machine_learning/naive_bayes.cpp

/*******************************************************
 * Copyright (c) 2014, ArrayFire
 * All rights reserved.
 *
 * This file is distributed under 3-clause BSD license.
 * The complete license agreement can be obtained at:
 * http://arrayfire.com/licenses/BSD-3-Clause
 ********************************************************/

#include <arrayfire.h>
#include <stdio.h>
#include <vector>
#include <string>
#include <af/util.h>
#include <math.h>
#include "mnist_common.h"

using namespace af;

// Get accuracy of the predicted results
float accuracy(const array& predicted, const array& target)
{
    return 100 * count<float>(predicted == target) / target.elements();
}

void naive_bayes_train(float *priors,
                       array &mu, array &sig2,
                       const array &train_feats,
                       const array &train_classes,
                       int num_classes)
{
    const int feat_len = train_feats.dims(0);
    const int num_samples = train_classes.elements();

    // Get mean and variance from trianing data
    mu  = constant(0, feat_len, num_classes);
    sig2 = constant(0, feat_len, num_classes);

    for (int ii = 0; ii < num_classes; ii++) {
        array idx = where(train_classes == ii);
        array train_feats_ii = lookup(train_feats, idx, 1);

        mu(span, ii)  = mean(train_feats_ii, 1);

        // Some pixels are always 0. Add a small variance.
        sig2(span,ii) = var(train_feats_ii, 0, 1) + 0.01;

        // Calculate priors
        priors[ii] = (float)idx.elements() / (float)num_samples;
    }

    mu.eval();
    sig2.eval();
}

array naive_bayes_predict(float *priors,
                          const array &mu, const array &sig2,
                          const array &test_feats, int num_classes)
{
    int num_test = test_feats.dims(1);

    // Predict the probabilities for testing data
    // Using log of probabilities to reduce rounding errors
    array log_probs = constant(1, num_test, num_classes);

    for (int ii = 0; ii < num_classes; ii++) {

        // Tile the current mean and variance to the testing data size
        array Mu  = tile(mu (span, ii), 1, num_test);
        array Sig2 = tile(sig2(span, ii), 1, num_test);

        // This is the same as log of the CDF of the normal distribution
        array Df = test_feats - Mu;
        array log_P =  (-(Df * Df) / (2 * Sig2))  - log(sqrt(2 * af::Pi * Sig2));

        // Accumulate the probabilities, multiply with priors (add log of priors)
        log_probs(span, ii) = log(priors[ii]) + sum(log_P).T();
    }

    // Get the location of the maximum value
    array val, idx;
    max(val, idx, log_probs, 1);
    return idx;
}

void benchmark_nb(const array &train_feats, const array test_feats,
                  const array &train_labels, int num_classes)
{
    array mu, sig2;
    int iter = 25;
    float *priors = new float[num_classes];

    timer::start();
    for (int i = 0; i < iter; i++) {
        naive_bayes_train(priors, mu, sig2, train_feats, train_labels, num_classes);
    }
    af::sync();
    printf("Training time: %4.4lf s\n", timer::stop() / iter);

    timer::start();
    for (int i = 0; i < iter; i++) {
        naive_bayes_predict(priors, mu, sig2, test_feats, num_classes);
    }
    af::sync();
    printf("Prediction time: %4.4lf s\n", timer::stop() / iter);

    delete[] priors;
}

void naive_bayes_demo(bool console, int perc)
{
    array train_images, train_labels;
    array test_images, test_labels;
    int num_train, num_test, num_classes;

    // Load mnist data
    float frac = (float)(perc) / 100.0;
    setup_mnist<false>(&num_classes, &num_train, &num_test,
                       train_images, test_images,
                       train_labels, test_labels, frac);

    int feature_length = train_images.elements() / num_train;
    array train_feats = moddims(train_images, feature_length, num_train);
    array test_feats  = moddims(test_images , feature_length, num_test );

    // Get training parameters
    array mu, sig2;
    float *priors = new float[num_classes];
    naive_bayes_train(priors, mu, sig2, train_feats, train_labels, num_classes);

    // Predict the classes
    array res_labels = naive_bayes_predict(priors, mu, sig2, test_feats, num_classes);
    delete[] priors;

    // Results
    printf("Trainng samples: %4d, Testing samples: %4d\n", num_train, num_test);
    printf("Accuracy on testing  data: %2.2f\n",
           accuracy(res_labels , test_labels));

    benchmark_nb(train_feats, test_feats, train_labels, num_classes);

    if (!console) {
        test_images = test_images.T();
        test_labels = test_labels.T();
        // FIXME: Crashing in mnist_common.h::classify
        //display_results<false>(test_images, res_labels, test_labels , 20);
    }
}

int main(int argc, char** argv)
{
    int device   = argc > 1 ? atoi(argv[1]) : 0;
    bool console = argc > 2 ? argv[2][0] == '-' : false;
    int perc     = argc > 3 ? atoi(argv[3]) : 60;

    try {

        af::setDevice(device);
        af::info();
        naive_bayes_demo(console, perc);

    } catch (af::exception &ae) {
        std::cerr << ae.what() << std::endl;
    }

    return 0;
}