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Java example source code file (MultivariateNormalMixtureModelDistributionTest.java)

This example Java source code file (MultivariateNormalMixtureModelDistributionTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

arraylist, list, mixturemultivariaterealdistribution, multivariatenormaldistribution, multivariatenormalmixturemodeldistribution, multivariatenormalmixturemodeldistributiontest, pair, test, util

The MultivariateNormalMixtureModelDistributionTest.java Java example source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math3.distribution;

import java.util.List;
import java.util.ArrayList;
import org.apache.commons.math3.exception.NotPositiveException;
import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.util.Pair;
import org.junit.Assert;
import org.junit.Test;

/**
 * Test that demonstrates the use of {@link MixtureMultivariateRealDistribution}
 * in order to create a mixture model composed of {@link MultivariateNormalDistribution
 * normal distributions}.
 */
public class MultivariateNormalMixtureModelDistributionTest {

    @Test
    public void testNonUnitWeightSum() {
        final double[] weights = { 1, 2 };
        final double[][] means = { { -1.5, 2.0 },
                                   { 4.0, 8.2 } };
        final double[][][] covariances = { { { 2.0, -1.1 },
                                             { -1.1, 2.0 } },
                                           { { 3.5, 1.5 },
                                             { 1.5, 3.5 } } };
        final MultivariateNormalMixtureModelDistribution d
            = create(weights, means, covariances);

        final List<Pair comp = d.getComponents();

        Assert.assertEquals(1d / 3, comp.get(0).getFirst().doubleValue(), Math.ulp(1d));
        Assert.assertEquals(2d / 3, comp.get(1).getFirst().doubleValue(), Math.ulp(1d));
    }

    @Test(expected=MathArithmeticException.class)
    public void testWeightSumOverFlow() {
        final double[] weights = { 0.5 * Double.MAX_VALUE, 0.51 * Double.MAX_VALUE };
        final double[][] means = { { -1.5, 2.0 },
                                   { 4.0, 8.2 } };
        final double[][][] covariances = { { { 2.0, -1.1 },
                                             { -1.1, 2.0 } },
                                           { { 3.5, 1.5 },
                                             { 1.5, 3.5 } } };
        create(weights, means, covariances);
    }

    @Test(expected=NotPositiveException.class)
    public void testPreconditionPositiveWeights() {
        final double[] negativeWeights = { -0.5, 1.5 };
        final double[][] means = { { -1.5, 2.0 },
                                   { 4.0, 8.2 } };
        final double[][][] covariances = { { { 2.0, -1.1 },
                                             { -1.1, 2.0 } },
                                           { { 3.5, 1.5 },
                                             { 1.5, 3.5 } } };
        create(negativeWeights, means, covariances);
    }

    /**
     * Test the accuracy of the density calculation.
     */
    @Test
    public void testDensities() {
        final double[] weights = { 0.3, 0.7 };
        final double[][] means = { { -1.5, 2.0 },
                                   { 4.0, 8.2 } };
        final double[][][] covariances = { { { 2.0, -1.1 },
                                             { -1.1, 2.0 } },
                                           { { 3.5, 1.5 },
                                             { 1.5, 3.5 } } };
        final MultivariateNormalMixtureModelDistribution d
            = create(weights, means, covariances);

        // Test vectors
        final double[][] testValues = { { -1.5, 2 },
                                        { 4, 8.2 },
                                        { 1.5, -2 },
                                        { 0, 0 } };

        // Densities that we should get back.
        // Calculated by assigning weights to multivariate normal distribution
        // and summing
        // values from dmvnorm function in R 2.15 CRAN package Mixtools v0.4.
        // Like: .3*dmvnorm(val,mu1,sigma1)+.7*dmvnorm(val,mu2,sigma2)
        final double[] correctDensities = { 0.02862037278930575,
                                            0.03523044847314091,
                                            0.000416241365629767,
                                            0.009932042831700297 };

        for (int i = 0; i < testValues.length; i++) {
            Assert.assertEquals(correctDensities[i], d.density(testValues[i]), Math.ulp(1d));
        }
    }

    /**
     * Test the accuracy of sampling from the distribution.
     */
    @Test
    public void testSampling() {
        final double[] weights = { 0.3, 0.7 };
        final double[][] means = { { -1.5, 2.0 },
                                   { 4.0, 8.2 } };
        final double[][][] covariances = { { { 2.0, -1.1 },
                                             { -1.1, 2.0 } },
                                           { { 3.5, 1.5 },
                                             { 1.5, 3.5 } } };
        final MultivariateNormalMixtureModelDistribution d
            = create(weights, means, covariances);
        d.reseedRandomGenerator(50);

        final double[][] correctSamples = getCorrectSamples();
        final int n = correctSamples.length;
        final double[][] samples = d.sample(n);

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < samples[i].length; j++) {
                Assert.assertEquals(correctSamples[i][j], samples[i][j], 1e-16);
            }
        }
    }

    /**
     * Creates a mixture of Gaussian distributions.
     *
     * @param weights Weights.
     * @param means Means.
     * @param covariances Covariances.
     * @return the mixture distribution.
     */
    private MultivariateNormalMixtureModelDistribution create(double[] weights,
                                                              double[][] means,
                                                              double[][][] covariances) {
        final List<Pair mvns
            = new ArrayList<Pair();

        for (int i = 0; i < weights.length; i++) {
            final MultivariateNormalDistribution dist
                = new MultivariateNormalDistribution(means[i], covariances[i]);
            mvns.add(new Pair<Double, MultivariateNormalDistribution>(weights[i], dist));
        }

        return new MultivariateNormalMixtureModelDistribution(mvns);
    }

    /**
     * Values used in {@link #testSampling()}.
     */
    private double[][] getCorrectSamples() {
        // These were sampled from the MultivariateNormalMixtureModelDistribution class
        // with seed 50.
        //
        // They were then fit to a MVN mixture model in R using mixtools.
        //
        // The optimal parameters were:
        // - component weights: {0.3595186, 0.6404814}
        // - mean vectors: {-1.645879, 1.989797}, {3.474328, 7.782232}
        // - covariance matrices:
        //     { 1.397738 -1.167732
        //       -1.167732 1.801782 }
        //   and
        //     { 3.934593 2.354787
        //       2.354787 4.428024 }
        //
        // It is considered fairly close to the actual test parameters,
        // considering that the sample size is only 100.
        return new double[][] {
            { 6.259990922080121, 11.972954175355897 },
            { -2.5296544304801847, 1.0031292519854365 },
            { 0.49037886081440396, 0.9758251727325711 },
            { 5.022970993312015, 9.289348879616787 },
            { -1.686183146603914, 2.007244382745706 },
            { -1.4729253946002685, 2.762166644212484 },
            { 4.329788143963888, 11.514016497132253 },
            { 3.008674596114442, 4.960246550446107 },
            { 3.342379304090846, 5.937630105198625 },
            { 2.6993068328674754, 7.42190871572571 },
            { -2.446569340219571, 1.9687117791378763 },
            { 1.922417883170056, 4.917616702617099 },
            { -1.1969741543898518, 2.4576126277884387 },
            { 2.4216948702967196, 8.227710158117134 },
            { 6.701424725804463, 9.098666475042428 },
            { 2.9890253545698964, 9.643807939324331 },
            { 0.7162632354907799, 8.978811120287553 },
            { -2.7548699149775877, 4.1354812280794215 },
            { 8.304528180745018, 11.602319388898287 },
            { -2.7633253389165926, 2.786173883989795 },
            { 1.3322228389460813, 5.447481218602913 },
            { -1.8120096092851508, 1.605624499560037 },
            { 3.6546253437206504, 8.195304526564376 },
            { -2.312349539658588, 1.868941220444169 },
            { -1.882322136356522, 2.033795570464242 },
            { 4.562770714939441, 7.414967958885031 },
            { 4.731882017875329, 8.890676665580747 },
            { 3.492186010427425, 8.9005225241848 },
            { -1.619700190174894, 3.314060142479045 },
            { 3.5466090064003315, 7.75182101001913 },
            { 5.455682472787392, 8.143119287755635 },
            { -2.3859602945473197, 1.8826732217294837 },
            { 3.9095306088680015, 9.258129209626317 },
            { 7.443020189508173, 7.837840713329312 },
            { 2.136004873917428, 6.917636475958297 },
            { -1.7203379410395119, 2.3212878757611524 },
            { 4.618991257611526, 12.095065976419436 },
            { -0.4837044029854387, 0.8255970441255125 },
            { -4.438938966557163, 4.948666297280241 },
            { -0.4539625134045906, 4.700922454655341 },
            { 2.1285488271265356, 8.457941480487563 },
            { 3.4873561871454393, 11.99809827845933 },
            { 4.723049431412658, 7.813095742563365 },
            { 1.1245583037967455, 5.20587873556688 },
            { 1.3411933634409197, 6.069796875785409 },
            { 4.585119332463686, 7.967669543767418 },
            { 1.3076522817963823, -0.647431033653445 },
            { -1.4449446442803178, 1.9400424267464862 },
            { -2.069794456383682, 3.5824162107496544 },
            { -0.15959481421417276, 1.5466782303315405 },
            { -2.0823081278810136, 3.0914366458581437 },
            { 3.521944615248141, 10.276112932926408 },
            { 1.0164326704884257, 4.342329556442856 },
            { 5.3718868590295275, 8.374761158360922 },
            { 0.3673656866959396, 8.75168581694866 },
            { -2.250268955954753, 1.4610850300996527 },
            { -2.312739727403522, 1.5921126297576362 },
            { 3.138993360831055, 6.7338392374947365 },
            { 2.6978650950790115, 7.941857288979095 },
            { 4.387985088655384, 8.253499976968 },
            { -1.8928961721456705, 0.23631082388724223 },
            { 4.43509029544109, 8.565290285488782 },
            { 4.904728034106502, 5.79936660133754 },
            { -1.7640371853739507, 2.7343727594167433 },
            { 2.4553674733053463, 7.875871017408807 },
            { -2.6478965122565006, 4.465127753193949 },
            { 3.493873671142299, 10.443093773532448 },
            { 1.1321916197409103, 7.127108479263268 },
            { -1.7335075535240392, 2.550629648463023 },
            { -0.9772679734368084, 4.377196298969238 },
            { 3.6388366973980357, 6.947299283206256 },
            { 0.27043799318823325, 6.587978599614367 },
            { 5.356782352010253, 7.388957912116327 },
            { -0.09187745751354681, 0.23612399246659743 },
            { 2.903203580353435, 3.8076727621794415 },
            { 5.297014824937293, 8.650985262326508 },
            { 4.934508602170976, 9.164571423190052 },
            { -1.0004911869654256, 4.797064194444461 },
            { 6.782491700298046, 11.852373338280497 },
            { 2.8983678524536014, 8.303837362117521 },
            { 4.805003269830865, 6.790462904325329 },
            { -0.8815799740744226, 1.3015810062131394 },
            { 5.115138859802104, 6.376895810201089 },
            { 4.301239328205988, 8.60546337560793 },
            { 3.276423626317666, 9.889429652591947 },
            { -4.001924973153122, 4.3353864592328515 },
            { 3.9571892554119517, 4.500569057308562 },
            { 4.783067027436208, 7.451125480601317 },
            { 4.79065438272821, 9.614122776979698 },
            { 2.677655270279617, 6.8875223698210135 },
            { -1.3714746289327362, 2.3992153193382437 },
            { 3.240136859745249, 7.748339397522042 },
            { 5.107885374416291, 8.508324480583724 },
            { -1.5830830226666048, 0.9139127045208315 },
            { -1.1596156791652918, -0.04502759384531929 },
            { -0.4670021307952068, 3.6193633227841624 },
            { -0.7026065228267798, 0.4811423031997131 },
            { -2.719979836732917, 2.5165041618080104 },
            { 1.0336754331123372, -0.34966029029320644 },
            { 4.743217291882213, 5.750060115251131 }
        };
    }
}

/**
 * Class that implements a mixture of Gaussian ditributions.
 */
class MultivariateNormalMixtureModelDistribution
    extends MixtureMultivariateRealDistribution<MultivariateNormalDistribution> {

    public MultivariateNormalMixtureModelDistribution(List<Pair components) {
        super(components);
    }
}

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