mirror of https://github.com/jlizier/jidt
274 lines
11 KiB
Java
Executable File
274 lines
11 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.measures.continuous;
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import infodynamics.utils.EmpiricalNullDistributionComputer;
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/**
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* Interface for implementations of
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* Predictive Information / Excess Entropy estimators on
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* continuous univariate data (ie double[] arrays).
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*
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* <p>See definition of Predictive Information (PI) / Excess Entropy in the citations below.
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* Basically, PI is the mutual information between the past <i>state</i>
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* of a time-series process <i>X</i> and its future <i>state</i>.
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* The past <i>state</i> at time <code>n</code>
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* is represented by an embedding vector of <code>k</code> values from <code>X_n</code> backwards,
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* each separated by <code>\tau</code> steps, giving
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* <code><b>X^k_n</b> = [ X_{n-(k-1)\tau}, ... , X_{n-\tau}, X_n]</code>.
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* The future <i>state</i> from time <code>n+1</code>
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* is represented by an embedding vector of <code>k</code> values from <code>X_{n+1}</code> forwards,
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* each separated by <code>\tau</code> steps, giving
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* <code><b>X^{k+}_{n+1}</b> = [ X_{n+1}, X_{n+1+\tau}, ... , X_{n+1+(k-1)\tau}]</code>.
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* We call <code>k</code> the embedding dimension, and <code>\tau</code>
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* the embedding delay.
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* PI is then the mutual information between <b>X^k_n</b> and <b>X^{k+}_{n+1}</b>.</p>
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*
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* <p>
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* Usage of the child classes implementing this interface is intended to follow this paradigm:
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* </p>
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* <ol>
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* <li>Construct the calculator;</li>
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* <li>Set properties using {@link #setProperty(String, String)};</li>
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* <li>Initialise the calculator using {@link #initialise()} or
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* {@link #initialise(int)} or {@link #initialise(int, int)};
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* </li>
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* <li>Provide the observations/samples for the calculator
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* to set up the PDFs, using:
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* <ul>
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* <li>{@link #setObservations(double[])} or
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* {@link #setObservations(double[], boolean[])} for calculations
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* based on single time-series, OR</li>
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* <li>The following sequence:<ol>
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* <li>{@link #startAddObservations()}, then</li>
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* <li>One or more calls to {@link #addObservations(double[])} or
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* {@link #addObservations(double[], int, int)}, then</li>
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* <li>{@link #finaliseAddObservations()};</li>
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* </ol></li>
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* </ul>
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* </li>
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* <li>Compute the required quantities, being one or more of:
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* <ul>
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* <li>the average PI: {@link #computeAverageLocalOfObservations()};</li>
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* <li>the local PI values for these samples: {@link #computeLocalOfPreviousObservations()}</li>
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* <li>local PI values for a specific set of samples: {@link #computeLocalUsingPreviousObservations(double[])}</li>
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* <li>the distribution of PI values under the null hypothesis
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* of no relationship between past sequences in the series
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* and the next sequence: {@link #computeSignificance(int)} or
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* {@link #computeSignificance(int[][])}.</li>
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* </ul>
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* </li>
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* <li>
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* Return to step 2 or 3 to re-use the calculator on a new data set.
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* </li>
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* </ol>
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*
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* <p><b>References:</b><br/>
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* <ul>
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* <li>Bialek, W., Nemenman, I., and Tishby, N.,
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* <a href="http://dx.doi.org/10.1016/S0378-4371(01)00444-7">
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* "Complexity through nonextensivity"</a>,
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* Physica A, 302, 89-99. (2001).</li>
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* <li>J. P. Crutchfield, D. P. Feldman,
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* <a href="http://dx.doi.org/10.1063/1.1530990">
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* "Regularities Unseen, Randomness Observed: Levels of Entropy Convergence"</a>,
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* Chaos, Vol. 13, No. 1. (2003), pp. 25-54.</li>
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* </ul>
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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 interface PredictiveInfoCalculator
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extends InfoMeasureCalculatorContinuous, EmpiricalNullDistributionComputer {
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/**
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* Property name for embedding length <code>k</code> of
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* the past and future vectors (1 by default).
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*/
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public static final String K_EMBEDDING_PROP_NAME = "k_EMBEDDING";
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/**
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* Alternative property name for embedding length <code>k</code> of
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* the past and future vectors (1 by default);
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* a second option, in order to provide compatibility with
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* {@link ActiveInfoStorageCalculator#K_PROP_NAME}
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*/
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public static final String K_PROP_NAME = "k_HISTORY";
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/**
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* Property name for embedding delay <code>\tau</code> of the vectors
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* (1 by default).
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* The delay exists between points in the k-vectors
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* but there is always only one time step between the
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* past k-vector and the next k-vector.
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*/
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public static final String TAU_PROP_NAME = "TAU";
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/**
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* Initialise the calculator for (re-)use, with some parameters
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* supplied here, and existing (or default) values of other parameters
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* to be used.
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*
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* @param k embedding length of past and future vectors
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*/
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public void initialise(int k) throws Exception;
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/**
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* Initialise the calculator for (re-)use, with some parameters
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* supplied here, and existing (or default) values of other parameters
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* to be used.
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*
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* @param k embedding length of past and future vectors
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* @param tau embedding delay of past and future vectors
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*/
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public void initialise(int k, int tau) throws Exception;
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/**
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* Set properties for the underlying calculator implementation.
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* New property values are not guaranteed to take effect until the next call
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* to an initialise method.
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*
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* <p>Property names defined at the interface level, and what their
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* values should represent, include:</p>
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* <ul>
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* <li>{@link #K_PROP_NAME} or {@link #K__EMBEDDING_PROP_NAME} --
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* embedding length <code>k</code> of
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* the past and future vectors</li>
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* <li>{@link #TAU_PROP_NAME} -- embedding delay between each of the
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* <code>k</code> points in the vectors.</li>
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* </ul>
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*
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* <p>Unknown property values are ignored.</p>
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*
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* <p>Note that implementing classes may defined additional properties.</p>
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*
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* @param propertyName name of the property
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* @param propertyValue value of the property
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* @throws Exception for invalid property values
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*/
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@Override
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public void setProperty(String propertyName, String propertyValue) throws Exception;
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/**
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* Sets a single time-series from which to compute the PDF for the PI.
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* Cannot be called in conjunction with other methods for setting/adding
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* observations.
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*
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* @param observations time-series array of (univariate) samples,
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* where the array index is time.
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*/
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public void setObservations(double observations[]) throws Exception;
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/**
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* Signal that we will add in the samples for computing the PDF
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* from several disjoint time-series or trials via calls to
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* {@link #addObservations(double[])} etc.
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*
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*/
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public void startAddObservations();
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/**
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* Add more time-series for the computation of the PDF.
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* The array observations must not be over-written by the user
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* until after finaliseAddObservations() has been called.
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*
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* @param observations time-series array of (univariate) samples,
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* where the array index is time.
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*/
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public void addObservations(double[] observations) throws Exception;
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/**
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* Add more time-series for the computation of the PDF, using
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* only a sub-series of <code>observations</code>.
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* The array observations must not be over-written by the user
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* until after finaliseAddObservations() has been called.
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*
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* @param observations time-series array of (univariate) samples,
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* where the array index is time.
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* @param startTime first time index to extract samples from
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* @param numTimeSteps number of time steps to extract starting from startTime
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*/
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public void addObservations(double[] observations,
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int startTime, int numTimeSteps) throws Exception ;
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/**
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* Signal that the observations are now all added, PDFs can now be constructed.
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*
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* @throws Exception
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*/
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public void finaliseAddObservations() throws Exception;
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/**
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* Sets a single time-series from which to compute the PDF for the AIS,
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* subject to the validity of each sample in that series.
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* Cannot be called in conjunction with other methods for setting/adding
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* observations.
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*
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* @param observations time-series array of (univariate) samples,
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* where the array index is time.
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* @param valid a time series (with indices the same as observations)
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* indicating whether the entry in observations at that index is valid;
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* we only take vectors as samples to add to the observation set where
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* all points in the time series (even between points in
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* the embedded k-vector with embedding delays) are valid.
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*/
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public void setObservations(double[] observations,
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boolean[] valid) throws Exception;
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/**
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* Compute the local PI values for each of the
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* previously-supplied samples.
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*
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* <p>PDFs are computed using all of the previously supplied
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* observations.</p>
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*
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* <p>If the samples were supplied via a single call such as
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* {@link #setObservations(double[])},
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* then the return value is a single time-series of local
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* PI values corresponding to these samples (with the first, and last,
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* <code>(k-1)*tau + 1</code>
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* values set to 0 since PI is undefined there).</p>
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*
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* <p>Otherwise where disjoint time-series observations were supplied using several
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* calls such as {@link addObservations(double[])}
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* then the local values for each disjoint observation set will be appended here
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* to create a single "time-series" return array (without any <code>(k-1)*tau + 1</code>
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* leading or lagging 0 values).</p>
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*
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* @return the "time-series" of local AIS values.
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*/
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public double[] computeLocalOfPreviousObservations() throws Exception;
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/**
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* Compute the local PI values for each of the
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* supplied samples in <code>newObservations</code>.
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*
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* <p>PDFs are computed using all of the previously supplied
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* observations, but not those in <code>newObservations</code> (unless they were
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* some of the previously supplied samples).</p>
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*
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* @param newObservations time-series for which to compute local PI values
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* @return time-series of local PI values corresponding to newObservations
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* (the first, and last, <code>(k-1)*tau + 1</code>
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* values are set to 0 since PI is undefined there)
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* @throws Exception for an invalid input array, e.g. of length
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* less than <code>2*k</code>
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*/
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public double[] computeLocalUsingPreviousObservations(double[] newObservations) throws Exception;
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}
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