use of org.apache.commons.math3.optim.univariate.SearchInterval in project gatk-protected by broadinstitute.
the class OptimizationUtils method argmax.
public static double argmax(final Function<Double, Double> function, final double min, final double max, final double guess, final double relativeTolerance, final double absoluteTolerance, final int maxEvaluations) {
final BrentOptimizer optimizer = new BrentOptimizer(relativeTolerance, absoluteTolerance);
final SearchInterval interval = new SearchInterval(min, max, guess);
return optimizer.optimize(new UnivariateObjectiveFunction(function::apply), GoalType.MAXIMIZE, interval, new MaxEval(maxEvaluations)).getPoint();
}
use of org.apache.commons.math3.optim.univariate.SearchInterval in project gatk by broadinstitute.
the class PosteriorSummaryUtils method calculatePosteriorMode.
/**
* Given a list of posterior samples, returns an estimate of the posterior mode (using
* mllib kernel density estimation in {@link KernelDensity} and {@link BrentOptimizer}).
* Note that estimate may be poor if number of samples is small (resulting in poor kernel density estimation),
* or if posterior is not unimodal (or is sufficiently pathological otherwise). If the samples contain
* {@link Double#NaN}, {@link Double#NaN} will be returned.
* @param samples posterior samples, cannot be {@code null} and number of samples must be greater than 0
* @param ctx {@link JavaSparkContext} used by {@link KernelDensity} for mllib kernel density estimation
*/
public static double calculatePosteriorMode(final List<Double> samples, final JavaSparkContext ctx) {
Utils.nonNull(samples);
Utils.validateArg(samples.size() > 0, "Number of samples must be greater than zero.");
//calculate sample min, max, mean, and standard deviation
final double sampleMin = Collections.min(samples);
final double sampleMax = Collections.max(samples);
final double sampleMean = new Mean().evaluate(Doubles.toArray(samples));
final double sampleStandardDeviation = new StandardDeviation().evaluate(Doubles.toArray(samples));
//if samples are all the same or contain NaN, can simply return mean
if (sampleStandardDeviation == 0. || Double.isNaN(sampleMean)) {
return sampleMean;
}
//use Silverman's rule to set bandwidth for kernel density estimation from sample standard deviation
//see https://en.wikipedia.org/wiki/Kernel_density_estimation#Practical_estimation_of_the_bandwidth
final double bandwidth = SILVERMANS_RULE_CONSTANT * sampleStandardDeviation * Math.pow(samples.size(), SILVERMANS_RULE_EXPONENT);
//use kernel density estimation to approximate posterior from samples
final KernelDensity pdf = new KernelDensity().setSample(ctx.parallelize(samples, 1)).setBandwidth(bandwidth);
//use Brent optimization to find mode (i.e., maximum) of kernel-density-estimated posterior
final BrentOptimizer optimizer = new BrentOptimizer(RELATIVE_TOLERANCE, RELATIVE_TOLERANCE * (sampleMax - sampleMin));
final UnivariateObjectiveFunction objective = new UnivariateObjectiveFunction(f -> pdf.estimate(new double[] { f })[0]);
//search for mode within sample range, start near sample mean
final SearchInterval searchInterval = new SearchInterval(sampleMin, sampleMax, sampleMean);
return optimizer.optimize(objective, GoalType.MAXIMIZE, searchInterval, BRENT_MAX_EVAL).getPoint();
}
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