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jidt/java/source/infodynamics/measures/continuous/PredictiveInfoCalculator.java

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/*
* Java Information Dynamics Toolkit (JIDT)
* Copyright (C) 2012, Joseph T. Lizier
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU 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 General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
package infodynamics.measures.continuous;
import infodynamics.utils.EmpiricalMeasurementDistribution;
/**
* Interface for implementations of
* Predictive Information / Excess Entropy estimators on
* continuous univariate data (ie double[] arrays).
*
* <p>See definition of Predictive Information (PI) / Excess Entropy in the citations below.
* Basically, PI is the mutual information between the past <i>state</i>
* of a time-series process <i>X</i> and its future <i>state</i>.
* The past <i>state</i> at time <code>n</code>
* is represented by an embedding vector of <code>k</code> values from <code>X_n</code> backwards,
* each separated by <code>\tau</code> steps, giving
* <code><b>X^k_n</b> = [ X_{n-(k-1)\tau}, ... , X_{n-\tau}, X_n]</code>.
* The future <i>state</i> from time <code>n+1</code>
* is represented by an embedding vector of <code>k</code> values from <code>X_{n+1}</code> forwards,
* each separated by <code>\tau</code> steps, giving
* <code><b>X^{k+}_{n+1}</b> = [ X_{n+1}, X_{n+1+\tau}, ... , X_{n+1+(k-1)\tau}]</code>.
* We call <code>k</code> the embedding dimension, and <code>\tau</code>
* the embedding delay.
* PI is then the mutual information between <b>X^k_n</b> and <b>X^{k+}_{n+1}</b>.</p>
*
* <p>
* Usage of the child classes implementing this interface is intended to follow this paradigm:
* </p>
* <ol>
* <li>Construct the calculator;</li>
* <li>Set properties using {@link #setProperty(String, String)};</li>
* <li>Initialise the calculator using {@link #initialise()} or
* {@link #initialise(int)} or {@link #initialise(int, int)};
* </li>
* <li>Provide the observations/samples for the calculator
* to set up the PDFs, using:
* <ul>
* <li>{@link #setObservations(double[])} or
* {@link #setObservations(double[], boolean[])} for calculations
* based on single time-series, OR</li>
* <li>The following sequence:<ol>
* <li>{@link #startAddObservations()}, then</li>
* <li>One or more calls to {@link #addObservations(double[])} or
* {@link #addObservations(double[], int, int)}, then</li>
* <li>{@link #finaliseAddObservations()};</li>
* </ol></li>
* </ul>
* </li>
* <li>Compute the required quantities, being one or more of:
* <ul>
* <li>the average PI: {@link #computeAverageLocalOfObservations()};</li>
* <li>the local PI values for these samples: {@link #computeLocalOfPreviousObservations()}</li>
* <li>local PI values for a specific set of samples: {@link #computeLocalUsingPreviousObservations(double[])}</li>
* <li>the distribution of PI values under the null hypothesis
* of no relationship between past sequences in the series
* and the next sequence: {@link #computeSignificance(int)} or
* {@link #computeSignificance(int[][])}.</li>
* </ul>
* </li>
* <li>
* Return to step 2 or 3 to re-use the calculator on a new data set.
* </li>
* </ol>
*
* <p><b>References:</b><br/>
* <ul>
* <li>Bialek, W., Nemenman, I., and Tishby, N.,
* <a href="http://dx.doi.org/10.1016/S0378-4371(01)00444-7">
* "Complexity through nonextensivity"</a>,
* Physica A, 302, 89-99. (2001).</li>
* <li>J. P. Crutchfield, D. P. Feldman,
* <a href="http://dx.doi.org/10.1063/1.1530990">
* "Regularities Unseen, Randomness Observed: Levels of Entropy Convergence"</a>,
* Chaos, Vol. 13, No. 1. (2003), pp. 25-54.</li>
* </ul>
*
* @author Joseph Lizier (<a href="joseph.lizier at gmail.com">email</a>,
* <a href="http://lizier.me/joseph/">www</a>)
*/
public interface PredictiveInfoCalculator {
/**
* Property name for embedding length <code>k</code> of
* the past and future vectors (1 by default).
*/
public static final String K_EMBEDDING_PROP_NAME = "k_EMBEDDING";
/**
* Alternative property name for embedding length <code>k</code> of
* the past and future vectors (1 by default);
* a second option, in order to provide compatibility with
* {@link ActiveInfoStorageCalculator#K_PROP_NAME}
*/
public static final String K_PROP_NAME = "k_HISTORY";
/**
* Property name for embedding delay <code>\tau</code> of the vectors
* (1 by default).
* The delay exists between points in the k-vectors
* but there is always only one time step between the
* past k-vector and the next k-vector.
*/
public static final String TAU_PROP_NAME = "TAU";
/**
* Initialise the calculator for (re-)use, with the existing (or default) values of parameters
* Clears any PDFs of previously supplied observations.
*
*/
public void initialise() throws Exception;
/**
* Initialise the calculator for (re-)use, with some parameters
* supplied here, and existing (or default) values of other parameters
* to be used.
*
* @param k embedding length of past and future vectors
*/
public void initialise(int k) throws Exception;
/**
* Initialise the calculator for (re-)use, with some parameters
* supplied here, and existing (or default) values of other parameters
* to be used.
*
* @param k embedding length of past and future vectors
* @param tau embedding delay of past and future vectors
*/
public void initialise(int k, int tau) throws Exception;
/**
* Set properties for the underlying calculator implementation.
* New property values are not guaranteed to take effect until the next call
* to an initialise method.
*
* <p>Property names defined at the interface level, and what their
* values should represent, include:</p>
* <ul>
* <li>{@link #K_PROP_NAME} or {@link #K__EMBEDDING_PROP_NAME} --
* embedding length <code>k</code> of
* the past and future vectors</li>
* <li>{@link #TAU_PROP_NAME} -- embedding delay between each of the
* <code>k</code> points in the vectors.</li>
* </ul>
*
* <p>Unknown property values are ignored.</p>
*
* <p>Note that implementing classes may defined additional properties.</p>
*
* @param propertyName name of the property
* @param propertyValue value of the property
* @throws Exception for invalid property values
*/
public void setProperty(String propertyName, String propertyValue) throws Exception;
/**
* Sets a single time-series from which to compute the PDF for the PI.
* Cannot be called in conjunction with other methods for setting/adding
* observations.
*
* @param observations time-series array of (univariate) samples,
* where the array index is time.
*/
public void setObservations(double observations[]) throws Exception;
/**
* Signal that we will add in the samples for computing the PDF
* from several disjoint time-series or trials via calls to
* {@link #addObservations(double[])} etc.
*
*/
public void startAddObservations();
/**
* Add more time-series for the computation of the PDF.
* The array observations must not be over-written by the user
* until after finaliseAddObservations() has been called.
*
* @param observations time-series array of (univariate) samples,
* where the array index is time.
*/
public void addObservations(double[] observations) throws Exception;
/**
* Add more time-series for the computation of the PDF, using
* only a sub-series of <code>observations</code>.
* The array observations must not be over-written by the user
* until after finaliseAddObservations() has been called.
*
* @param observations time-series array of (univariate) samples,
* where the array index is time.
* @param startTime first time index to extract samples from
* @param numTimeSteps number of time steps to extract starting from startTime
*/
public void addObservations(double[] observations,
int startTime, int numTimeSteps) throws Exception ;
/**
* Signal that the observations are now all added, PDFs can now be constructed.
*
* @throws Exception
*/
public void finaliseAddObservations() throws Exception;
/**
* Sets a single time-series from which to compute the PDF for the AIS,
* subject to the validity of each sample in that series.
* Cannot be called in conjunction with other methods for setting/adding
* observations.
*
* @param observations time-series array of (univariate) samples,
* where the array index is time.
* @param valid a time series (with indices the same as observations)
* indicating whether the entry in observations at that index is valid;
* we only take vectors as samples to add to the observation set where
* all points in the time series (even between points in
* the embedded k-vector with embedding delays) are valid.
*/
public void setObservations(double[] observations,
boolean[] valid) throws Exception;
/**
* Compute the PI from the previously-supplied samples.
*
* @return the PI estimate
*/
public double computeAverageLocalOfObservations() throws Exception;
/**
* Compute the local PI values for each of the
* previously-supplied samples.
*
* <p>PDFs are computed using all of the previously supplied
* observations.</p>
*
* <p>If the samples were supplied via a single call such as
* {@link #setObservations(double[])},
* then the return value is a single time-series of local
* PI values corresponding to these samples (with the first, and last,
* <code>(k-1)*tau + 1</code>
* values set to 0 since PI is undefined there).</p>
*
* <p>Otherwise where disjoint time-series observations were supplied using several
* calls such as {@link addObservations(double[])}
* then the local values for each disjoint observation set will be appended here
* to create a single "time-series" return array (without any <code>(k-1)*tau + 1</code>
* leading or lagging 0 values).</p>
*
* @return the "time-series" of local AIS values.
*/
public double[] computeLocalOfPreviousObservations() throws Exception;
/**
* Compute the local PI values for each of the
* supplied samples in <code>newObservations</code>.
*
* <p>PDFs are computed using all of the previously supplied
* observations, but not those in <code>newObservations</code> (unless they were
* some of the previously supplied samples).</p>
*
* @param newObservations time-series for which to compute local PI values
* @return time-series of local PI values corresponding to newObservations
* (the first, and last, <code>(k-1)*tau + 1</code>
* values are set to 0 since PI is undefined there)
* @throws Exception for an invalid input array, e.g. of length
* less than <code>2*k</code>
*/
public double[] computeLocalUsingPreviousObservations(double[] newObservations) throws Exception;
/**
* Generate a bootstrapped distribution of what the PI would look like,
* under a null hypothesis that the previous <code>k</code> values of our
* samples had no relation to the next <code>k</code> values in the time-series.
*
* <p>See Section II.E "Statistical significance testing" of
* the JIDT paper below for a description of how this is done for PI
* as a mutual information. Basically, the marginal PDFs
* of the past <code>k</code> values, and that of the next <code>k</code> values,
* are preserved, while their joint PDF is destroyed, and the
* distribution of PI under these conditions is generated.</p>
*
* <p>Note that if several disjoint time-series have been added
* as observations using {@link #addObservations(double[])} etc.,
* then these separate "trials" will be mixed up in the generation
* of surrogates here.</p>
*
* <p>This method (in contrast to {@link #computeSignificance(int[][])})
* creates <i>random</i> shufflings of the next vectors for the surrogate PI
* calculations.</p>
*
* @param numPermutationsToCheck number of surrogate samples to bootstrap
* to generate the distribution.
* @return the distribution of PI scores under this null hypothesis.
* @see "J.T. Lizier, 'JIDT: An information-theoretic
* toolkit for studying the dynamics of complex systems', 2014."
* @throws Exception
*/
public EmpiricalMeasurementDistribution computeSignificance(int numPermutationsToCheck) throws Exception;
/**
* Generate a bootstrapped distribution of what the PI would look like,
* under a null hypothesis that the previous <code>k</code> values of our
* samples had no relation to the next <code>k</code> values in the time-series.
*
* <p>See Section II.E "Statistical significance testing" of
* the JIDT paper below for a description of how this is done for PI
* as a mutual information. Basically, the marginal PDFs
* of the past <code>k</code> values, and that of the next <code>k</code> values,
* are preserved, while their joint PDF is destroyed, and the
* distribution of PI under these conditions is generated.</p>
*
* <p>Note that if several disjoint time-series have been added
* as observations using {@link #addObservations(double[])} etc.,
* then these separate "trials" will be mixed up in the generation
* of surrogates here.</p>
*
* <p>This method (in contrast to {@link #computeSignificance(int)})
* allows the user to specify how to construct the surrogates,
* such that repeatable results may be obtained.</p>
*
* @param newOrderings a specification of how to shuffle the next <code>k</code> values vectors
* to create the surrogates to generate the distribution with. The first
* index is the permutation number (i.e. newOrderings.length is the number
* of surrogate samples we use to bootstrap to generate the distribution here.)
* Each array newOrderings[i] should be an array of length L being
* the value returned by {@link #getNumObservations()},
* containing a permutation of the values in 0..(L-1).
* @return the distribution of PI scores under this null hypothesis.
* @see "J.T. Lizier, 'JIDT: An information-theoretic
* toolkit for studying the dynamics of complex systems', 2014."
* @throws Exception where the length of each permutation in newOrderings
* is not equal to the number L observations that were previously supplied.
*/
public EmpiricalMeasurementDistribution computeSignificance(
int[][] newOrderings) throws Exception;
/**
* Set or clear debug mode for extra debug printing to stdout
*
* @param debug new setting for debug mode (on/off)
*/
public void setDebug(boolean debug);
/**
* Return the PI last calculated in a call to {@link #computeAverageLocalOfObservations()}
* or {@link #computeLocalOfPreviousObservations()} after the previous
* {@link #initialise()} call.
*
* @return the last computed PI value
*/
public double getLastAverage();
/**
* Get the number of samples to be used for the PDFs here
* which have been supplied by calls to
* {@link #setObservations(double[])}, {@link #addObservations(double[])}
* etc.
*
* <p>Note that the number of samples is not equal to the length of time-series
* supplied (since we need to accumulate the first and last
* <code>(k-1)*tau + 1</code>
* values of each time-series).
* </p>
*
* @return the number of samples to be used for the PDFs
* @throws Exception
*/
public int getNumObservations() throws Exception;
}
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