{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Notebook 7: Logistic Regression and SoftMax for MNIST" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Learning Goal\n", "\n", "The goal of this notebook is to familiarize the reader with SoftMax regression (a generalization of logistic regression to more than two categories), categorical predictions, and the MNIST handwritten dataset. The reader will understand how to use the Scikit Logistic regression package and visualize learned weights.\n", "\n", "## Overview\n", "### The MNIST dataset:\n", "The MNIST classification problem is one of the classical ML problems for learning classification on high-dimensional data with a fairly sizable number of examples (60000). Yann LeCun and collaborators collected and processed $70000$ handwritten digits (60000 are used for training and 10000 for testing) to produce what became known as one of the most widely used datasets in ML: the [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. Each handwritten digit comes in a grayscale square image in the shape of a $28\\times 28$ pixel grid. Every pixel takes a value in the range $[0,255]$, representing $256$ nuances of the gray color. The problem of image classification finds applications in a wide range of fields and is important for numerous industry applications of ML. \n", "### SoftMax regression:\n", "We will use SoftMax regression, which can be thought of as a statistical model which assigns a probability that a given input image corresponds to any of the 10 handwritten digits. The model is a generalization of the logistic regression and reads:\n", "\\begin{align}\n", "p(y=i|\\boldsymbol{x};W) = \\frac{e^{\\boldsymbol{w}_i^T \\boldsymbol{x}}}{\\sum_{j=0}^9 e^{\\boldsymbol{w}_j^T}},\n", "\\end{align}\n", "Where $p(y=i|\\boldsymbol{x};W)$ is the probability that input $\\boldsymbol{x}$ is the $i$-th digit, $i\\in[0,9]$.\n", "The model also has 10 weight vectors $\\boldsymbol{w}_i$ which we will train below. Finally, one can use this information for prediction by taking the value of $y$ for which this probability is maximized:\n", "\\begin{align}\n", "y_{pred}=\\arg\\max_i p(y=i|\\boldsymbol{x})\n", "\\end{align}\n", "\n", "## Numerical Experiments\n", "\n", "The reader is invited to check out the code below to build up their intuition about SoftMax regression. The following notebook is a slight modification of [this Scikit tutorial](http://scikit-learn.org/dev/auto_examples/linear_model/plot_sparse_logistic_regression_mnist.html) by Arthur Mensch on studying the MNIST problem using Logistic Regression." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Automatically created module for IPython interactive environment\n", "Example run in 47.833 s\n", "Sparsity with L2 penalty: 9.18%\n", "Test score with L2 penalty: 0.8948\n" ] } ], "source": [ "import time\n", "import numpy as np\n", "\n", "from sklearn.datasets import fetch_openml # MNIST data\n", "from sklearn.linear_model import LogisticRegression\n", "from sklearn.model_selection import train_test_split\n", "from sklearn.preprocessing import StandardScaler\n", "from sklearn.utils import check_random_state\n", "\n", "print(__doc__)\n", "\n", "# Turn down for faster convergence\n", "t0 = time.time()\n", "train_size = 50000\n", "test_size = 10000\n", "\n", "### load MNIST data from https://www.openml.org/d/554\n", "X, y = fetch_openml('mnist_784', version=1, return_X_y=True)\n", "\n", "# shuffle data\n", "random_state = check_random_state(0)\n", "permutation = random_state.permutation(X.shape[0])\n", "X = X[permutation]\n", "y = y[permutation]\n", "X = X.reshape((X.shape[0], -1))\n", "\n", "# pick training and test data sets \n", "X_train, X_test, y_train, y_test = train_test_split(X,y,train_size=train_size,test_size=test_size)\n", "\n", "# scale data to have zero mean and unit variance [required by regressor]\n", "scaler = StandardScaler()\n", "X_train = scaler.fit_transform(X_train)\n", "X_test = scaler.transform(X_test)\n", "\n", "# apply logistic regressor with 'sag' solver, C is the inverse regularization strength\n", "clf = LogisticRegression(C=1e5,\n", " multi_class='multinomial',\n", " penalty='l2', solver='sag', tol=0.1)\n", "# fit data\n", "clf.fit(X_train, y_train)\n", "# percentage of nonzero weights\n", "sparsity = np.mean(clf.coef_ == 0) * 100\n", "# compute accuracy\n", "score = clf.score(X_test, y_test)\n", "\n", "#display run time\n", "run_time = time.time() - t0\n", "print('Example run in %.3f s' % run_time)\n", "\n", "print(\"Sparsity with L2 penalty: %.2f%%\" % sparsity)\n", "print(\"Test score with L2 penalty: %.4f\" % score)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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