/**
* Copyright (C) 2001-2017 by RapidMiner and the contributors
*
* Complete list of developers available at our web site:
*
* http://rapidminer.com
*
* This program is free software: you can redistribute it and/or modify it under the terms of the
* GNU Affero General Public License as published by the Free Software Foundation, either version 3
* of the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without
* even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Affero General Public License for more details.
*
* You should have received a copy of the GNU Affero General Public License along with this program.
* If not, see http://www.gnu.org/licenses/.
*/
package com.rapidminer.operator.learner.igss.utility;
import com.rapidminer.operator.learner.igss.hypothesis.Hypothesis;
/**
* The utility function Binomial.
*
* @author Dirk Dach
*/
public class Binomial extends AbstractUtility {
/** Constructs a new Binomial with the given default probability. */
public Binomial(double[] priors, int large) {
super(priors, large);
}
/** Calculates the utility for the given number of examples,positive examples and hypothesis */
@Override
public double utility(double totalWeight, double totalPositiveWeight, Hypothesis hypo) {
double g = hypo.getCoveredWeight() / totalWeight;
double p = hypo.getPositiveWeight() / hypo.getCoveredWeight();
if (hypo.getPrediction() == Hypothesis.POSITIVE_CLASS) {
return Math.sqrt(g) * (p - this.priors[Hypothesis.POSITIVE_CLASS]);
} else {
return Math.sqrt(g) * (p - this.priors[Hypothesis.NEGATIVE_CLASS]);
}
}
/** Calculate confidence intervall without a specific rule */
@Override
public double conf(double totalWeight, double delta) {
double inverseNormal = inverseNormal(1 - delta / 4);
return Math.sqrt(inverseNormal / (2 * Math.sqrt(totalWeight))) + inverseNormal / (2 * Math.sqrt(totalWeight))
+ Math.pow(inverseNormal / (2 * Math.sqrt(totalWeight)), 1.5d);
}
/** Calculate confidence intervall for a specific rule. */
@Override
public double conf(double totalWeight, double totalPositiveWeight, Hypothesis hypo, double delta) {
double g = hypo.getCoveredWeight() / totalWeight;
double p = hypo.getPositiveWeight() / hypo.getCoveredWeight();
double sg = variance(g, totalWeight);
double sp = variance(p, hypo.getCoveredWeight());
double inverseNormal = inverseNormal(1 - delta / 4);
return Math.sqrt(sg * inverseNormal) + sp * inverseNormal + Math.sqrt(sg * inverseNormal) * sp * inverseNormal;
}
/** Calculates the variance for a binomial distribution. */
private double variance(double p, double totalWeight) {
return (p * (1 - p)) / totalWeight;
}
/** Calculate confidence intervall without a specific rule for small m. */
@Override
public double confSmallM(double totalExampleWeight, double delta) {
double term = Math.log(4 / delta) / (2 * totalExampleWeight);
return Math.sqrt(term) + Math.pow(term, 0.25) + Math.pow(term, 0.75);
}
/** Returns an upper bound for the utility of refinements for the given hypothesis. */
@Override
public double getUpperBound(double totalWeight, double totalPositiveWeight, Hypothesis hypo, double delta) {
double p0;
if (hypo.getPrediction() == Hypothesis.POSITIVE_CLASS) {
p0 = this.priors[Hypothesis.POSITIVE_CLASS];
} else {
p0 = this.priors[Hypothesis.NEGATIVE_CLASS];
}
Utility cov = new Coverage(this.priors, this.large);
Hypothesis h = hypo.clone();
h.setCoveredWeight(hypo.getPositiveWeight()); // all fp become tn
double g = cov.utility(totalWeight, totalPositiveWeight, h);
double conf = cov.confidenceIntervall(totalWeight, delta);
return (Math.sqrt(g + conf) * (1.0d - p0));
}
}