mirror of https://github.com/jlizier/jidt
147 lines
6.3 KiB
Java
Executable File
147 lines
6.3 KiB
Java
Executable File
/*
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* Java Information Dynamics Toolkit (JIDT)
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* Copyright (C) 2012, Joseph T. Lizier
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*
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* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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package infodynamics.utils;
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/**
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* Generic class to represent analytic distributions of info theoretic measurements under
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* some null hypothesis of a relationship between the variables.
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* This class is not designed to be creatable - it's children (which represent
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* various concrete distributions) are those which should be created.
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*
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* @author Joseph Lizier (<a href="joseph.lizier at gmail.com">email</a>,
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* <a href="http://lizier.me/joseph/">www</a>)
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*/
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public abstract class AnalyticMeasurementDistribution extends MeasurementDistribution {
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/**
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* Construct the instance
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*
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* @param actualValue observed value of the information-theoretic measure
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* @param pValue p-value that surrogate measurements are greater than
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* the observed value. (1 - CDF of null at the observed value)
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*/
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protected AnalyticMeasurementDistribution(double actualValue, double pValue) {
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super(actualValue, pValue);
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}
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/**
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* Compute the <b>analytic</b> p-value
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* for the given estimate (i.e. the input argument, not the
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* estimate produced by any particular observations supplied)
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* under a null hypothesis that the source values of our
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* samples had no relation to the destination value (possibly
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* in the context of a conditional value).
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*
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* <p>See Section II.E "Statistical significance testing" of
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* the JIDT paper below for a description of how this is done for MI,
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* conditional MI and TE as per the references below.
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* </p>
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*
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* <p><b>References:</b><br/>
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* <ul>
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* <li>J.T. Lizier, "JIDT: An information-theoretic
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* toolkit for studying the dynamics of complex systems", 2014.</li>
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* <li>Brillinger, <a href="http://www.stat.berkeley.edu/~brill/Papers/MIBJPS.pdf">
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* "Some data analyses using mutual information"</a>,
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* Brazilian Journal of Probability and Statistics, <b>18</b>, p. 163, (2004)</li>
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* <li>Cheng et al., <a href="http://www.jds-online.com/file_download/112/JDS-369.pdf">
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* "Data Information in Contingency Tables: A Fallacy of Hierarchical Loglinear Models"</a>,
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* Journal of Data Science, <b>4</b>, p. 387 (2006).</li>
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* <li>Geweke, <a href="http://dx.doi.org/10.1080/01621459.1982.10477803">
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* "Measurement of Linear Dependence and Feedback between Multiple Time Series"</a>,
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* Journal of the American Statistical Association, <b>77</b>, p. 304-313 (1982).</li>
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* <li>Barnett and Bossomaier, <a href="http://arxiv.org/abs/1205.6339">
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* "Transfer Entropy as a Log-likelihood Ratio"</a>,
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* Physical Review Letters, <b>109</b>, p. 138105+ (2012).</li>
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* </ul>
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*
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* @return p-value for the given channel measure score under this null hypothesis.
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* @throws Exception
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*/
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public abstract double computePValueForGivenEstimate(double estimate);
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/**
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* Computes p-values corresponding to a set of estimates, each done via
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* {@link #computePValueForGivenEstimate(double)}
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*
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* @param estimates array of estimates to return corresponding p-values for.
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* @return
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*/
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public double[] computePValuesForGivenEstimates(double[] estimates) {
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double[] pValues = new double[estimates.length];
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for (int i = 0; i < estimates.length; i++) {
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pValues[i] = computePValueForGivenEstimate(estimates[i]);
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}
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return estimates;
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}
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/**
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* Compute the estimated observed measured value corresponding to
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* a given p-value
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* (derived from how the given estimates are <b>analytically</b> distributed
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* under a null hypothesis that the source values of our
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* samples had no relation to the destination value, possibly
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* in the context of a conditional value).
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*
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* <p>See Section II.E "Statistical significance testing" of
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* the JIDT paper below for a description of how this is done for MI,
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* conditional MI and TE as per the references below.
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* </p>
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*
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* <p><b>References:</b><br/>
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* <ul>
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* <li>J.T. Lizier, "JIDT: An information-theoretic
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* toolkit for studying the dynamics of complex systems", 2014.</li>
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* <li>Brillinger, <a href="http://www.stat.berkeley.edu/~brill/Papers/MIBJPS.pdf">
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* "Some data analyses using mutual information"</a>,
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* Brazilian Journal of Probability and Statistics, <b>18</b>, p. 163, (2004)</li>
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* <li>Cheng et al., <a href="http://www.jds-online.com/file_download/112/JDS-369.pdf">
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* "Data Information in Contingency Tables: A Fallacy of Hierarchical Loglinear Models"</a>,
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* Journal of Data Science, <b>4</b>, p. 387 (2006).</li>
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* <li>Geweke, <a href="http://dx.doi.org/10.1080/01621459.1982.10477803">
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* "Measurement of Linear Dependence and Feedback between Multiple Time Series"</a>,
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* Journal of the American Statistical Association, <b>77</b>, p. 304-313 (1982).</li>
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* <li>Barnett and Bossomaier, <a href="http://arxiv.org/abs/1205.6339">
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* "Transfer Entropy as a Log-likelihood Ratio"</a>,
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* Physical Review Letters, <b>109</b>, p. 138105+ (2012).</li>
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* </ul>
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*
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* @param pValue the sample p-value for the given channel measure score under this null hypothesis.
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* @return the estimate of the channel measure score corresponding to
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* the given p-value under this null hypothesis.
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* @throws Exception
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*/
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public abstract double computeEstimateForGivenPValue(double pValue);
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/**
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* Computes estimates corresponding to a set of p-values, each done via
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* {@link #computeEstimateForGivenPValue(double)}
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*
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* @param pValues array of p-values to return corresponding estimates for.
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* @return
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*/
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public double[] computeEstimatesForGivenPValues(double[] pValues) {
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double[] estimates = new double[pValues.length];
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for (int i = 0; i < pValues.length; i++) {
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estimates[i] = computeEstimateForGivenPValue(pValues[i]);
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}
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return estimates;
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}
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}
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