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Added KSG implementation of various multivariate IT measures and unit tests.

This commit is contained in:
Pedro Mediano 2021-01-25 12:41:01 +00:00
parent a58a01fbfd
commit bc8c233e68
7 changed files with 1240 additions and 0 deletions
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132
java/source/infodynamics/measures/continuous/kraskov/DualTotalCorrelationCalculatorKraskov.java Executable file
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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.kraskov;
import infodynamics.utils.EuclideanUtils;
import infodynamics.utils.NeighbourNodeData;
import infodynamics.utils.KdTree;
import infodynamics.utils.MathsUtils;
import infodynamics.utils.MatrixUtils;
import java.util.PriorityQueue;
import java.util.Calendar;
import java.util.Random;
/**
* <p>Computes the differential dual total correlation of a given multivariate
* set of observations, using Kraskov-Stoegbauer-Grassberger (KSG) estimation
* (see Kraskov et al., below).</p>
*
* <p>Usage is as per the paradigm outlined for
* {@link MultiVariateInfoMeasureCalculatorCommon}.</p>
*
* <p>Finally, note that {@link Cloneable} is implemented allowing clone()
* to produce only an automatic shallow copy, which is fine
* for the statistical significance calculation it is intended for
* (none of the array
* data will be changed there).
* </p>
*
* <p><b>References:</b><br/>
* <ul>
* <li>Rosas, F., Mediano, P., Gastpar, M, Jensen, H.,
* <a href="http://dx.doi.org/10.1103/PhysRevE.100.032305">"Quantifying high-order
* interdependencies via multivariate extensions of the mutual information"</a>,
* Physical Review E 100, (2019) 032305.</li>
*
* <li>Kraskov, A., Stoegbauer, H., Grassberger, P.,
* <a href="http://dx.doi.org/10.1103/PhysRevE.69.066138">"Estimating mutual information"</a>,
* Physical Review E 69, (2004) 066138.</li>
* </ul>
*
* @author Pedro A.M. Mediano (<a href="pmediano at pm.me">email</a>,
* <a href="http://www.doc.ic.ac.uk/~pam213">www</a>)
*/
public class DualTotalCorrelationCalculatorKraskov
extends MultiVariateInfoMeasureCalculatorKraskov
implements Cloneable { // See comments on clonability above
protected double[] partialComputeFromObservations(
int startTimePoint, int numTimePoints, boolean returnLocals) throws Exception {
double startTime = Calendar.getInstance().getTimeInMillis();
double[] localMi = null;
if (returnLocals) {
localMi = new double[numTimePoints];
}
// Constants:
double dimensionsMinus1TimesDiGammaN = (double) (dimensions - 1) * digammaN;
// Count the average number of points within eps_x for each marginal x of each point
double totalSumF = 0.0;
for (int t = startTimePoint; t < startTimePoint + numTimePoints; t++) {
// Compute eps for this time step by
// finding the kth closest neighbour for point t:
PriorityQueue<NeighbourNodeData> nnPQ =
kdTreeJoint.findKNearestNeighbours(k, t, dynCorrExclTime);
// First element in the PQ is the kth NN,
// and epsilon = kthNnData.distance
NeighbourNodeData kthNnData = nnPQ.poll();
// Distance to kth neighbour in joint space
double eps = kthNnData.distance;
double sumF = 0.0;
sumF += (digammaK - digammaN);
for (int d = 0; d < dimensions; d++) {
int n = rangeSearchersInBigMarginals[d].countPointsStrictlyWithinR(
t, eps, dynCorrExclTime);
sumF -= (MathsUtils.digamma(n + 1) - digammaN)/(dimensions - 1);
}
sumF *= (dimensions - 1);
totalSumF += sumF;
if (returnLocals) {
localMi[t-startTimePoint] = sumF;
}
}
if (debug) {
Calendar rightNow2 = Calendar.getInstance();
long endTime = rightNow2.getTimeInMillis();
System.out.println("Subset " + startTimePoint + ":" +
(startTimePoint + numTimePoints) + " Calculation time: " +
((endTime - startTime)/1000.0) + " sec" );
}
// Select what to return:
if (returnLocals) {
return localMi;
} else {
double[] returnArray = new double[] {totalSumF/((double) totalObservations)};
return returnArray;
}
}
}

538
java/source/infodynamics/measures/continuous/kraskov/MultiVariateInfoMeasureCalculatorKraskov.java Executable file
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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.kraskov;
import infodynamics.measures.continuous.MultiVariateInfoMeasureCalculatorCommon;
import infodynamics.utils.EuclideanUtils;
import infodynamics.utils.NeighbourNodeData;
import infodynamics.utils.KdTree;
import infodynamics.utils.UnivariateNearestNeighbourSearcher;
import infodynamics.utils.MathsUtils;
import infodynamics.utils.MatrixUtils;
import java.util.PriorityQueue;
import java.util.Calendar;
import java.util.Random;
/**
* <p>Base class with common functionality for child class implementations of
* multivariate information measures on a given multivariate
* <code>double[][]</code> set of
* observations (extending {@link MultiVariateInfoMeasureCalculatorCommon}),
* using Kraskov-Stoegbauer-Grassberger (KSG) estimation
* (see Kraskov et al., below).</p>
*
* <p>Usage is as per the paradigm outlined for {@link MultiVariateInfoMeasureCalculatorCommon},
* with:
* <ul>
* <li>For constructors see the child classes.</li>
* <li>Further properties are defined in {@link #setProperty(String, String)}.</li>
* <li>Computed values are in <b>nats</b>, not bits!</li>
* </ul>
* </p>
*
* <p>Finally, note that {@link Cloneable} is implemented allowing clone()
* to produce only an automatic shallow copy, which is fine
* for the statistical significance calculation it is intended for
* (none of the array data will be changed there).
* </p>
*
* <p><b>References:</b><br/>
* <ul>
* <li>Rosas, F., Mediano, P., Gastpar, M, Jensen, H.,
* <a href="http://dx.doi.org/10.1103/PhysRevE.100.032305">"Quantifying high-order
* interdependencies via multivariate extensions of the mutual information"</a>,
* Physical Review E 100, (2019) 032305.</li>
*
* <li>Kraskov, A., Stoegbauer, H., Grassberger, P.,
* <a href="http://dx.doi.org/10.1103/PhysRevE.69.066138">"Estimating mutual information"</a>,
* Physical Review E 69, (2004) 066138.</li>
* </ul>
* @author Pedro A.M. Mediano (<a href="pmediano at pm.me">email</a>,
* <a href="http://www.doc.ic.ac.uk/~pam213">www</a>)
*/
public abstract class MultiVariateInfoMeasureCalculatorKraskov
extends MultiVariateInfoMeasureCalculatorCommon
implements Cloneable { // See comments on clonability above
/**
* we compute distances to the kth nearest neighbour
*/
protected int k = 4;
/**
* The norm type in use (see {@link #PROP_NORM_TYPE})
*/
protected int normType = EuclideanUtils.NORM_MAX_NORM;
/**
* Property name for the number of K nearest neighbours used in
* the KSG algorithm (default 4).
*/
public final static String PROP_K = "k";
/**
* Property name for what type of norm to use between data points
* for each marginal variable -- Options are defined by
* {@link KdTree#setNormType(String)} and the
* default is {@link EuclideanUtils#NORM_MAX_NORM}.
*/
public final static String PROP_NORM_TYPE = "NORM_TYPE";
/**
* Property name for an amount of random Gaussian noise to be
* added to the data (default 1e-8 to match the noise order in MILCA toolkit.).
*/
public static final String PROP_ADD_NOISE = "NOISE_LEVEL_TO_ADD";
/**
* Property name for a dynamics exclusion time window
* otherwise known as Theiler window (see Kantz and Schreiber).
* Default is 0 which means no dynamic exclusion window.
*/
public static final String PROP_DYN_CORR_EXCL_TIME = "DYN_CORR_EXCL";
/**
* Property name for the number of parallel threads to use in the
* computation (default is to use all available)
*/
public static final String PROP_NUM_THREADS = "NUM_THREADS";
/**
* Valid property value for {@link #PROP_NUM_THREADS} to indicate
* that all available processors should be used.
*/
public static final String USE_ALL_THREADS = "USE_ALL";
/**
* Whether to add an amount of random noise to the incoming data
*/
protected boolean addNoise = true;
/**
* Amount of random Gaussian noise to add to the incoming data
*/
protected double noiseLevel = (double) 1e-8;
/**
* Whether we use dynamic correlation exclusion
*/
protected boolean dynCorrExcl = false;
/**
* Size of dynamic correlation exclusion window.
*/
protected int dynCorrExclTime = 0;
/**
* Number of parallel threads to use in the computation;
* defaults to use all available.
*/
protected int numThreads = Runtime.getRuntime().availableProcessors();
/**
* Protected k-d tree data structure (for fast nearest neighbour searches)
* representing the joint space
*/
protected KdTree kdTreeJoint;
// /**
// * protected data structures (for fast nearest neighbour searches)
// * representing the marginal spaces
// */
// protected KdTree[] rangeSearchersInMarginals;
/**
* Protected data structures (for fast nearest neighbour searches)
* representing the marginal spaces of each individual variable
*/
protected UnivariateNearestNeighbourSearcher[] rangeSearchersInSmallMarginals;
/**
* Protected data structures (for fast nearest neighbour searches)
* representing the marginal spaces of each set of (D-1) variables
*/
protected KdTree[] rangeSearchersInBigMarginals;
/**
* Constant for digamma(k), with k the number of nearest neighbours selected
*/
protected double digammaK;
/**
* Constant for digamma(N), with N the number of samples.
*/
protected double digammaN;
public void initialise(int dimensions) {
this.dimensions = dimensions;
lastAverage = 0.0;
totalObservations = 0;
isComputed = false;
observations = null;
kdTreeJoint = null;
rangeSearchersInSmallMarginals = null;
rangeSearchersInBigMarginals = null;
}
/**
* Sets properties for the KSG multivariate measure calculator.
* New property values are not guaranteed to take effect until the next call
* to an initialise method.
*
* <p>Valid property names, and what their
* values should represent, include:</p>
* <ul>
* <li>{@link #PROP_K} -- number of k nearest neighbours to use in joint kernel space
* in the KSG algorithm (default is 4).</li>
* <li>{@link #PROP_NORM_TYPE} -- normalization type to apply to
* working out the norms between the points in each marginal space.
* Options are defined by {@link KdTree#setNormType(String)} -
* default is {@link EuclideanUtils#NORM_MAX_NORM}.</li>
* <li>{@link #PROP_DYN_CORR_EXCL_TIME} -- a dynamics exclusion time window,
* also known as Theiler window (see Kantz and Schreiber);
* default is 0 which means no dynamic exclusion window.</li>
* <li>{@link #PROP_ADD_NOISE} -- a standard deviation for an amount of
* random Gaussian noise to add to
* each variable, to avoid having neighbourhoods with artificially
* large counts. (We also accept "false" to indicate "0".)
* The amount is added in after any normalisation,
* so can be considered as a number of standard deviations of the data.
* (Recommended by Kraskov. MILCA uses 1e-8; but adds in
* a random amount of noise in [0,noiseLevel) ).
* Default 1e-8 to match the noise order in MILCA toolkit..</li>
* </ul>
*
* <p>Unknown property values are ignored.</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 {
boolean propertySet = true;
if (propertyName.equalsIgnoreCase(PROP_K)) {
k = Integer.parseInt(propertyValue);
} else if (propertyName.equalsIgnoreCase(PROP_NORM_TYPE)) {
normType = KdTree.validateNormType(propertyValue);
} else if (propertyName.equalsIgnoreCase(PROP_DYN_CORR_EXCL_TIME)) {
dynCorrExclTime = Integer.parseInt(propertyValue);
dynCorrExcl = (dynCorrExclTime > 0);
} else if (propertyName.equalsIgnoreCase(PROP_ADD_NOISE)) {
if (propertyValue.equals("0") ||
propertyValue.equalsIgnoreCase("false")) {
addNoise = false;
noiseLevel = 0;
} else {
addNoise = true;
noiseLevel = Double.parseDouble(propertyValue);
}
} else if (propertyName.equalsIgnoreCase(PROP_NUM_THREADS)) {
if (propertyValue.equalsIgnoreCase(USE_ALL_THREADS)) {
numThreads = Runtime.getRuntime().availableProcessors();
} else { // otherwise the user has passed in an integer:
numThreads = Integer.parseInt(propertyValue);
}
} else {
// No property was set here
propertySet = false;
// try the superclass:
super.setProperty(propertyName, propertyValue);
}
if (debug && propertySet) {
System.out.println(this.getClass().getSimpleName() + ": Set property " + propertyName +
" to " + propertyValue);
}
}
@Override
public void finaliseAddObservations() throws Exception {
super.finaliseAddObservations();
if ((observations == null) || (observations[0].length == 0)) {
throw new Exception("Computing measure with a null set of data");
}
if (observations.length <= k + 2*dynCorrExclTime) {
throw new Exception("There are less observations provided (" +
observations.length +
") than required for the number of nearest neighbours parameter (" +
k + ") and any dynamic correlation exclusion (" + dynCorrExclTime + ")");
}
// Normalise the data if required
if (normalise) {
// We can overwrite these since they're already
// a copy of the users' data.
MatrixUtils.normalise(observations);
}
// Add small random noise if required
if (addNoise) {
Random random = new Random();
// Add Gaussian noise of std dev noiseLevel to the data
for (int r = 0; r < observations.length; r++) {
for (int c = 0; c < dimensions; c++) {
observations[r][c] += random.nextGaussian()*noiseLevel;
}
}
}
// Set the constants:
digammaK = MathsUtils.digamma(k);
digammaN = MathsUtils.digamma(totalObservations);
}
/**
* Internal method to ensure that the Kd-tree data structures to represent the
* observational data have been constructed (should be called prior to attempting
* to use these data structures)
*/
protected void ensureKdTreesConstructed() throws Exception {
// We need to construct the k-d trees for use by the child
// classes. We check each tree for existence separately
// since source can be used across original and surrogate data
// TODO can parallelise these -- best done within the kdTree --
// though it's unclear if there's much point given that
// the tree construction itself afterwards can't really be well parallelised.
if (kdTreeJoint == null) {
kdTreeJoint = new KdTree(observations);
kdTreeJoint.setNormType(normType);
}
if (rangeSearchersInSmallMarginals == null) {
rangeSearchersInSmallMarginals = new UnivariateNearestNeighbourSearcher[dimensions];
for (int d = 0; d < dimensions; d++) {
rangeSearchersInSmallMarginals[d] = new UnivariateNearestNeighbourSearcher(
MatrixUtils.selectColumn(observations, d));
rangeSearchersInSmallMarginals[d].setNormType(normType);
}
}
if (rangeSearchersInBigMarginals == null) {
rangeSearchersInBigMarginals = new KdTree[dimensions];
for (int d = 0; d < dimensions; d++) {
rangeSearchersInBigMarginals[d] = new KdTree(
MatrixUtils.selectColumns(observations, allExcept(d, dimensions)));
rangeSearchersInBigMarginals[d].setNormType(normType);
}
}
}
/**
* {@inheritDoc}
*
* @return the average measure in nats (not bits!)
*/
public double computeAverageLocalOfObservations() throws Exception {
// Compute the measure
double startTime = Calendar.getInstance().getTimeInMillis();
lastAverage = computeFromObservations(false)[0];
isComputed = true;
if (debug) {
Calendar rightNow2 = Calendar.getInstance();
long endTime = rightNow2.getTimeInMillis();
System.out.println("Calculation time: " + ((endTime - startTime)/1000.0) + " sec" );
}
return lastAverage;
}
/**
* {@inheritDoc}
*
* @return the "time-series" of local measure values in nats (not bits!)
* @throws Exception
*/
public double[] computeLocalOfPreviousObservations() throws Exception {
double[] localValues = computeFromObservations(true);
lastAverage = MatrixUtils.mean(localValues);
isComputed = true;
return localValues;
}
/**
* This method, specified in {@link MultiVariateInfoMeasureCalculatorCommon}
* is not implemented yet here.
*/
public double[] computeLocalUsingPreviousObservations(double[][] states) throws Exception {
// TODO If this is implemented, will need to normalise the incoming
// observations the same way that previously supplied ones were
// normalised (if they were normalised, that is)
throw new Exception("Local method not implemented yet");
}
/**
* This protected method handles the multiple threads which
* computes either the average or local measure (over parts of the total
* observations), computing the
* distances between all tuples in time.
*
* <p>The method returns:<ol>
* <li>for (returnLocals == false), an array of size 1,
* containing the average measure </li>
* <li>for (returnLocals == true), the array of local
* measure values</li>
* </ol>
*
* @param returnLocals whether to return an array or local values, or else
* sums of these values
* @return either the average measure, or array of local measure value,
* in nats not bits
* @throws Exception
*/
protected double[] computeFromObservations(boolean returnLocals) throws Exception {
double[] returnValues = null;
ensureKdTreesConstructed();
if (numThreads == 1) {
// Single-threaded implementation:
returnValues = partialComputeFromObservations(0, totalObservations, returnLocals);
} else {
// We're going multithreaded:
if (returnLocals) {
// We're computing locals
returnValues = new double[totalObservations];
} else {
// We're computing average
returnValues = new double[1];
}
// Distribute the observations to the threads for the parallel processing
int lTimesteps = totalObservations / numThreads; // each thread gets the same amount of data
int res = totalObservations % numThreads; // the first thread gets the residual data
if (debug) {
System.out.printf("Computing Kraskov Multi-Info with %d threads (%d timesteps each, plus %d residual)\n",
numThreads, lTimesteps, res);
}
Thread[] tCalculators = new Thread[numThreads];
KraskovThreadRunner[] runners = new KraskovThreadRunner[numThreads];
for (int t = 0; t < numThreads; t++) {
int startTime = (t == 0) ? 0 : lTimesteps * t + res;
int numTimesteps = (t == 0) ? lTimesteps + res : lTimesteps;
if (debug) {
System.out.println(t + ".Thread: from " + startTime +
" to " + (startTime + numTimesteps)); // Trace Message
}
runners[t] = new KraskovThreadRunner(this, startTime, numTimesteps, returnLocals);
tCalculators[t] = new Thread(runners[t]);
tCalculators[t].start();
}
// Here, we should wait for the termination of the all threads
// and collect their results
for (int t = 0; t < numThreads; t++) {
if (tCalculators[t] != null) { // TODO Ipek: can you comment on why we're checking for null here?
tCalculators[t].join();
}
// Now we add in the data from this completed thread:
if (returnLocals) {
// We're computing local measure; copy these local values
// into the full array of locals
System.arraycopy(runners[t].getReturnValues(), 0,
returnValues, runners[t].myStartTimePoint, runners[t].numberOfTimePoints);
} else {
// We're computing the average measure, keep the running sums of digammas and counts
MatrixUtils.addInPlace(returnValues, runners[t].getReturnValues());
}
}
}
return returnValues;
}
/**
* Protected method to be used internally for threaded implementations. This
* method implements the guts of each Kraskov algorithm, computing the number
* of nearest neighbours in each dimension for a sub-set of the data points.
* It is intended to be called by one thread to work on that specific sub-set
* of the data.
*
* <p>Child classes should implement the computation of any specific measure
* using this method.</p>
*
* <p>The method returns:<ol>
* <li>for average measures (returnLocals == false), the relevant sums of
* digamma(n_x+1) in each marginal
* for a partial set of the observations</li>
* <li>for local measures (returnLocals == true), the array of local values</li>
* </ol>
*
* @param startTimePoint start time for the partial set we examine
* @param numTimePoints number of time points (including startTimePoint to examine)
* @param returnLocals whether to return an array or local values, or else
* sums of these values
* @return an array of sum of digamma(n_x+1) for each marginal x, then
* sum of n_x for each marginal x (these latter ones are for debugging purposes).
* @throws Exception
*/
protected abstract double[] partialComputeFromObservations(
int startTimePoint, int numTimePoints, boolean returnLocals) throws Exception;
/**
* Private class to handle multi-threading of the Kraskov algorithms.
* Each instance calls partialComputeFromObservations()
* to compute nearest neighbours for a part of the data.
*
*
* @author Joseph Lizier (<a href="joseph.lizier at gmail.com">email</a>,
* <a href="http://lizier.me/joseph/">www</a>)
* @author Ipek Özdemir
*/
private class KraskovThreadRunner implements Runnable {
protected MultiVariateInfoMeasureCalculatorKraskov calc;
protected int myStartTimePoint;
protected int numberOfTimePoints;
protected boolean computeLocals;
protected double[] returnValues = null;
protected Exception problem = null;
public static final int INDEX_SUM_DIGAMMAS = 0;
public KraskovThreadRunner(
MultiVariateInfoMeasureCalculatorKraskov calc,
int myStartTimePoint, int numberOfTimePoints,
boolean computeLocals) {
this.calc = calc;
this.myStartTimePoint = myStartTimePoint;
this.numberOfTimePoints = numberOfTimePoints;
this.computeLocals = computeLocals;
}
/**
* Return the values from this part of the data,
* or throw any exception that was encountered by the
* thread.
*
* @return an exception previously encountered by this thread.
* @throws Exception
*/
public double[] getReturnValues() throws Exception {
if (problem != null) {
throw problem;
}
return returnValues;
}
/**
* Start the thread for the given parameters
*/
public void run() {
try {
returnValues = calc.partialComputeFromObservations(
myStartTimePoint, numberOfTimePoints, computeLocals);
} catch (Exception e) {
// Store the exception for later retrieval
problem = e;
return;
}
}
}
// end class KraskovThreadRunner
}

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java/source/infodynamics/measures/continuous/kraskov/OInfoCalculatorKraskov.java Executable file
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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.kraskov;
import infodynamics.utils.EuclideanUtils;
import infodynamics.utils.NeighbourNodeData;
import infodynamics.utils.KdTree;
import infodynamics.utils.UnivariateNearestNeighbourSearcher;
import infodynamics.utils.MathsUtils;
import infodynamics.utils.MatrixUtils;
import java.util.PriorityQueue;
import java.util.Calendar;
import java.util.Random;
import java.util.Arrays;
/**
* <p>Computes the differential O-information of a given multivariate
* set of observations, using Kraskov-Stoegbauer-Grassberger (KSG) estimation
* (see Kraskov et al., below).</p>
*
* <p>Usage is as per the paradigm outlined for
* {@link MultiVariateInfoMeasureCalculatorCommon}.</p>
*
* <p>Finally, note that {@link Cloneable} is implemented allowing clone()
* to produce only an automatic shallow copy, which is fine
* for the statistical significance calculation it is intended for
* (none of the array
* data will be changed there).
* </p>
*
* <p><b>References:</b><br/>
* <ul>
* <li>Rosas, F., Mediano, P., Gastpar, M., Jensen, H.,
* "Quantifying high-order effects via multivariate extensions of the
* mutual information".</li>
*
* <li>Kraskov, A., Stoegbauer, H., Grassberger, P.,
* <a href="http://dx.doi.org/10.1103/PhysRevE.69.066138">"Estimating mutual information"</a>,
* Physical Review E 69, (2004) 066138.</li>
* </ul>
*
* @author Pedro A.M. Mediano (<a href="pmediano at pm.me">email</a>,
* <a href="http://www.doc.ic.ac.uk/~pam213">www</a>)
*/
public class OInfoCalculatorKraskov
extends MultiVariateInfoMeasureCalculatorKraskov
implements Cloneable { // See comments on clonability above
protected double[] partialComputeFromObservations(
int startTimePoint, int numTimePoints, boolean returnLocals) throws Exception {
// If data is 2D, return 0 before doing any computation
if (dimensions == 2) {
if (returnLocals) {
double[] localMi = new double[numTimePoints];
Arrays.fill(localMi, 0);
return localMi;
} else {
return new double[] {0};
}
}
double startTime = Calendar.getInstance().getTimeInMillis();
double[] localMi = null;
if (returnLocals) {
localMi = new double[numTimePoints];
}
// Constants:
double dimensionsMinus1TimesDiGammaN = (double) (dimensions - 1) * digammaN;
// Count the average number of points within eps_x for each marginal x of each point
double totalSumF = 0.0;
for (int t = startTimePoint; t < startTimePoint + numTimePoints; t++) {
// Compute eps for this time step by
// finding the kth closest neighbour for point t:
PriorityQueue<NeighbourNodeData> nnPQ =
kdTreeJoint.findKNearestNeighbours(k, t, dynCorrExclTime);
// First element in the PQ is the kth NN,
// and epsilon = kthNnData.distance
NeighbourNodeData kthNnData = nnPQ.poll();
// Distance to kth neighbour in joint space
double eps = kthNnData.distance;
double sumF = 0.0;
sumF += (digammaK - digammaN);
for (int d = 0; d < dimensions; d++) {
int n_small = rangeSearchersInSmallMarginals[d].countPointsStrictlyWithinR(
t, eps, dynCorrExclTime);
int n_big = rangeSearchersInBigMarginals[d].countPointsStrictlyWithinR(
t, eps, dynCorrExclTime);
sumF -= (MathsUtils.digamma(n_big + 1) - digammaN)/(dimensions - 2);
sumF += (MathsUtils.digamma(n_small + 1) - digammaN)/(dimensions - 2);
if (debug) {
// Only tracking this for debugging purposes:
System.out.printf("t=%d, d=%d, n_small=%d, n_big=%d, sumF=%.3f\n",
t, d, n_small, n_big, sumF);
}
}
sumF *= (2 - dimensions);
totalSumF += sumF;
if (returnLocals) {
localMi[t-startTimePoint] = sumF;
}
}
if (debug) {
Calendar rightNow2 = Calendar.getInstance();
long endTime = rightNow2.getTimeInMillis();
System.out.println("Subset " + startTimePoint + ":" +
(startTimePoint + numTimePoints) + " Calculation time: " +
((endTime - startTime)/1000.0) + " sec" );
}
// Select what to return:
if (returnLocals) {
return localMi;
} else {
double[] returnArray = new double[] {totalSumF/((double) totalObservations)};
return returnArray;
}
}
}

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java/source/infodynamics/measures/continuous/kraskov/SInfoCalculatorKraskov.java Executable file
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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.kraskov;
import infodynamics.utils.EuclideanUtils;
import infodynamics.utils.NeighbourNodeData;
import infodynamics.utils.KdTree;
import infodynamics.utils.UnivariateNearestNeighbourSearcher;
import infodynamics.utils.MathsUtils;
import infodynamics.utils.MatrixUtils;
import java.util.PriorityQueue;
import java.util.Calendar;
import java.util.Random;
import java.util.Arrays;
/**
* <p>Computes the differential S-information of a given multivariate
* set of observations, using Kraskov-Stoegbauer-Grassberger (KSG) estimation
* (see Kraskov et al., below).</p>
*
* <p>Usage is as per the paradigm outlined for
* {@link MultiVariateInfoMeasureCalculatorCommon}.</p>
*
* <p>Finally, note that {@link Cloneable} is implemented allowing clone()
* to produce only an automatic shallow copy, which is fine
* for the statistical significance calculation it is intended for
* (none of the array
* data will be changed there).
* </p>
*
* <p><b>References:</b><br/>
* <ul>
* <li>Rosas, F., Mediano, P., Gastpar, M., Jensen, H.,
* "Quantifying high-order effects via multivariate extensions of the
* mutual information".</li>
*
* <li>Kraskov, A., Stoegbauer, H., Grassberger, P.,
* <a href="http://dx.doi.org/10.1103/PhysRevE.69.066138">"Estimating mutual information"</a>,
* Physical Review E 69, (2004) 066138.</li>
* </ul>
*
* @author Pedro A.M. Mediano (<a href="pmediano at pm.me">email</a>,
* <a href="http://www.doc.ic.ac.uk/~pam213">www</a>)
*/
public class SInfoCalculatorKraskov
extends MultiVariateInfoMeasureCalculatorKraskov
implements Cloneable { // See comments on clonability above
protected double[] partialComputeFromObservations(
int startTimePoint, int numTimePoints, boolean returnLocals) throws Exception {
double startTime = Calendar.getInstance().getTimeInMillis();
double[] localMi = null;
if (returnLocals) {
localMi = new double[numTimePoints];
}
// Constants:
double dimensionsMinus1TimesDiGammaN = (double) (dimensions - 1) * digammaN;
// Count the average number of points within eps_x for each marginal x of each point
double totalSumF = 0.0;
for (int t = startTimePoint; t < startTimePoint + numTimePoints; t++) {
// Compute eps for this time step by
// finding the kth closest neighbour for point t:
PriorityQueue<NeighbourNodeData> nnPQ =
kdTreeJoint.findKNearestNeighbours(k, t, dynCorrExclTime);
// First element in the PQ is the kth NN,
// and epsilon = kthNnData.distance
NeighbourNodeData kthNnData = nnPQ.poll();
// Distance to kth neighbour in joint space
double eps = kthNnData.distance;
double sumF = 0.0;
sumF += (digammaK - digammaN);
for (int d = 0; d < dimensions; d++) {
int n_small = rangeSearchersInSmallMarginals[d].countPointsStrictlyWithinR(
t, eps, dynCorrExclTime);
int n_big = rangeSearchersInBigMarginals[d].countPointsStrictlyWithinR(
t, eps, dynCorrExclTime);
sumF -= (MathsUtils.digamma(n_big + 1) - digammaN)/dimensions;
sumF -= (MathsUtils.digamma(n_small + 1) - digammaN)/dimensions;
if (debug) {
// Only tracking this for debugging purposes:
System.out.printf("t=%d, d=%d, n_small=%d, n_big=%d, sumF=%.3f\n",
t, d, n_small, n_big, sumF);
}
}
sumF *= dimensions;
totalSumF += sumF;
if (returnLocals) {
localMi[t-startTimePoint] = sumF;
}
}
if (debug) {
Calendar rightNow2 = Calendar.getInstance();
long endTime = rightNow2.getTimeInMillis();
System.out.println("Subset " + startTimePoint + ":" +
(startTimePoint + numTimePoints) + " Calculation time: " +
((endTime - startTime)/1000.0) + " sec" );
}
// Select what to return:
if (returnLocals) {
return localMi;
} else {
double[] returnArray = new double[] {totalSumF/((double) totalObservations)};
return returnArray;
}
}
}

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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.kraskov;
import infodynamics.measures.continuous.gaussian.DualTotalCorrelationCalculatorGaussian;
import infodynamics.utils.ArrayFileReader;
import infodynamics.utils.MatrixUtils;
import infodynamics.utils.RandomGenerator;
import junit.framework.TestCase;
public class DualTotalCorrelationCalculatorKraskovTester extends TestCase {
/**
* For two variables, DTC is equal to mutual information.
*/
public void testTwoVariables() throws Exception {
double[][] data;
ArrayFileReader afr = new ArrayFileReader("demos/data/2randomCols-1.txt");
data = afr.getDouble2DMatrix();
DualTotalCorrelationCalculatorKraskov dtcCalc = new DualTotalCorrelationCalculatorKraskov();
dtcCalc.setProperty("NOISE_LEVEL_TO_ADD", "0");
dtcCalc.initialise(2);
dtcCalc.setObservations(data);
double dtc = dtcCalc.computeAverageLocalOfObservations();
MutualInfoCalculatorMultiVariateKraskov1 miCalc = new MutualInfoCalculatorMultiVariateKraskov1();
miCalc.setProperty("NOISE_LEVEL_TO_ADD", "0");
miCalc.initialise(1,1);
miCalc.setObservations(MatrixUtils.selectColumn(data, 0),
MatrixUtils.selectColumn(data, 1));
double mi = miCalc.computeAverageLocalOfObservations();
assertEquals(dtc, mi, 1e-6);
}
/**
* Compare against the values obtained by the Gaussian DTC calculator when the data
* is actually Gaussian.
*/
public void testCompareWithGaussian() throws Exception {
int N = 100000, D = 3;
RandomGenerator rg = new RandomGenerator();
rg.setSeed(1);
double[][] data = rg.generateNormalData(N, D, 0, 1);
for (int i = 0; i < N; i++) {
data[i][2] = data[i][2] + 0.1*data[i][0];
data[i][1] = data[i][1] + 0.5*data[i][0];
}
DualTotalCorrelationCalculatorKraskov dtcCalc_ksg = new DualTotalCorrelationCalculatorKraskov();
dtcCalc_ksg.setProperty("NOISE_LEVEL_TO_ADD", "0");
dtcCalc_ksg.initialise(3);
dtcCalc_ksg.setObservations(data);
double dtc_ksg = dtcCalc_ksg.computeAverageLocalOfObservations();
DualTotalCorrelationCalculatorGaussian dtcCalc_gau = new DualTotalCorrelationCalculatorGaussian();
dtcCalc_gau.initialise(3);
dtcCalc_gau.setObservations(data);
double dtc_gau = dtcCalc_gau.computeAverageLocalOfObservations();
assertEquals(dtc_ksg, dtc_gau, 0.001);
}
/**
* Confirm that the local values average correctly back to the average value
*
*/
public void testLocalsAverageCorrectly() throws Exception {
int dimensions = 4;
int timeSteps = 1000;
DualTotalCorrelationCalculatorKraskov dtcCalc = new DualTotalCorrelationCalculatorKraskov();
dtcCalc.initialise(dimensions);
// generate some random data
RandomGenerator rg = new RandomGenerator();
double[][] data = rg.generateNormalData(timeSteps, dimensions,
0, 1);
dtcCalc.setObservations(data);
double dtc = dtcCalc.computeAverageLocalOfObservations();
double[] dtcLocal = dtcCalc.computeLocalOfPreviousObservations();
System.out.printf("Average was %.5f\n", dtc);
assertEquals(dtc, MatrixUtils.mean(dtcLocal), 0.00001);
}
/**
* Confirm that for 2D the local values equal the local MI values
*
*/
public void testLocalsEqualMI() throws Exception {
int dimensions = 2;
int timeSteps = 100;
DualTotalCorrelationCalculatorKraskov dtcCalc = new DualTotalCorrelationCalculatorKraskov();
dtcCalc.initialise(dimensions);
// generate some random data
RandomGenerator rg = new RandomGenerator();
double[][] data = rg.generateNormalData(timeSteps, dimensions,
0, 1);
dtcCalc.setObservations(data);
double[] dtcLocal = dtcCalc.computeLocalOfPreviousObservations();
MutualInfoCalculatorMultiVariateKraskov1 miCalc = new MutualInfoCalculatorMultiVariateKraskov1();
miCalc.initialise(1, 1);
miCalc.setObservations(MatrixUtils.selectColumn(data, 0), MatrixUtils.selectColumn(data, 1));
double[] miLocal = miCalc.computeLocalOfPreviousObservations();
for (int t = 0; t < timeSteps; t++) {
assertEquals(dtcLocal[t], miLocal[t], 0.00001);
}
}
}

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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.kraskov;
import infodynamics.measures.continuous.gaussian.OInfoCalculatorGaussian;
import infodynamics.utils.ArrayFileReader;
import infodynamics.utils.MatrixUtils;
import infodynamics.utils.RandomGenerator;
import junit.framework.TestCase;
public class OInfoCalculatorKraskovTester extends TestCase {
/**
* Compare against the values obtained by the Gaussian O-info calculator when the data
* is actually Gaussian.
*/
public void testCompareWithGaussian() throws Exception {
int N = 100000, D = 3;
RandomGenerator rg = new RandomGenerator();
rg.setSeed(3);
double[][] data = rg.generateNormalData(N, D, 0, 1);
for (int i = 0; i < N; i++) {
data[i][2] = data[i][2] + 0.4*data[i][0];
data[i][1] = data[i][1] + 0.5*data[i][0];
}
OInfoCalculatorKraskov oCalc_ksg = new OInfoCalculatorKraskov();
oCalc_ksg.setProperty("NOISE_LEVEL_TO_ADD", "0");
oCalc_ksg.initialise(3);
oCalc_ksg.setObservations(data);
double o_ksg = oCalc_ksg.computeAverageLocalOfObservations();
OInfoCalculatorGaussian oCalc_gau = new OInfoCalculatorGaussian();
oCalc_gau.initialise(3);
oCalc_gau.setObservations(data);
double o_gau = oCalc_gau.computeAverageLocalOfObservations();
assertEquals(o_ksg, o_gau, 0.001);
}
}

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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.kraskov;
import infodynamics.measures.continuous.gaussian.SInfoCalculatorGaussian;
import infodynamics.utils.ArrayFileReader;
import infodynamics.utils.MatrixUtils;
import infodynamics.utils.RandomGenerator;
import junit.framework.TestCase;
public class SInfoCalculatorKraskovTester extends TestCase {
/**
* Compare against the values obtained by the Gaussian S-info calculator when the data
* is actually Gaussian.
*/
public void testCompareWithGaussian() throws Exception {
int N = 100000, D = 3;
RandomGenerator rg = new RandomGenerator();
rg.setSeed(3);
double[][] data = rg.generateNormalData(N, D, 0, 1);
for (int i = 0; i < N; i++) {
data[i][2] = data[i][2] + 0.4*data[i][0];
data[i][1] = data[i][1] + 0.5*data[i][0];
}
SInfoCalculatorKraskov sCalc_ksg = new SInfoCalculatorKraskov();
sCalc_ksg.setProperty("NOISE_LEVEL_TO_ADD", "0");
sCalc_ksg.initialise(3);
sCalc_ksg.setObservations(data);
double s_ksg = sCalc_ksg.computeAverageLocalOfObservations();
SInfoCalculatorGaussian sCalc_gau = new SInfoCalculatorGaussian();
sCalc_gau.initialise(3);
sCalc_gau.setObservations(data);
double s_gau = sCalc_gau.computeAverageLocalOfObservations();
assertEquals(s_ksg, s_gau, 0.001);
}
}