From 75bc9270c43936cf2c4b0f167eb31fb1f7c13710 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Gerardo=20Marx=20Cha=CC=81vez-Campos?= Date: Tue, 4 Jul 2023 19:10:58 -0600 Subject: [PATCH] logistic --- 2-linear-regressor/main.ipynb | 160 ++- 3-logistic-regressor/logistic-regressor.ipynb | 941 ++++++++++++++++++ slides/bgd.pdf | Bin 0 -> 2567044 bytes 3 files changed, 1073 insertions(+), 28 deletions(-) create mode 100644 3-logistic-regressor/logistic-regressor.ipynb create mode 100644 slides/bgd.pdf diff --git a/2-linear-regressor/main.ipynb b/2-linear-regressor/main.ipynb index 01e4a20..ac98320 100644 --- a/2-linear-regressor/main.ipynb +++ b/2-linear-regressor/main.ipynb @@ -180,7 +180,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "id": "d2670f5b", "metadata": {}, "outputs": [ @@ -191,22 +191,23 @@ " [1.000e+00, 2.196e+00]])" ] }, - "execution_count": 1, + "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", - "X = np.array([[1,0.001],[1, 2.196]])\n", - "Xo = np.array([[0.001],[2.196]])\n", + "X0 = np.array([[0.001],\n", + " [2.196]])\n", + "X = np.c_[np.ones(2),X0]\n", "y = np.array([4.314825, 10.877373])\n", "X" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "id": "d95f739b", "metadata": {}, "outputs": [ @@ -216,7 +217,7 @@ "array([4.31183523, 2.9897713 ])" ] }, - "execution_count": 2, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -228,7 +229,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "id": "b241fb39", "metadata": {}, "outputs": [], @@ -256,7 +257,7 @@ ], "source": [ "import matplotlib.pyplot as plt\n", - "plt.plot(Xo,y, '*k')\n", + "plt.plot(X0,y, '*k')\n", "plt.show()" ] }, @@ -268,7 +269,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -278,10 +279,10 @@ } ], "source": [ - "Xvec = np.linspace(0,2,2)\n", + "Xvec = np.linspace(0,2.5,2)\n", "Xnew = np.c_[np.ones((2, 1)), Xvec]\n", "ypre = Xnew.dot(theta)\n", - "plt.plot(Xo,y, '*k')\n", + "plt.plot(X0,y, '*k')\n", "plt.plot(Xvec, ypre, '-r')\n", "plt.show()" ] @@ -305,7 +306,7 @@ { "data": { "text/plain": [ - "[]" + "[]" ] }, "execution_count": 9, @@ -325,10 +326,10 @@ ], "source": [ "np.random.seed(42)\n", - "Xo = 2 * np.random.rand(100, 1)\n", - "X = np.c_[np.ones((100, 1)), Xo] # add x0 = 1 to each instance\n", - "y = 4 + 3 * Xo + np.random.randn(100, 1)\n", - "plt.plot(Xo, y, '.k')" + "X0 = 2 * np.random.rand(100, 1)\n", + "X = np.c_[np.ones((100, 1)), X0] # add x0 = 1 to each instance\n", + "y = 4 + 3 * X0 + np.random.randn(100, 1)\n", + "plt.plot(X0, y, '.k')" ] }, { @@ -372,7 +373,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 10, "id": "17481af6", "metadata": {}, "outputs": [ @@ -382,7 +383,7 @@ "(array([4.21509616]), array([[0. , 2.77011339]]))" ] }, - "execution_count": 11, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } @@ -397,7 +398,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 11, "id": "c5e85264", "metadata": {}, "outputs": [ @@ -408,7 +409,7 @@ " [9.75532293]])" ] }, - "execution_count": 16, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } @@ -422,17 +423,17 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 13, "id": "20da996b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 23, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, @@ -448,7 +449,7 @@ } ], "source": [ - "plt.plot(Xo,y, '.k', label='data')\n", + "plt.plot(X0,y, '.k', label='data')\n", "plt.plot(X_new, y_Pred, '-r', label='SK-model')\n", "plt.legend()" ] @@ -458,16 +459,119 @@ "id": "19ad47f6", "metadata": {}, "source": [ - "# Gradient Descent" + "# Batch Gradient Descent Example for Linear Model\n", + "\n", + "$\\nabla MSE(\\theta)=\\frac{2}{m} X^T(X\\theta-y)$ \n", + "\n", + "$\\theta_N=\\theta-\\eta \\nabla MSE(\\theta)$" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 19, + "id": "da8103f8", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "X = 2 * np.random.rand(100, 1)\n", + "Xb = np.c_[np.ones((100, 1)), X] # add x0 = 1 to each instance\n", + "y = 4 + 3 * X + np.random.randn(100, 1)\n", + "plt.plot(X, y, '.k')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "c93a4eb5", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-0.52563093],\n", + " [ 0.03240701]])" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "eta = 0.01 # learning rate\n", + "ni = 20 # iterations\n", + "m = 100 # dataset size\n", + "theta = np.random.randn(2,1) # random initialization\n", + "theta" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "19aaf38d", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[4.24631965],\n", + " [2.93425959]])" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "for iteration in range(ni):\n", + " gradients = 2/m * Xb.T.dot(Xb.dot(theta) - y)\n", + " theta = theta - eta * gradients\n", + "theta" + ] + }, + { + "cell_type": "code", + "execution_count": 30, "id": "1a8ec08d", "metadata": {}, - "outputs": [], - "source": [] + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for iteration in range(ni):\n", + " gradients = 2/m * Xb.T.dot(Xb.dot(theta) - y)\n", + " theta = theta - eta * gradients\n", + " Xnew = 2 * np.random.rand(100, 1)\n", + " plt.plot(X,y,'.k')\n", + " Xbw = np.c_[np.ones((100, 1)), Xnew] # add x0 = 1 to each instance\n", + " ypre = Xbw.dot(theta)\n", + " plt.plot(Xnew, ypre, '-r')" + ] } ], "metadata": { diff --git a/3-logistic-regressor/logistic-regressor.ipynb b/3-logistic-regressor/logistic-regressor.ipynb new file mode 100644 index 0000000..8e86492 --- /dev/null +++ b/3-logistic-regressor/logistic-regressor.ipynb @@ -0,0 +1,941 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "03f8827e-7e96-494f-8f87-4eb8a2a03ff9", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "['data',\n", + " 'target',\n", + " 'frame',\n", + " 'target_names',\n", + " 'DESCR',\n", + " 'feature_names',\n", + " 'filename',\n", + " 'data_module']" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn import datasets\n", + "iris = datasets.load_iris()\n", + "list(iris.keys())" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "df29211b-b8ae-4d64-a903-de8ba22daa5f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'data': array([[5.1, 3.5, 1.4, 0.2],\n", + " [4.9, 3. , 1.4, 0.2],\n", + " [4.7, 3.2, 1.3, 0.2],\n", + " [4.6, 3.1, 1.5, 0.2],\n", + " [5. , 3.6, 1.4, 0.2],\n", + " [5.4, 3.9, 1.7, 0.4],\n", + " [4.6, 3.4, 1.4, 0.3],\n", + " [5. , 3.4, 1.5, 0.2],\n", + " [4.4, 2.9, 1.4, 0.2],\n", + " [4.9, 3.1, 1.5, 0.1],\n", + " [5.4, 3.7, 1.5, 0.2],\n", + " [4.8, 3.4, 1.6, 0.2],\n", + " [4.8, 3. , 1.4, 0.1],\n", + " [4.3, 3. , 1.1, 0.1],\n", + " [5.8, 4. , 1.2, 0.2],\n", + " [5.7, 4.4, 1.5, 0.4],\n", + " [5.4, 3.9, 1.3, 0.4],\n", + " [5.1, 3.5, 1.4, 0.3],\n", + " [5.7, 3.8, 1.7, 0.3],\n", + " [5.1, 3.8, 1.5, 0.3],\n", + " [5.4, 3.4, 1.7, 0.2],\n", + " [5.1, 3.7, 1.5, 0.4],\n", + " [4.6, 3.6, 1. , 0.2],\n", + " [5.1, 3.3, 1.7, 0.5],\n", + " [4.8, 3.4, 1.9, 0.2],\n", + " [5. , 3. , 1.6, 0.2],\n", + " [5. , 3.4, 1.6, 0.4],\n", + " [5.2, 3.5, 1.5, 0.2],\n", + " [5.2, 3.4, 1.4, 0.2],\n", + " [4.7, 3.2, 1.6, 0.2],\n", + " [4.8, 3.1, 1.6, 0.2],\n", + " [5.4, 3.4, 1.5, 0.4],\n", + " [5.2, 4.1, 1.5, 0.1],\n", + " [5.5, 4.2, 1.4, 0.2],\n", + " [4.9, 3.1, 1.5, 0.2],\n", + " [5. , 3.2, 1.2, 0.2],\n", + " [5.5, 3.5, 1.3, 0.2],\n", + " [4.9, 3.6, 1.4, 0.1],\n", + " [4.4, 3. , 1.3, 0.2],\n", + " [5.1, 3.4, 1.5, 0.2],\n", + " [5. , 3.5, 1.3, 0.3],\n", + " [4.5, 2.3, 1.3, 0.3],\n", + " [4.4, 3.2, 1.3, 0.2],\n", + " [5. , 3.5, 1.6, 0.6],\n", + " [5.1, 3.8, 1.9, 0.4],\n", + " [4.8, 3. , 1.4, 0.3],\n", + " [5.1, 3.8, 1.6, 0.2],\n", + " [4.6, 3.2, 1.4, 0.2],\n", + " [5.3, 3.7, 1.5, 0.2],\n", + " [5. , 3.3, 1.4, 0.2],\n", + " [7. , 3.2, 4.7, 1.4],\n", + " [6.4, 3.2, 4.5, 1.5],\n", + " [6.9, 3.1, 4.9, 1.5],\n", + " [5.5, 2.3, 4. , 1.3],\n", + " [6.5, 2.8, 4.6, 1.5],\n", + " [5.7, 2.8, 4.5, 1.3],\n", + " [6.3, 3.3, 4.7, 1.6],\n", + " [4.9, 2.4, 3.3, 1. ],\n", + " [6.6, 2.9, 4.6, 1.3],\n", + " [5.2, 2.7, 3.9, 1.4],\n", + " [5. , 2. , 3.5, 1. ],\n", + " [5.9, 3. , 4.2, 1.5],\n", + " [6. , 2.2, 4. , 1. ],\n", + " [6.1, 2.9, 4.7, 1.4],\n", + " [5.6, 2.9, 3.6, 1.3],\n", + " [6.7, 3.1, 4.4, 1.4],\n", + " [5.6, 3. , 4.5, 1.5],\n", + " [5.8, 2.7, 4.1, 1. ],\n", + " [6.2, 2.2, 4.5, 1.5],\n", + " [5.6, 2.5, 3.9, 1.1],\n", + " [5.9, 3.2, 4.8, 1.8],\n", + " [6.1, 2.8, 4. , 1.3],\n", + " [6.3, 2.5, 4.9, 1.5],\n", + " [6.1, 2.8, 4.7, 1.2],\n", + " [6.4, 2.9, 4.3, 1.3],\n", + " [6.6, 3. , 4.4, 1.4],\n", + " [6.8, 2.8, 4.8, 1.4],\n", + " [6.7, 3. , 5. , 1.7],\n", + " [6. , 2.9, 4.5, 1.5],\n", + " [5.7, 2.6, 3.5, 1. ],\n", + " [5.5, 2.4, 3.8, 1.1],\n", + " [5.5, 2.4, 3.7, 1. ],\n", + " [5.8, 2.7, 3.9, 1.2],\n", + " [6. , 2.7, 5.1, 1.6],\n", + " [5.4, 3. , 4.5, 1.5],\n", + " [6. , 3.4, 4.5, 1.6],\n", + " [6.7, 3.1, 4.7, 1.5],\n", + " [6.3, 2.3, 4.4, 1.3],\n", + " [5.6, 3. , 4.1, 1.3],\n", + " [5.5, 2.5, 4. , 1.3],\n", + " [5.5, 2.6, 4.4, 1.2],\n", + " [6.1, 3. , 4.6, 1.4],\n", + " [5.8, 2.6, 4. , 1.2],\n", + " [5. , 2.3, 3.3, 1. ],\n", + " [5.6, 2.7, 4.2, 1.3],\n", + " [5.7, 3. , 4.2, 1.2],\n", + " [5.7, 2.9, 4.2, 1.3],\n", + " [6.2, 2.9, 4.3, 1.3],\n", + " [5.1, 2.5, 3. , 1.1],\n", + " [5.7, 2.8, 4.1, 1.3],\n", + " [6.3, 3.3, 6. , 2.5],\n", + " [5.8, 2.7, 5.1, 1.9],\n", + " [7.1, 3. , 5.9, 2.1],\n", + " [6.3, 2.9, 5.6, 1.8],\n", + " [6.5, 3. , 5.8, 2.2],\n", + " [7.6, 3. , 6.6, 2.1],\n", + " [4.9, 2.5, 4.5, 1.7],\n", + " [7.3, 2.9, 6.3, 1.8],\n", + " [6.7, 2.5, 5.8, 1.8],\n", + " [7.2, 3.6, 6.1, 2.5],\n", + " [6.5, 3.2, 5.1, 2. ],\n", + " [6.4, 2.7, 5.3, 1.9],\n", + " [6.8, 3. , 5.5, 2.1],\n", + " [5.7, 2.5, 5. , 2. ],\n", + " [5.8, 2.8, 5.1, 2.4],\n", + " [6.4, 3.2, 5.3, 2.3],\n", + " [6.5, 3. , 5.5, 1.8],\n", + " [7.7, 3.8, 6.7, 2.2],\n", + " [7.7, 2.6, 6.9, 2.3],\n", + " [6. , 2.2, 5. , 1.5],\n", + " [6.9, 3.2, 5.7, 2.3],\n", + " [5.6, 2.8, 4.9, 2. ],\n", + " [7.7, 2.8, 6.7, 2. ],\n", + " [6.3, 2.7, 4.9, 1.8],\n", + " [6.7, 3.3, 5.7, 2.1],\n", + " [7.2, 3.2, 6. , 1.8],\n", + " [6.2, 2.8, 4.8, 1.8],\n", + " [6.1, 3. , 4.9, 1.8],\n", + " [6.4, 2.8, 5.6, 2.1],\n", + " [7.2, 3. , 5.8, 1.6],\n", + " [7.4, 2.8, 6.1, 1.9],\n", + " [7.9, 3.8, 6.4, 2. ],\n", + " [6.4, 2.8, 5.6, 2.2],\n", + " [6.3, 2.8, 5.1, 1.5],\n", + " [6.1, 2.6, 5.6, 1.4],\n", + " [7.7, 3. , 6.1, 2.3],\n", + " [6.3, 3.4, 5.6, 2.4],\n", + " [6.4, 3.1, 5.5, 1.8],\n", + " [6. , 3. , 4.8, 1.8],\n", + " [6.9, 3.1, 5.4, 2.1],\n", + " [6.7, 3.1, 5.6, 2.4],\n", + " [6.9, 3.1, 5.1, 2.3],\n", + " [5.8, 2.7, 5.1, 1.9],\n", + " [6.8, 3.2, 5.9, 2.3],\n", + " [6.7, 3.3, 5.7, 2.5],\n", + " [6.7, 3. , 5.2, 2.3],\n", + " [6.3, 2.5, 5. , 1.9],\n", + " [6.5, 3. , 5.2, 2. ],\n", + " [6.2, 3.4, 5.4, 2.3],\n", + " [5.9, 3. , 5.1, 1.8]]),\n", + " 'target': array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n", + " 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n", + " 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]),\n", + " 'frame': None,\n", + " 'target_names': array(['setosa', 'versicolor', 'virginica'], dtype=']" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "lp=iris.data[:,0:1]\n", + "wp=iris.data[:,1:2]\n", + "plt.plot(lp,wp,'.k')" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "2874984a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(lp,'.k')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "68274907", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n", + " 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n", + " 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "iris.target" + ] + }, + { + "cell_type": "markdown", + "id": "6120b70a", + "metadata": {}, + "source": [ + "# Logistic regressor\n", + "## Decision boudaries" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "a75ea97f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "t=np.linspace(-100, 100, 1000)\n", + "sig=1/(1+np.exp(-t+3))\n", + "plt.plot(t,sig, '.b', label=r\"$\\sigma=\\frac{1}{1+e^{-t}}$\")\n", + "plt.legend(loc='upper left', fontsize=20)\n", + "plt.axis([-5, 5, -0.1, 1])\n", + "plt.plot([0,0], [0,1], 'r--')" + ] + }, + { + "cell_type": "markdown", + "id": "2be6077b", + "metadata": {}, + "source": [ + "# Iris-Setosa Classifier based on petal width" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "f59aa9ba", + "metadata": {}, + "outputs": [], + "source": [ + "X=iris.data[:,1:2]\n", + "y=(iris.target==0).astype(int)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "25839b5d", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
LogisticRegression(random_state=42)
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "LogisticRegression(random_state=42)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.linear_model import LogisticRegression\n", + "mylr=LogisticRegression(solver='lbfgs', random_state=42)\n", + "mylr.fit(X,y)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "4539a843", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Xnew=np.linspace(2,5,70).reshape(-1,1)\n", + "yPred=mylr.predict_proba(Xnew)\n", + "plt.plot(Xnew,yPred[:,0],'.r', label='No Iris-Set')\n", + "plt.plot(Xnew,yPred[:,1],'.b', label='Iris-Set')\n", + "plt.legend()\n", + "plt.plot(X,y,'*g')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7474195c", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "0196eda3", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Iris-Setosa Classifier based on petal width\n", + "\n", + "X=iris.data[:,0:1]\n", + "y=(iris.target==0).astype(int)\n", + "\n", + "from sklearn.linear_model import LogisticRegression\n", + "mylr=LogisticRegression(solver='lbfgs', random_state=42)\n", + "mylr.fit(X,y)\n", + "\n", + "Xnew=np.linspace(2,8,70).reshape(-1,1)\n", + "yPred=mylr.predict_proba(Xnew)\n", + "#plt.plot(Xnew,yPred[:,0],'.r', label='No Iris-Set')\n", + "plt.plot(Xnew,yPred[:,1],'.b', label='Iris-Set')\n", + "plt.legend()\n", + "plt.plot(X,y,'*g')" + ] + }, + { + "cell_type": "markdown", + "id": "4d56c901", + "metadata": {}, + "source": [ + "# Session 2: Softmax regression\n", + "\n", + "## Multiple features binary classifier (Virginica)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "00ba053b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "pl=iris.data[:,2:3]\n", + "pw=iris.data[:,3:]\n", + "tg = iris.target\n", + "plt.plot(pl[tg==0,0],pw[tg==0,0],'.r',label='Set')\n", + "plt.plot(pl[tg==1,0],pw[tg==1,0],'.b',label='Ver')\n", + "plt.plot(pl[tg==2,0],pw[tg==2,0],'.g',label='Vir')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "b3849a04", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
LogisticRegression(C=10, random_state=42, solver='newton-cg', tol=1e-05)
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "LogisticRegression(C=10, random_state=42, solver='newton-cg', tol=1e-05)" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.linear_model import LogisticRegression\n", + "X=iris.data[:,2:]\n", + "y=(iris.target==2).astype(int)\n", + "\n", + "lrvir=LogisticRegression(random_state=42, tol=1e-5, C=10, max_iter=100, solver='newton-cg')\n", + "lrvir.fit(X,y)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "3fa13847", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "x0, x1=np.meshgrid(\n", + " np.linspace(1,6.9,500).reshape(-1,1),\n", + " np.linspace(0.1,2.5,200).reshape(-1,1))\n", + "Xnew=np.c_[x0.ravel(), x1.ravel()]\n", + "yProb=lrvir.predict_proba(Xnew)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "f34d82b2", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10,4))\n", + "plt.plot(X[y==0,0], X[y==0,1],'bs',label='No Virg')\n", + "plt.plot(X[y==1,0], X[y==1,1],'g^',label='Virginica')\n", + "zz=yProb[:,1].reshape(x0.shape)\n", + "contour=plt.contour(x0,x1,zz)\n", + "plt.clabel(contour, inline=1,fontsize=15)\n", + "plt.xlabel(\"Petal Length\")\n", + "plt.ylabel(\"Petal Width\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "b566781b", + "metadata": {}, + "source": [ + "## Multiple features and multiclass classifier (Virginica)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "090c8abc", + "metadata": {}, + "outputs": [], + "source": [ + "X=iris.data[:,2:]\n", + "y=iris.target" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "aa59ee97", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "lrmfmc=LogisticRegression(multi_class='multinomial',\n", + " solver='lbfgs',\n", + " C=100,\n", + " random_state=42)\n", + "lrmfmc.fit(X,y)\n", + "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", + "Xnew=np.c_[x0.ravel(), x1.ravel()]\n", + "yProba=lrmfmc.predict_proba(Xnew)\n", + "#yPred=lrmfmc.predict(Xnew)\n", + "\n", + "from matplotlib.colors import ListedColormap\n", + "#customc=ListedColormap(['#fafab0', '#9898ff', '#a0faa0'])\n", + "zz=yProba[:,1].reshape(x0.shape)\n", + "#zz=yPred.reshape(x0.shape)\n", + "plt.figure(figsize=(10,4))\n", + "plt.plot(X[y==2,0], X[y==2,1],'g^',label='Virg')\n", + "plt.plot(X[y==1,0], X[y==1,1],'bs',label='Versic')\n", + "plt.plot(X[y==0,0], X[y==0,1],'yo',label='Setos')\n", + "contour=plt.contour(x0,x1,zz,cmap=plt.cm.brg)\n", + "plt.clabel(contour,inline=1,fontsize=12)\n", + "#plt.contourf(x0,x1,zz,cmap=customc)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "ef386db5", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "yPred=lrmfmc.predict(Xnew)\n", + "zPred=yPred.reshape(x0.shape)\n", + "plt.contourf(x0,x1,zPred,alpha=0.4)\n", + "plt.plot(X[y==2,0], X[y==2,1],'g^',label='Virg')\n", + "plt.plot(X[y==1,0], X[y==1,1],'bs',label='Versic')\n", + "plt.plot(X[y==0,0], X[y==0,1],'yo',label='Setos')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "a9531c07", + "metadata": {}, + "source": [ + "## Homework: Sepal multi-features and multi-class" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "d99ec4da", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
LogisticRegression(C=10, multi_class='multinomial', random_state=42)
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "LogisticRegression(C=10, multi_class='multinomial', random_state=42)" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X=iris.data[:,0:2]\n", + "y=iris.target\n", + "mlr3=LogisticRegression(\n", + " multi_class='multinomial',\n", + " solver='lbfgs',\n", + " C=10,\n", + " random_state=42)\n", + "mlr3.fit(X,y)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "7c28a9a5", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "x0,x1=np.meshgrid(\n", + " np.linspace(0,9,500).reshape(-1,1),\n", + " np.linspace(0,7,200).reshape(-1,1))" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "258b2dd7", + "metadata": {}, + "outputs": [], + "source": [ + "Xnew=np.c_[x0.ravel(), x1.ravel()]\n", + "yPred=mlr3.predict_proba(Xnew)\n", + "yProba=mlr3.predict(Xnew)\n", + "zz=yProba.reshape(x0.shape)\n", + "zz1=yPred[:,1].reshape(x0.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "2d1cc5a0", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from matplotlib.colors import ListedColormap\n", + "plt.plot(X[y==2,0], X[y==2,1],'y*', label='Virg')\n", + "plt.plot(X[y==1,0], X[y==1,1],'g^', label='Vers')\n", + "plt.plot(X[y==0,0], X[y==0,1],'bs', label='Set')\n", + "contour=plt.contour(x0,x1,zz1, cmap=plt.cm.brg)\n", + "ccmap=ListedColormap(['#fafab0', '#9898ff', '#a0faa0'])\n", + "plt.contourf(x0,x1,zz,cmap=ccmap)\n", + "plt.clabel(contour, inline=1,fontsize=12)\n", + "plt.xlabel('Sepal Width', fontsize=12)\n", + "plt.ylabel('Sepal Length', fontsize=12)\n", + "plt.axis([4,8.5,1,5])\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "37b5eb33", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "840fcc9a", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/slides/bgd.pdf b/slides/bgd.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f795af3dd6e99508e57299b6f983935409dc5aa2 GIT binary patch literal 2567044 zcmeFZXFObA^fyW(LK=~ZXwiH0I!Fk{=)Fs#j~2a$AWHNZW1T@Zo*H^`KQG&%rRRtRt?A(!VrjObloHG|kS0o# z{rf72fh8sR_TNa%7I~1hMD=6l$`Oa8?7EkQ>Ms3l`-g5L*E5)2XrjR8uRrg;C2_s| zkp835ri+n3XJF#Zydc#Q|7()HpwLYXRQ$D{auoKvQiOqCxAzlB7Ugy2+&9Fy8WeM| zRh~@r%FZ7;ZlB{qNPeu|VHTs5Q`6qIHn25rY!{34Q{*F#Qa*gdwgKC?B3p}#*&SzC zX`G>a?%p#ZoghF-vnKh60g^9OLowSP)JFz3LWNB)>lvQw=UnLN|24m8y;Z(G&7@{( zc%lqBzX-fQz8Q&mRd)H{rsD~ldX3RnKij0jzPBq8fF9ey%D 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