAPprXnmtjAk+Orrw3hkbnxTPrbNuZUfMDq4OvppFwxZRIqCE02EpD6FJXnm9uDi7MPjgwXYYpzBJSkli4NyBrD+wnpCyISwdsZTyxcs7HZbyIJrkldcrXx5GjYKUFBgwADZscDqigmGMYdyicXwd+TUVS1Tk2xHfUqNMjZzfqAoVTfLKJ0yeDCNHQnw89OwJUVFOR5T//vPDf5j+y3SKFynO4mGLaVixodMhKQ+kSV75BBH44APo1s3Wt+nWDY4dczqq/DNr2yyeXvk0gjC7/2xaVG/hdEjKQ2mSVz4jIADmzoXQUNuT79sXEhOdjsr9ftj3A3dE3AHAq91epU+jPg5HpDyZJnnlU0qXhsWLoXZtuO02m/h9yc7YnZnKFTzY8kGnQ1IeTufJK59TpQps3w4lSzodiXvFnI2hx6wexCXE0atBL17r9prezapypD155ZMyJvg//4SFC52LxR3OJZ+jz+d9+PPEn4RWDWVW/1m6LqtyifbklU87dMjeHXvmjF1SsHVrpyPKPWMM9yy8h/UH1lOzTE0WDV1EqaKlnA5LeQntySufVrWqnTt//jz06QN79zodUe69tO4lZm6dScmAkiwatoiqpas6HZLyIprklU8TgTffhK5d7dTKW2+F06edjsp1i3Yt4p/L/wnAjH4zaFq5qcMRKW+jSV75vIAA+OILW7Hyt99gxAjvKE/827HfGDZ/2MXFt/s17ud0SMoLaZJXhUJQkL34Wq6c/frss05HdHnH44/T+/PenEk8w+BrBvNUO12bVeWNJnlVaNStC3Pm2PViK1Z0OppLu1B07MJMmul9putUSZVnOrtGFSpdu9oplZ5ch/7hpQ+zcu9KKpeszFeDv9KyweqKaE9eFToZE3xkJBw/7lwsWU3bNI0pG6ZQ1L8oXw35ipplazodkvJymuRVofXDD9Ciha1Dn5zsdDR2Ae4HvnkAgGm3TqNVjVYOR6R8gUtJXkQ6iMhmEdkqIhtFJNv/fSJSUUTmich2EdkkIv91b7hKuU/t2nZ8fsUK+Mc/nI3lePxxBswdQGJKIuObj2dUs1HOBqR8Ro5JXkSCgHBgvDGmKTARiBCRElnaFQMWAW8YY641xtwAvJwPMSvlFjVr2iUDAwLg9dfhk0+ciSPVpDLiyxFEn4qmZfWWvHLzK84EonySKz35bsBOY8x6AGPMKuAw0DlLu5HAj8CEtN7+DMDHagAqX9O2Lbz9tn08dixs3lzwMUxaPYklu5dQoXgF5g6cS7EixQo+COWzXEnydYCs6+xEpe3PqD028f8DaAHsAz7L7gNFZEzaL4KNMTExuYtYKTcbM8Zu589D//52zdiCsnT3Up5d9ezFxT/0QqtyN1eSvAApWfYlZ/PeSsDHxpi9xphU4EWgk4j8rZKSMWaaMSbMGBMWHBycl7iVcqs33oCwMDh4ENauLZjvue/kPoaF2zta/93x33St27VgvrEqVFyZJ38A6JJlXwgwL8u+Y0DGqiCpGTalPFpgIMybZ6tWFkSlyvPJ5xk4dyBxCXF0r9edp9rrHa0qf7jSk48AmopIEwARaQE0Ar4TkbUiUj+tXTgwRkRKpz1/CPjOGBPv7qCVyg+1amVO8ElJ+fe9Hl76MBsObaBW2VrMvG0mfqKzmVX+yPF/ljHmFDAQmC4iPwOvAz2AEkAtoGxauy+BL4ANIrIFaA6Mzp+wlcpfERHQoIG9O9bdZm6dydSNUynqX5R5g+ZRvnh5938TpdK4VNbAGLMSm7SzqpGl3UvAS26ISynHGAMffWRrz/fvD+vWQfHi7vnsbUe3MWbhGADe6v4WYdXC3PPBSl2C/o2oVBYi8PHHtqDZL7/AfffZxH+lTp8/Tf8v+pOQnMCo60ZxT+g9V/6hSuVAk7xS2QgKsjdKFS9uE/7771/Z5xljuCPiDiLjImlauSnv9HxHK0uqAqFJXqlLuO46mDbNPn7gAfj557x/1qvrXyX893DKFCvD/EHztbKkKjCa5JW6jBEjYPx4SEyE4cPzVsjsh30/8PjyxwH4pO8n1Ctfz81RKnVpWk9eqRy8+iocOwYTJ0KRXP7EHPnrCIPmDSLFpPDYjY/Rt1Hf/AlSqUvQJK9UDooWtWvE5lZyajKD5w3myF9H6FCrA5M7T3Z/cErlQIdrlMql+fNhyZKc2z254klW71tN1VJV+XzA5xTx0z6VKnj6v06pXFi+HAYMgPLlYdMmW5M+O+G/h/PSupfwF3/mDJhDlVJVCjROpS7QnrxSuXDTTdCzp61UOWAAnDv39zaRxyO5I+IOAP7X9X+0q9WugKNUKp0meaVywc8PZsywPfhNm+ChhzK/Hp8UT/8v+tsbnxr35+FWDzsSp1IXaJJXKpfKlbPj8sWKwXvvpa8oZYxh3KJxbDu2jQYVGjC9z3S94Uk5TpO8UnkQGgpTptjH48bBr7/CtE3TmLF1BiUCSjB/0HzKFCvjbJBKoRdelcqzu+6yxctWrICth39jwsYJAEy7dRrXVrrW4eiUsjTJK3UF3n4bDh6Po/O8HiSmJHJf2H0Mbzrc6bCUukiHa5S6AsUCU3ng++FEn4qmRfUW3HvVa06HpFQmmuSVugKTVk9iye4llA+sQJPNy2jWtCirVjkdlVLpNMkrlUdLdy/l2VXPIgizB8yiUlAZUlJgyBC7VqxSnkCTvFJ5sO/kPoaFD8NgeLbjs9xc92aee87eLHX0KAwenL9rxCrlKk3ySuXS+eTzDJw7kLiEOLrX687T7Z8GbIXK2bOhWjVYswb++U+HA1UKTfJK5dojSx9hw6EN1Cpbixn9ZuAn6T9GlSrZipVFitgSxfPmORioUmiSVypXZm6dyTsb36Gof1HmDZpHhRIV/tamTRt4+WX7eNIkSE0t4CCVykDnySvlom1HtzFm4RgA3rzlTcKqhV2y7YQJkJICd9xh690o5RRN8kq54PT50/T/oj8JyQmMvG4kY24Yc9n2IvDIIwUUnFKXoX0MpXJgjOHOiDuJjIukSaUmTO05NVeFxxIT7ULg77yTj0EqdQnak1cqB6+sf4X5v9uCY/MHzadEQIlcvX/FClv+ICAAwsKgRYt8ClSpbGhPXqnLWLlnJY8vfxyAT/t+Sv0K9XP9Gd272558UpJdaCQ21t1RKnVpmuSVuoQDpw8weN5gUk0qT7R9gj6N+uT5s15+GVq1gv37Yfhwe1FWqYKgSV6pbCSmJDJw7kBi4mPofFVnnu/0/BV9XtGiMHcuVKwI334Lz1/ZxynlMk3ySmXj0aWP8uOBH6lRpgaz+8/G38//ij+zRg17R6wIPPccLFvmhkCVyoFeeFUqi5lbZ/L2hrcp6l+U+YPmE1wy2G2f3aWL7cX//DM0b+62j1XqkjTJK5XB1qNbM93w1KK6+6fCPPGE/ao3SamC4NJ/MxHpICKbRWSriGwUkVY5tH9GRJJEpLY7glSqIJw8d/LiDU+jrhuV4w1PeeXnl57gz5+3QzhK5Zcce/IiEgSEA7caY9aLSEcgQkSuMsbEZ9O+F1AVOOjuYJXKL6kmlZFfjmR33G6aVWmW6xue8vQ9U+Hmm2H1aju9cuTIfP12qpBypSffDdhpjFkPYIxZBRwGOmdtKCINgYeAB90Yo1L57oU1L7Bw10KCAoOYP2g+xQOK5/v39POD22+3j8eNg61b8/1bqkLIlSRfB4jKsi8qbf9FIlIG+BC40xhz/nIfKCJj0oZ9NsbExOQmXqXc7pvIb3j6O1sTfma/mdQpVyeHd7jPXXfZImYJCdC/P5w6VWDfWhUSriR5AbLeupGc8b1i/679BHjeGLMvpw80xkwzxoQZY8KCg903c0Gp3Np1fBdD5w+1Kzx1eJaeDXoW6PcXgSlT4LrrYPduGD0ajCnQEJSPcyXJHwBCsuwLSdt/QWmgGfBvEflRRH7Ejst/KSKj3RGoUu52+vxp+n7el1PnT9G3UV/+1eFfjsRRvDjMnw9ly8JXX6XXolfKHVxJ8hFAUxFpAiAiLYBGwHcislZE6htjThtjrjLGtLqwYcft+xljPs636JXKo1STyojwEfwe+zvXBF/Dp30/zbTCU0GrWxc+/dQ+3rhRe/PKfXKcXWOMOSUiA4HpImKwQzU9gBJALaBs/oaolPs9s/IZFu5aSLnAckQMiaB0sdJOh0Tv3namTdu2dhhHKXdw6WYoY8xKILv782pc5j218xiTUvlq/o75TPphEn7ix5wBc6hbvq7TIV3Url364/h4W8istPO/f5QX03vuVKGy7eg2Rn01CoD/dfkfXet2dTii7O3fb3v0w4ZpxUp1ZTTJq0LjePxx+nzeh7NJZxnRdASPtPbc9fkSE2HfPli0CJ56yulolDfTJK8KhaSUJAbOHciek3sIqxbGtFun5fsdrVeibl1bmtjfH158EWbOdDoi5a00ySufZ4zhvsX3sXLvSiqXrEz4oPACuaP1St10E7z5pn18993w00/OxqO8kyZ55fNeWf8KH2z5gMAigSwYuoCaZWs6HZLL7r0Xxo61hcz69YODWhFK5ZImeeXTIv6I4LFljwEwo9+MfCkdnJ9E4K23oEMHOHw4fS69Uq7SevLKZ205vIVh4cMwGCbfNJkBVw9wOqQ8CQiAefNgzhy47z6no1HeRnvyyicdPH2QXrN7EZ8Uz8jrRvJE2yecDumKVKwI48en3ySVkOBsPMp7aJJXPuds4ll6f96bg2cO0i6kncfPpMmtffsgLAzeeMPpSJQ30CSvfEpyajLDwoex+fBm6parS/jgcIoVKeZ0WG7100+wYwc8/LAtaKbU5WiSVz7DGMP4xeNZsHMB5YuXZ9GwRVQsUdHpsNxu0CCYNMkWMRs2DDZscDoi5ck0ySufMWn1JKZtnmanSg5ZQKOKjZwOKd88+STceacdm+/VC/budToi5ak0ySufMH3LdP5v1f/hJ37M7j+bNiFtnA4pX4nAu+9C585w9Ch06wa6yJrKjiZ55fW+jvyaMQvHAPB297fp26ivwxEVjIAAu9jIddfBrl12iqVSWek8eeXVNhzcwMC5A0kxKTzZ9knubX6v0yEVqLJlYckSewF23Dino1GeSHvyymv9EfsHPWf1vDgXftJNk5wOyRFVqmRO8MePa3lilU6TvPJKe0/upcunXYiJj6Fb3W580OsDn5oLn1d//gktW8KDD+oSgsrSJK+8zuEzh+nyaRcOnjlI25C2hA8OJ8A/wOmwPMKBA3abMgWee87paJQn0CSvvMrx+ON0ndGVqBNRhFYNZdHQRZQIKOF0WB6jfXuYPRv8/ODZZ+GVV5yOSDlNk7zyGmfOn6H7Z935LeY3GldszNIRSykbqOvIZ9WvH3zwgX08caLt1avCS5O88grxSfH0mt2LDYc2cFXQVSy7fZlP3s3qLnfcAVOn2sf335+e9FXho0leebwLCf77fd9TtVRVlo9cTvUy1Z0Oy+ONGwc/myfCAAASDklEQVSvv24fHznibCzKOTpPXnm0Cwn+uz3fUblkZVaMXEGdcnWcDstrPPggtG4NLbxrrRTlRtqTVx4ra4JfNXoVjYMbOx2W18mY4PfsgS+/dC4WVfA0ySuPlDHBVylVhVWjV/l0wbGCcPKkXRx8wABdRrAw0SSvPM5fiX9lSvArR63UBO8GZcvaypWpqTB6NLz/vtMRqYKgSV55lLiEOLrO6KoJPh+IwL/+BS++aO+GHTMG3n7b6ahUftMkrzzGkb+O0PHjjvx44EdCyoawevRqTfD54LHH0pcOfOABeOklZ+NR+UuTvPIIe0/upe30tmw7to1GFRux9s611K9Q3+mwfNaECbYePdik/9NPzsaj8o9OoVSO+z3md7rO6MrBMwcJrRrKkuFLCC4Z7HRYPm/sWChRwi4M3rKl09Go/KJJXjlq3f519J7dm+MJx2kX0o6FQxdqqYICdPvtmZ/v3g1Vq0LJks7Eo9xPh2uUY+btmMdNn9zE8YTj9KzfkyUjlmiCd9D+/dCpE3TpYmvSK9/gUpIXkQ4isllEtorIRhFplU2byiLynoj8LiI/i8gPItLE/SErb2eM4dX1rzJo7iDOp5xn7A1j+WrIV1pN0mHx8bZ65Y8/Qps2EBXldETKHXJM8iISBIQD440xTYGJQISIZP2JDAWWGmMaG2NaAF8BWuhUZZKSmsKEbybw6LePYjC80PkFpvacShE/HTl0WsOGsG4dNGkCO3facfrVq52OSl0pV3ry3YCdxpj1AMaYVcBhoHPGRsaYb4wx4Rl2HUbH/FUGp8+fpt+cfry94W2K+hdldv/ZPN72cV3RyYNUrw5r1kCPHnbIpksX+Ogjp6NSV8KVJF8HyPqHW1Ta/myJSGXgOeDfl3h9TNqwz8aYmBhXY1VeLPJ4JK0+aMXCXQspF1iOZbcvY8i1Q5wOS2WjTBlYsAAeegiSkuxdstu3Ox2VyitXetoCZF0WOJlL/IIQkQrA18Czxpjvs2tjjJkGTAMICwvTlSh93NLdSxkyfwgnz53k6uCriRgSQb3y9ZwOS12Gvz+89ho0amRr3lx7rdMRqbxyJckfALpk2RcCzMvaUESqAt8A/zPGzLry8JQ3u3CB9bHlj5FqUunbqC+f9v2U0sVKOx2actHYsZmfr1sHpUvbcXvlHVwZrokAml6YKSMiLYBGwHcislZE6qftrwWsAJ7XBK9OnTvF4HmDmbhsIqkmlWc6PMP8QfM1wXuxQ4fs0oKtWsEs/Qn3Gjn25I0xp0RkIDBdRAx2qKYHUAKoBVyY2PwKUBn4h4j8I23feWNMB/eHrTzZ5sObGTR3EFEnoihdtDQf9/2Y2xrf5nRY6goFBcEtt9gyxcOH26mWL78MRYs6HZm6HDHG2SHxsLAws3HjRkdjUO5hjOG9Te/x4JIHSUxJpFmVZnwx4AutQeNDjIH33rO1b5KS4IYbYPZsqK+nuMCJyCZjTFhO7fSOV+UWJxJOMHT+UO5dfC+JKYmMu2Ec6+9arwnex4jYtWN/+AFq14ZNm+D66+GLL5yOTF2KJnl1xZb/uZwmU5sw57c5lCpailm3zWLqrVMJLBLodGgqn7RsCb/8AkOG2DtlK1Z0OiJ1KZrkVZ4lJCXw0JKHLlaQbFWjFVvGbmFok6FOh6YKQNmy9gLsxo12WcELdu1yLib1d5rkVZ5sPLSRsPfDeOOnNyjiV4TnOz3PD3f8oPPfCxkRCA1Nf/7dd3Zu/bhxcOaMc3GpdJrkVa6cTTzLxG8n0vKDluyI2UHDCg1Zf9d6nm7/tNafUURGQpEi9uLstdfC8uVOR6Q0ySuXLYtaRpOpTXhlva0790irR9g8djNh1XK8wK8KibFj7cXY0FCIjoauXeHuu7V0sZM0yascHf3rKKO+GsXNM29mz8k9XFf5On66+yde6faKlgdWf9OkiZ1DP3kyBATAhx9Cgwa28JkqeJrk1SUlpSTx6vpXafB2Az799VOK+Rfjv53/y4Z7NmjvXV1WQAA8+SRs3QqdO9taONdc43RUhZMOoqpsLYtaxoQlE/gj9g8AetbvyWvdXtN57ypXGjWCZcvs0E25cnZfQgI89xw8/DBUquRsfIWB9uRVJjtidtDn8z7cPPNm/oj9g/rl67No6CIWDVukCV7liQjUqpX+/PXX4YUXoF49+M9/7Dx7lX80ySsAok9Fc2fEnTSZ2oQFOxdQqmgpXuzyItvu3UbPBj2dDk/5kN69oWdPO8XyqafsilSffAKpqU5H5ps0yRdysfGxPLr0URq81YCPfvkIP/HjvrD72HX/Lh5r8xjFihRzOkTlY665BhYtstMrmzWDAwdg9Gh7wfbbb52OzvfomHwhdeSvI7yy7hWmbpzK2aSzAAy9dijPdXpOb2hSBaJzZzvd8rPP4OmnYccOOHvW6ah8jyb5Qib6VDQvrX2J9ze/z/mU8wB0r9edyTdN5vqq1zscnSps/Pzg9tth8GCYPx/69El/bfJkO5Y/eLCdraPyRksNFxJbDm/hjZ/eYNa2WSSlJgHQr1E/nmr3FDdUu8Hh6JTKbM8eO7c+ORlq1IAHH4R77rH1cpSlpYYVKakphP8eToePOxA6LZRPfv2EFJPCsCbD2HbvNsIHh2uCVx6pWjV4911o3NiO2f/jH1CzJjz6qP0FoFynPXkfdPSvo3zy6ydM3TiVvSf3AlC6aGnuuv4u7m9xP3XL13U2QKVclJoKS5bYFahWrrT7ihSBw4e1vLGrPXkdk/cRyanJLN29lA+3fMjCXQtJTk0GoF75ekxoMYHRzUbr+qrK6/j5QY8edtu0yc6xP38+PcEbY/cNGGB7+urvtCfv5X6P+Z3Ptn3Gx798zMEzBwHwF39ubXAr94TeQ/f63fETHZVTvsMYe4MV2NLGnTvb5x062Iu4/fsXjrF77cn7sD0n9jDntzl8vv1zfj3668X99cvX567r72LkdSOpWrqqgxEqlX8uJHiAChVg0CCIiIBVq+w2fry94WrECHvTlV8h7+NoT95LRB6PZMHOBczdMZefDv50cX9QYBC3NbqNUc1G0S6kHZLxJ0CpQuLkSTsFc+ZMm+gBQkJg7970XwrnzkGgD61IqT15L5eSmsL6A+tZsHMBC3YuYOfxnRdfKxlQkj6N+jDkmiHcXPdmvStVFXpBQXDXXXaLjrY3WAUGpif4I0egbl07tNOnD9xyC1Sv7mzMBUWTvAeJPhXN8j+Xs/zP5Xwb9S3HE9JXWggKDKJn/Z70adiHng16ah13pS4hJASeeCLzvnXrbPXLhQvtBra8wi23QLdu0LGj795wpcM1DoqNj2X1vtUXE3tkXGSm1+uWq0vvhr3p3bA3bWq2IcDfR/8XKlUAjhyxY/eLF9sLthdKKBQpYleuKlPGPv/jD6hTB4oWdS5WV+hwjYdJNansjN3Juv3rWLt/Lev2r8s0BANQplgZOtXuRJc6XehSpwsNKzTUMXal3KRKFbs84dixkJhoe/dLlsCJE+kJPjUVWre24/etWkG7dtC+PTRv7r0zdrQnnw+MMRw4fYDNhzez5cgWNh7ayPoD64lLiMvUrniR4rSo3uJiUg+rFqaLYSvloMOH7bq0v/3299caNoQpU+y4vifQnnwBSUxJJPJ4JNuPbWfLkS1sObKFzYc3Exsf+7e21UpXo03NNtxY80ba1GxDsyrNdAhGKQ9StSps3w6xsXZN2h9+sNuvv8LOnfYC7wVPP21LJjdtCtdea0slN2liL+h60h/gmuRdFJ8Uz67ju9gRs4MdMTv4PfZ3dsTsIPJ4JCkm5W/tyxcvT2jVUK6vcj2hVUNpXaM1IWVDdPhFKS9QsSL07Ws3sHfZbttmE/oF69fb5P/rr5nfGxRkK2e++659npxsp3LWrm3H/wuaJvk0xhiOnT3Gnyf+JOpEVOavcVEc/utwtu8ThDrl6tC4YuOLCT20aqgmdKV8SLFiEJZlYCQiwi5Uvn27/QVwYYuLg6Sk9HZRUXat2yJF7AXd+vXtdvPN0L17/sdeKJK8MYbY+FgOnD6QeTtjvx48fZD9p/cTn3TpxSaL+BWhbrm6XB189cWtccXGNKzYUKczKlUIlSoFN95otwuMseP6ycnp++LibLnkAwdg1y67Afj7a5K/rISkBI6dPUZMfAzHzh7Ldsv4WmJKYo6fWS6wHHXK1aFu+brUCUr7Wq4OdcrVoWaZmvj7+RfAkSmlvJWILZOcUevWsH+/XbA8Ksom+chIu78geG2SbzylMftO7XO5fbnActQoUyPbrXrp6tQoU4OygV46R0op5fFKlEi/OFuQXEryItIBeC2tfSJwvzHmxyxtBHgOGASkAJuBscaYfFm1MaRsCCkmheASwVQqWSnTlnVfcMlgHVJRShVKOSZ5EQkCwoFbjTHrRaQjECEiVxljMg5ijwJ6AM2MMQki8hHwInB/PsTN6jtW58fHKqWUT3GlCGc3YKcxZj2AMWYVcBjIekvAYOA9Y0xC2vM3gKFuilMppVQeuJLk6wBRWfZFpe2/XLsooLyI/G2gW0TGiMhGEdkYExOTm3iVUkrlgitJXrBj7BklZ/PerO0uTCL62/cwxkwzxoQZY8KCg4NdjVUppVQuuZLkDwAhWfaFpO2/XLsQ4C/gZJ6jU0opdUVcSfIRQFMRaQIgIi2ARsB3IrJWROqntZsB3C0iFwp0PgCEG6croCmlVCGW4+waY8wpERkITBcRgx2G6QGUAGoBF8bcPwXqAT+LSDKwg3yaWaOUUso1Ls2TN8asBJpn81KNDG1SgKfSNqWUUh6gkK9jrpRSvs3xRUNEJAZwvT5BZhWBvxdu9056LJ7HV44D9Fg81ZUcSy1jTI7TEx1P8ldCRDa6sjKKN9Bj8Ty+chygx+KpCuJYdLhGKaV8mCZ5pZTyYd6e5Kc5HYAb6bF4Hl85DtBj8VT5fixePSavlFLq8ry9J6+UUuoyNMkrpZQP8/gkLyIdRGSziGxNK0/cKps2IiLPi8hOEdkhIjNFpKQT8V6Oi8dyg4jEiciPGbZHnYj3UkQkQEQmikiSiAy5RBtvOSeuHIvHnxMAERkrIr+m/d/aKiL3XaLdeBH5Q0S2i8giEalc0LHmxJVjEZEKInI2y3l52Yl4LyXtZ+BXEfk57Wf/3ku0y79zYozx2A0IAo4DrdOedwSOAiWytBsNbAKKpz3/CHjb6fjzeCzdgPedjjeHY7kPeBT4ARhyiTYef05ycSzecE78gZeBUmnPqwMJQPUs7ToC0UBw2vNngUVOx5/HY2kILHM63hyO5REgIO1xMLYy71UFeU4c/0fI4R9oMLAuy75fgF5Z9n0DjMnwvBlw3On483gsw7F3AP+Utk0GSjsd/yWOadVlEqPHn5NcHIvXnJMMMQcCp4CQLPunAv/J8LwctuhgWadjzsOxtMF2lNYDG4C3gMpOx3uZ42gOHMn6b53f58TTh2vcviqVg1w9lnCgtjGmJdAduApb4dPbeMM5cZU3npPXgTnGmOgs+zOdF2PMCWwCrV1woeXapY5lI1DNGNMa2xtOBL4WESng+C5LROqLSCSwFBhhjDmVpUm+nhOXqlA6yO2rUjnIpWMx6WvkYoyJSxv73S8ixTO+5gW84Zy4xNvOiYhMwg5x9M/uZVz7mfIIlzsWY8z5DI/PishjwGlsyfPIAgsyB8aYSKC+iFwPLBaRrsaY3zI0yddz4pEnNgNfWpXK1WPJyh84B5zPoZ2n8YZzklcee07SLjxeA/Q3xiRm0yTTeRGREkAFcv5/WOBcOJa/vQWb007na2B5ZIzZgh1a6pTlpXw9J56e5H1pVSqXjkVEhohIUNrjIsB/gRnGmFSH4nZJ2kwHbzsn2cp6LN5wTkTET0TeBWoCAy8kRRHxF5EVItIurekMYHiGYbPxwFpjTEzBR509V49FRHqLSNW0xwI8B6wyxhx1KvaMRKSJiAy6MHwkItWBlsCWgjwnHj1cY3xoVapcHEtxYIWIpAIG+B74PwdCzi2vOyeX4Y3npAcwFjtOvSbDsPQk7DWE8mAXABKRKcD3IpIEHAKynTrqIJeOBXsuwkUkAEgFtmIvknuKfcA44PG0f+uiwL+ws84K7JxoWQOllPJhnj5co5RS6gpokldKKR+mSV4ppXyYJnmllPJhmuSVUsqHaZJXSikfpkleKaV8mCZ5pZTyYZrklVLKh/0/swFtv2Kg6WkAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f133c26cbe0>"
]
},
"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",
"\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\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The figure in the book actually is actually a bit fancier:"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure logistic_regression_plot\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f13600c9128>"
]
},
"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": 56,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([1.61561562])"
]
},
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"decision_boundary"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([1, 0])"
]
},
"execution_count": 57,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"log_reg.predict([[1.7], [1.5]])"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure logistic_regression_contour_plot\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1344043cf8>"
]
},
"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": 59,
"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": 59,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X = iris[\"data\"][:, (2, 3)] # petal length, petal width\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": 60,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure softmax_regression_contour_plot\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1344043cc0>"
]
},
"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": 61,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([2])"
]
},
"execution_count": 61,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"softmax_reg.predict([[5, 2]])"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[6.33134078e-07, 5.75276067e-02, 9.42471760e-01]])"
]
},
"execution_count": 62,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"softmax_reg.predict_proba([[5, 2]])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Exercise solutions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1. to 11."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"See appendix A."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 12. Batch Gradient Descent with early stopping for Softmax Regression\n",
"(without using Scikit-Learn)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's start by loading the data. We will just reuse the Iris dataset we loaded earlier."
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {},
"outputs": [],
"source": [
"X = iris[\"data\"][:, (2, 3)] # petal length, petal width\n",
"y = iris[\"target\"]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We need to add the bias term for every instance ($x_0 = 1$):"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {},
"outputs": [],
"source": [
"X_with_bias = np.c_[np.ones([len(X), 1]), X]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And let's set the random seed so the output of this exercise solution is reproducible:"
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {},
"outputs": [],
"source": [
"np.random.seed(2042)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The easiest option to split the dataset into a training set, a validation set and a test set would be to use Scikit-Learn's `train_test_split()` function, but the point of this exercise is to try understand the algorithms by implementing them manually. So here is one possible implementation:"
]
},
{
"cell_type": "code",
"execution_count": 66,
"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": [
"The targets are currently class indices (0, 1 or 2), but we need target class probabilities to train the Softmax Regression model. Each instance will have target class probabilities equal to 0.0 for all classes except for the target class which will have a probability of 1.0 (in other words, the vector of class probabilities for ay given instance is a one-hot vector). Let's write a small function to convert the vector of class indices into a matrix containing a one-hot vector for each instance:"
]
},
{
"cell_type": "code",
"execution_count": 67,
"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": [
"Let's test this function on the first 10 instances:"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0, 1, 2, 1, 1, 0, 1, 1, 1, 0])"
]
},
"execution_count": 68,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y_train[:10]"
]
},
{
"cell_type": "code",
"execution_count": 69,
"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": 69,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"to_one_hot(y_train[:10])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looks good, so let's create the target class probabilities matrix for the training set and the test set:"
]
},
{
"cell_type": "code",
"execution_count": 70,
"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": [
"Now let's implement the Softmax function. Recall that it is defined by the following equation:\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": 71,
"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": [
"We are almost ready to start training. Let's define the number of inputs and outputs:"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {},
"outputs": [],
"source": [
"n_inputs = X_train.shape[1] # == 3 (2 features plus the bias term)\n",
"n_outputs = len(np.unique(y_train)) # == 3 (3 iris classes)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now here comes the hardest part: training! Theoretically, it's simple: it's just a matter of translating the math equations into Python code. But in practice, it can be quite tricky: in particular, it's easy to mix up the order of the terms, or the indices. You can even end up with code that looks like it's working but is actually not computing exactly the right thing. When unsure, you should write down the shape of each term in the equation and make sure the corresponding terms in your code match closely. It can also help to evaluate each term independently and print them out. The good news it that you won't have to do this everyday, since all this is well implemented by Scikit-Learn, but it will help you understand what's going on under the hood.\n",
"\n",
"So the equations we will need are the cost function:\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",
"And the equation for the gradients:\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",
"Note that $\\log\\left(\\hat{p}_k^{(i)}\\right)$ may not be computable if $\\hat{p}_k^{(i)} = 0$. So we will add a tiny value $\\epsilon$ to $\\log\\left(\\hat{p}_k^{(i)}\\right)$ to avoid getting `nan` values."
]
},
{
"cell_type": "code",
"execution_count": 73,
"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": [
"And that's it! The Softmax model is trained. Let's look at the model parameters:"
]
},
{
"cell_type": "code",
"execution_count": 74,
"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": 74,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Theta"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's make predictions for the validation set and check the accuracy score:"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9666666666666667"
]
},
"execution_count": 75,
"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": [
"Well, this model looks pretty good. For the sake of the exercise, let's add a bit of $\\ell_2$ regularization. The following training code is similar to the one above, but the loss now has an additional $\\ell_2$ penalty, and the gradients have the proper additional term (note that we don't regularize the first element of `Theta` since this corresponds to the bias term). Also, let's try increasing the learning rate `eta`."
]
},
{
"cell_type": "code",
"execution_count": 76,
"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 # regularization hyperparameter\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": [
"Because of the additional $\\ell_2$ penalty, the loss seems greater than earlier, but perhaps this model will perform better? Let's find out:"
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0"
]
},
"execution_count": 77,
"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": [
"Cool, perfect accuracy! We probably just got lucky with this validation set, but still, it's pleasant."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's add early stopping. For this we just need to measure the loss on the validation set at every iteration and stop when the error starts growing."
]
},
{
"cell_type": "code",
"execution_count": 78,
"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 # regularization hyperparameter\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": 79,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0"
]
},
"execution_count": 79,
"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": [
"Still perfect, but faster."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's plot the model's predictions on the whole dataset:"
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f13555d0a90>"
]
},
"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": [
"And now let's measure the final model's accuracy on the test set:"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9333333333333333"
]
},
"execution_count": 81,
"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": [
"Our perfect model turns out to have slight imperfections. This variability is likely due to the very small size of the dataset: depending on how you sample the training set, validation set and the test set, you can get quite different results. Try changing the random seed and running the code again a few times, you will see that the results will vary."
]
},
{
"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": "3.5.4"
},
"nav_menu": {},
"toc": {
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