org.apache.commons.math.stat.correlation.Covariance Java Examples

The following examples show how to use org.apache.commons.math.stat.correlation.Covariance. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. You may check out the related API usage on the sidebar.
Example #1
Source File: GLSMultipleLinearRegressionTest.java    From astor with GNU General Public License v2.0 4 votes vote down vote up
/**
 * Generate an error covariance matrix and sample data representing models
 * with this error structure. Then verify that GLS estimated coefficients,
 * on average, perform better than OLS.
 */
@Test
public void testGLSEfficiency() throws Exception {
    RandomGenerator rg = new JDKRandomGenerator();
    rg.setSeed(200);  // Seed has been selected to generate non-trivial covariance
    
    // Assume model has 16 observations (will use Longley data).  Start by generating
    // non-constant variances for the 16 error terms.
    final int nObs = 16;
    double[] sigma = new double[nObs];
    for (int i = 0; i < nObs; i++) {
        sigma[i] = 10 * rg.nextDouble();
    }
    
    // Now generate 1000 error vectors to use to estimate the covariance matrix
    // Columns are draws on N(0, sigma[col])
    final int numSeeds = 1000;
    RealMatrix errorSeeds = MatrixUtils.createRealMatrix(numSeeds, nObs);
    for (int i = 0; i < numSeeds; i++) {
        for (int j = 0; j < nObs; j++) {
            errorSeeds.setEntry(i, j, rg.nextGaussian() * sigma[j]);
        }
    }
    
    // Get covariance matrix for columns
    RealMatrix cov = (new Covariance(errorSeeds)).getCovarianceMatrix();
      
    // Create a CorrelatedRandomVectorGenerator to use to generate correlated errors
    GaussianRandomGenerator rawGenerator = new GaussianRandomGenerator(rg);
    double[] errorMeans = new double[nObs];  // Counting on init to 0 here
    CorrelatedRandomVectorGenerator gen = new CorrelatedRandomVectorGenerator(errorMeans, cov,
     1.0e-12 * cov.getNorm(), rawGenerator);
    
    // Now start generating models.  Use Longley X matrix on LHS
    // and Longley OLS beta vector as "true" beta.  Generate
    // Y values by XB + u where u is a CorrelatedRandomVector generated
    // from cov.
    OLSMultipleLinearRegression ols = new OLSMultipleLinearRegression();
    ols.newSampleData(longley, nObs, 6);
    final RealVector b = ols.calculateBeta().copy();
    final RealMatrix x = ols.X.copy();
    
    // Create a GLS model to reuse
    GLSMultipleLinearRegression gls = new GLSMultipleLinearRegression();
    gls.newSampleData(longley, nObs, 6);
    gls.newCovarianceData(cov.getData());
    
    // Create aggregators for stats measuring model performance
    DescriptiveStatistics olsBetaStats = new DescriptiveStatistics();
    DescriptiveStatistics glsBetaStats = new DescriptiveStatistics();
    
    // Generate Y vectors for 10000 models, estimate GLS and OLS and
    // Verify that OLS estimates are better
    final int nModels = 10000;
    for (int i = 0; i < nModels; i++) {
        
        // Generate y = xb + u with u cov
        RealVector u = MatrixUtils.createRealVector(gen.nextVector());
        double[] y = u.add(x.operate(b)).getData();
        
        // Estimate OLS parameters
        ols.newYSampleData(y);
        RealVector olsBeta = ols.calculateBeta();
        
        // Estimate GLS parameters
        gls.newYSampleData(y);
        RealVector glsBeta = gls.calculateBeta();
        
        // Record deviations from "true" beta
        double dist = olsBeta.getDistance(b);
        olsBetaStats.addValue(dist * dist);
        dist = glsBeta.getDistance(b);
        glsBetaStats.addValue(dist * dist);
        
    }
    
    // Verify that GLS is on average more efficient, lower variance
    assert(olsBetaStats.getMean() > 1.5 * glsBetaStats.getMean());
    assert(olsBetaStats.getStandardDeviation() > glsBetaStats.getStandardDeviation());  
}
 
Example #2
Source File: GLSMultipleLinearRegressionTest.java    From astor with GNU General Public License v2.0 4 votes vote down vote up
/**
 * Generate an error covariance matrix and sample data representing models
 * with this error structure. Then verify that GLS estimated coefficients,
 * on average, perform better than OLS.
 */
@Test
public void testGLSEfficiency() throws Exception {
    RandomGenerator rg = new JDKRandomGenerator();
    rg.setSeed(200);  // Seed has been selected to generate non-trivial covariance
    
    // Assume model has 16 observations (will use Longley data).  Start by generating
    // non-constant variances for the 16 error terms.
    final int nObs = 16;
    double[] sigma = new double[nObs];
    for (int i = 0; i < nObs; i++) {
        sigma[i] = 10 * rg.nextDouble();
    }
    
    // Now generate 1000 error vectors to use to estimate the covariance matrix
    // Columns are draws on N(0, sigma[col])
    final int numSeeds = 1000;
    RealMatrix errorSeeds = MatrixUtils.createRealMatrix(numSeeds, nObs);
    for (int i = 0; i < numSeeds; i++) {
        for (int j = 0; j < nObs; j++) {
            errorSeeds.setEntry(i, j, rg.nextGaussian() * sigma[j]);
        }
    }
    
    // Get covariance matrix for columns
    RealMatrix cov = (new Covariance(errorSeeds)).getCovarianceMatrix();
      
    // Create a CorrelatedRandomVectorGenerator to use to generate correlated errors
    GaussianRandomGenerator rawGenerator = new GaussianRandomGenerator(rg);
    double[] errorMeans = new double[nObs];  // Counting on init to 0 here
    CorrelatedRandomVectorGenerator gen = new CorrelatedRandomVectorGenerator(errorMeans, cov,
     1.0e-12 * cov.getNorm(), rawGenerator);
    
    // Now start generating models.  Use Longley X matrix on LHS
    // and Longley OLS beta vector as "true" beta.  Generate
    // Y values by XB + u where u is a CorrelatedRandomVector generated
    // from cov.
    OLSMultipleLinearRegression ols = new OLSMultipleLinearRegression();
    ols.newSampleData(longley, nObs, 6);
    final RealVector b = ols.calculateBeta().copy();
    final RealMatrix x = ols.X.copy();
    
    // Create a GLS model to reuse
    GLSMultipleLinearRegression gls = new GLSMultipleLinearRegression();
    gls.newSampleData(longley, nObs, 6);
    gls.newCovarianceData(cov.getData());
    
    // Create aggregators for stats measuring model performance
    DescriptiveStatistics olsBetaStats = new DescriptiveStatistics();
    DescriptiveStatistics glsBetaStats = new DescriptiveStatistics();
    
    // Generate Y vectors for 10000 models, estimate GLS and OLS and
    // Verify that OLS estimates are better
    final int nModels = 10000;
    for (int i = 0; i < nModels; i++) {
        
        // Generate y = xb + u with u cov
        RealVector u = MatrixUtils.createRealVector(gen.nextVector());
        double[] y = u.add(x.operate(b)).getData();
        
        // Estimate OLS parameters
        ols.newYSampleData(y);
        RealVector olsBeta = ols.calculateBeta();
        
        // Estimate GLS parameters
        gls.newYSampleData(y);
        RealVector glsBeta = gls.calculateBeta();
        
        // Record deviations from "true" beta
        double dist = olsBeta.getDistance(b);
        olsBetaStats.addValue(dist * dist);
        dist = glsBeta.getDistance(b);
        glsBetaStats.addValue(dist * dist);
        
    }
    
    // Verify that GLS is on average more efficient, lower variance
    assert(olsBetaStats.getMean() > 1.5 * glsBetaStats.getMean());
    assert(olsBetaStats.getStandardDeviation() > glsBetaStats.getStandardDeviation());  
}
 
Example #3
Source File: GLSMultipleLinearRegressionTest.java    From astor with GNU General Public License v2.0 4 votes vote down vote up
/**
 * Generate an error covariance matrix and sample data representing models
 * with this error structure. Then verify that GLS estimated coefficients,
 * on average, perform better than OLS.
 */
@Test
public void testGLSEfficiency() throws Exception {
    RandomGenerator rg = new JDKRandomGenerator();
    rg.setSeed(200);  // Seed has been selected to generate non-trivial covariance
    
    // Assume model has 16 observations (will use Longley data).  Start by generating
    // non-constant variances for the 16 error terms.
    final int nObs = 16;
    double[] sigma = new double[nObs];
    for (int i = 0; i < nObs; i++) {
        sigma[i] = 10 * rg.nextDouble();
    }
    
    // Now generate 1000 error vectors to use to estimate the covariance matrix
    // Columns are draws on N(0, sigma[col])
    final int numSeeds = 1000;
    RealMatrix errorSeeds = MatrixUtils.createRealMatrix(numSeeds, nObs);
    for (int i = 0; i < numSeeds; i++) {
        for (int j = 0; j < nObs; j++) {
            errorSeeds.setEntry(i, j, rg.nextGaussian() * sigma[j]);
        }
    }
    
    // Get covariance matrix for columns
    RealMatrix cov = (new Covariance(errorSeeds)).getCovarianceMatrix();
      
    // Create a CorrelatedRandomVectorGenerator to use to generate correlated errors
    GaussianRandomGenerator rawGenerator = new GaussianRandomGenerator(rg);
    double[] errorMeans = new double[nObs];  // Counting on init to 0 here
    CorrelatedRandomVectorGenerator gen = new CorrelatedRandomVectorGenerator(errorMeans, cov,
     1.0e-12 * cov.getNorm(), rawGenerator);
    
    // Now start generating models.  Use Longley X matrix on LHS
    // and Longley OLS beta vector as "true" beta.  Generate
    // Y values by XB + u where u is a CorrelatedRandomVector generated
    // from cov.
    OLSMultipleLinearRegression ols = new OLSMultipleLinearRegression();
    ols.newSampleData(longley, nObs, 6);
    final RealVector b = ols.calculateBeta().copy();
    final RealMatrix x = ols.X.copy();
    
    // Create a GLS model to reuse
    GLSMultipleLinearRegression gls = new GLSMultipleLinearRegression();
    gls.newSampleData(longley, nObs, 6);
    gls.newCovarianceData(cov.getData());
    
    // Create aggregators for stats measuring model performance
    DescriptiveStatistics olsBetaStats = new DescriptiveStatistics();
    DescriptiveStatistics glsBetaStats = new DescriptiveStatistics();
    
    // Generate Y vectors for 10000 models, estimate GLS and OLS and
    // Verify that OLS estimates are better
    final int nModels = 10000;
    for (int i = 0; i < nModels; i++) {
        
        // Generate y = xb + u with u cov
        RealVector u = MatrixUtils.createRealVector(gen.nextVector());
        double[] y = u.add(x.operate(b)).getData();
        
        // Estimate OLS parameters
        ols.newYSampleData(y);
        RealVector olsBeta = ols.calculateBeta();
        
        // Estimate GLS parameters
        gls.newYSampleData(y);
        RealVector glsBeta = gls.calculateBeta();
        
        // Record deviations from "true" beta
        double dist = olsBeta.getDistance(b);
        olsBetaStats.addValue(dist * dist);
        dist = glsBeta.getDistance(b);
        glsBetaStats.addValue(dist * dist);
        
    }
    
    // Verify that GLS is on average more efficient, lower variance
    assert(olsBetaStats.getMean() > 1.5 * glsBetaStats.getMean());
    assert(olsBetaStats.getStandardDeviation() > glsBetaStats.getStandardDeviation());  
}
 
Example #4
Source File: DoubleSeries.java    From incubator-pinot with Apache License 2.0 4 votes vote down vote up
public static double cov(Series a, Series b) {
  if(a.hasNull() || b.hasNull())
    return NULL;
  return new Covariance().covariance(a.getDoubles().values(), b.getDoubles().values());
}