{ "cells": [ { "cell_type": "markdown", "id": "9cb10ea7-ba09-44b5-b8f5-16164464afc9", "metadata": {}, "source": [ "# **Lecture 6: Examples for logistical Regression**\n", "\n", "**Two problems related to Logistical regression demonstrated**\n", "- Logistical classifier\n", "- Logistical regression" ] }, { "cell_type": "markdown", "id": "d0e26c6d-aa8e-49b4-9f79-2b9ede3e72e5", "metadata": {}, "source": [ "## **Part I: logistic classification**" ] }, { "cell_type": "code", "execution_count": 1, "id": "099644bb-883e-402e-9503-ddacd42eacb5", "metadata": {}, "outputs": [], "source": [ "# Code source: Gaël Varoquaux\n", "# Modified for documentation by Jaques Grobler\n", "# License: BSD 3 clause\n", "\n", "import matplotlib.pyplot as plt\n", "from sklearn.linear_model import LogisticRegression\n", "from sklearn import datasets\n", "from sklearn.inspection import DecisionBoundaryDisplay" ] }, { "cell_type": "markdown", "id": "c64a8687-4610-4202-a37d-a9b4d64e8e45", "metadata": {}, "source": [ "### 1.1, Import some data to play with" ] }, { "cell_type": "code", "execution_count": 2, "id": "ecdbdf12-dc29-4c06-92d9-d8f413f808dc", "metadata": {}, "outputs": [], "source": [ "# import some data to play with\n", "iris = datasets.load_iris()\n", "X = iris.data[:, :2] # we only take the first two features.\n", "Y = iris.target" ] }, { "cell_type": "markdown", "id": "f8b51501-19d5-4835-b7a8-bb73f0a678e6", "metadata": {}, "source": [ "### 1.2, Create an instance of Logistic Regression Classifier and fit the data." ] }, { "cell_type": "code", "execution_count": 6, "id": "6b98424d-ab84-4089-a477-efa873e56dc2", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
LogisticRegression(C=100000.0)
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=100000.0)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Create an instance of Logistic Regression Classifier and fit the data.\n", "logreg = LogisticRegression(C=1e5)\n", "logreg.fit(X, Y)\n" ] }, { "cell_type": "markdown", "id": "007863a0-cfc2-4a62-bde9-b8f0e5253788", "metadata": {}, "source": [ "### 1.3, Plot resluts" ] }, { "cell_type": "code", "execution_count": 7, "id": "77b4c453-0f25-46b4-a9e6-f06cffba769c", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_, ax = plt.subplots(figsize=(8, 6))\n", "\n", "DecisionBoundaryDisplay.from_estimator(\n", " logreg,\n", " X,\n", " cmap=plt.cm.Paired,\n", " ax=ax,\n", " response_method=\"predict\",\n", " plot_method=\"pcolormesh\",\n", " shading=\"auto\",\n", " xlabel=\"Sepal length\",\n", " ylabel=\"Sepal width\",\n", " eps=0.5,\n", ")\n", "\n", "# Plot also the training points\n", "plt.scatter(X[:, 0], X[:, 1], c=Y, edgecolors=\"k\", cmap=plt.cm.Paired)\n", "\n", "\n", "plt.xticks(())\n", "plt.yticks(())\n", "\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "d4a84213-16c6-44ec-9df6-adb7e40d516e", "metadata": {}, "source": [ "## **Part II: logistic regression**" ] }, { "cell_type": "markdown", "id": "e915d96c-c1f9-4db1-8aef-2262cbaf2957", "metadata": {}, "source": [ "### 2.1, a simple explanation case: numbers connected to logistics" ] }, { "cell_type": "code", "execution_count": 9, "id": "4b517ded-99b2-4569-baf1-6cd904240c45", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "19.33672738021736\n", "0.048945750079555296\n" ] } ], "source": [ "from __future__ import print_function, division\n", "from builtins import range\n", "# Note: you may need to update your version of future\n", "# sudo pip install -U future\n", "\n", "\n", "\n", "import numpy as np\n", "\n", "N = 100\n", "D = 2\n", "\n", "\n", "X = np.random.randn(N,D)\n", "\n", "# center the first 50 points at (-2,-2)\n", "X[:50,:] = X[:50,:] - 2*np.ones((50,D))\n", "\n", "# center the last 50 points at (2, 2)\n", "X[50:,:] = X[50:,:] + 2*np.ones((50,D))\n", "\n", "# labels: first 50 are 0, last 50 are 1\n", "T = np.array([0]*50 + [1]*50)\n", "\n", "# add a column of ones\n", "# ones = np.array([[1]*N]).T # old\n", "ones = np.ones((N, 1))\n", "Xb = np.concatenate((ones, X), axis=1)\n", "\n", "# randomly initialize the weights\n", "w = np.random.randn(D + 1)\n", "\n", "# calculate the model output\n", "z = Xb.dot(w)\n", "\n", "def sigmoid(z):\n", " return 1/(1 + np.exp(-z))\n", "\n", "Y = sigmoid(z)\n", "\n", "# calculate the cross-entropy error\n", "def cross_entropy(T, Y):\n", " E = 0\n", " for i in range(len(T)):\n", " if T[i] == 1:\n", " E -= np.log(Y[i])\n", " else:\n", " E -= np.log(1 - Y[i])\n", " return E\n", "\n", "print(cross_entropy(T, Y))\n", "\n", "# try it with our closed-form solution\n", "w = np.array([0, 4, 4])\n", "\n", "# calculate the model output\n", "z = Xb.dot(w)\n", "Y = sigmoid(z)\n", "\n", "# calculate the cross-entropy error\n", "print(cross_entropy(T, Y))\n", "\n" ] }, { "cell_type": "markdown", "id": "d59897c3-6681-4095-bcf5-cccca217979f", "metadata": {}, "source": [ "### 2.2, A bit more complex case use sklearn from scikit website\n", "**Multiclass sparse logistic regression on 20newgroups**\n", "\n", "- Comparison of multinomial logistic L1 vs one-versus-rest L1 logistic regression\n", "to classify documents from the newgroups20 dataset. Multinomial logistic\n", "regression yields more accurate results and is faster to train on the larger\n", "scale dataset.\n", "\n", "- Here we use the l1 sparsity that trims the weights of not informative\n", "features to zero. This is good if the goal is to extract the strongly\n", "discriminative vocabulary of each class. If the goal is to get the best\n", "predictive accuracy, it is better to use the non sparsity-inducing l2 penalty\n", "instead.\n", "\n", "- A more traditional (and possibly better) way to predict on a sparse subset of\n", "input features would be to use univariate feature selection followed by a\n", "traditional (l2-penalised) logistic regression model.\n" ] }, { "cell_type": "code", "execution_count": 8, "id": "c876b423-9f1f-4be1-9b2f-4de6f22d7b50", "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Dataset 20newsgroup, train_samples=4500, n_features=130107, n_classes=20\n", "[model=One versus Rest, solver=saga] Number of epochs: 1\n", "[model=One versus Rest, solver=saga] Number of epochs: 2\n", "[model=One versus Rest, solver=saga] Number of epochs: 3\n", "Test accuracy for model ovr: 0.5960\n", "% non-zero coefficients for model ovr, per class:\n", " [0.26593496 0.43348936 0.26362917 0.31973683 0.37815029 0.2928359\n", " 0.27054655 0.62717609 0.19522393 0.30897646 0.34586917 0.28207552\n", " 0.34125758 0.29898468 0.34279478 0.59489497 0.38353048 0.35278655\n", " 0.19829832 0.14603365]\n", "Run time (3 epochs) for model ovr:1.12\n", "[model=Multinomial, solver=saga] Number of epochs: 1\n", "[model=Multinomial, solver=saga] Number of epochs: 2\n", "[model=Multinomial, solver=saga] Number of epochs: 5\n", "Test accuracy for model multinomial: 0.6440\n", "% non-zero coefficients for model multinomial, per class:\n", " [0.36047253 0.1268187 0.10606655 0.17985197 0.5395559 0.07993421\n", " 0.06686804 0.21443888 0.11528972 0.2075215 0.10914094 0.11144673\n", " 0.13988486 0.09684337 0.26286057 0.11682692 0.55800226 0.17370318\n", " 0.11452112 0.14603365]\n", "Run time (5 epochs) for model multinomial:0.96\n", "Example run in 103.000 s\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Author: Arthur Mensch\n", "\n", "import timeit\n", "import warnings\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "from sklearn.datasets import fetch_20newsgroups_vectorized\n", "from sklearn.linear_model import LogisticRegression\n", "from sklearn.model_selection import train_test_split\n", "from sklearn.exceptions import ConvergenceWarning\n", "\n", "warnings.filterwarnings(\"ignore\", category=ConvergenceWarning, module=\"sklearn\")\n", "t0 = timeit.default_timer()\n", "\n", "# We use SAGA solver\n", "solver = \"saga\"\n", "\n", "# Turn down for faster run time\n", "n_samples = 5000\n", "\n", "X, y = fetch_20newsgroups_vectorized(subset=\"all\", return_X_y=True)\n", "X = X[:n_samples]\n", "y = y[:n_samples]\n", "\n", "X_train, X_test, y_train, y_test = train_test_split(\n", " X, y, random_state=42, stratify=y, test_size=0.1\n", ")\n", "train_samples, n_features = X_train.shape\n", "n_classes = np.unique(y).shape[0]\n", "\n", "print(\n", " \"Dataset 20newsgroup, train_samples=%i, n_features=%i, n_classes=%i\"\n", " % (train_samples, n_features, n_classes)\n", ")\n", "\n", "models = {\n", " \"ovr\": {\"name\": \"One versus Rest\", \"iters\": [1, 2, 3]},\n", " \"multinomial\": {\"name\": \"Multinomial\", \"iters\": [1, 2, 5]},\n", "}\n", "\n", "for model in models:\n", " # Add initial chance-level values for plotting purpose\n", " accuracies = [1 / n_classes]\n", " times = [0]\n", " densities = [1]\n", "\n", " model_params = models[model]\n", "\n", " # Small number of epochs for fast runtime\n", " for this_max_iter in model_params[\"iters\"]:\n", " print(\n", " \"[model=%s, solver=%s] Number of epochs: %s\"\n", " % (model_params[\"name\"], solver, this_max_iter)\n", " )\n", " lr = LogisticRegression(\n", " solver=solver,\n", " multi_class=model,\n", " penalty=\"l1\",\n", " max_iter=this_max_iter,\n", " random_state=42,\n", " )\n", " t1 = timeit.default_timer()\n", " lr.fit(X_train, y_train)\n", " train_time = timeit.default_timer() - t1\n", "\n", " y_pred = lr.predict(X_test)\n", " accuracy = np.sum(y_pred == y_test) / y_test.shape[0]\n", " density = np.mean(lr.coef_ != 0, axis=1) * 100\n", " accuracies.append(accuracy)\n", " densities.append(density)\n", " times.append(train_time)\n", " models[model][\"times\"] = times\n", " models[model][\"densities\"] = densities\n", " models[model][\"accuracies\"] = accuracies\n", " print(\"Test accuracy for model %s: %.4f\" % (model, accuracies[-1]))\n", " print(\n", " \"%% non-zero coefficients for model %s, per class:\\n %s\"\n", " % (model, densities[-1])\n", " )\n", " print(\n", " \"Run time (%i epochs) for model %s:%.2f\"\n", " % (model_params[\"iters\"][-1], model, times[-1])\n", " )\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "\n", "for model in models:\n", " name = models[model][\"name\"]\n", " times = models[model][\"times\"]\n", " accuracies = models[model][\"accuracies\"]\n", " ax.plot(times, accuracies, marker=\"o\", label=\"Model: %s\" % name)\n", " ax.set_xlabel(\"Train time (s)\")\n", " ax.set_ylabel(\"Test accuracy\")\n", "ax.legend()\n", "fig.suptitle(\"Multinomial vs One-vs-Rest Logistic L1\\nDataset %s\" % \"20newsgroups\")\n", "fig.tight_layout()\n", "fig.subplots_adjust(top=0.85)\n", "run_time = timeit.default_timer() - t0\n", "print(\"Example run in %.3f s\" % run_time)\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.13" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": {}, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 5 }