mirror of https://github.com/jlizier/jidt
1178 lines
48 KiB
Java
Executable File
1178 lines
48 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.kraskov;
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import java.util.Calendar;
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import java.util.PriorityQueue;
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import infodynamics.measures.continuous.MutualInfoCalculatorMultiVariate;
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import infodynamics.measures.continuous.MutualInfoMultiVariateCommon;
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import infodynamics.utils.EuclideanUtils;
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import infodynamics.utils.KdTree;
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import infodynamics.utils.MathsUtils;
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import infodynamics.utils.MatrixUtils;
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import infodynamics.utils.NearestNeighbourSearcher;
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import infodynamics.utils.NeighbourNodeData;
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import infodynamics.utils.EmpiricalMeasurementDistribution;
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import infodynamics.utils.NativeUtils;
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/**
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* <p>Computes the differential mutual information of two given multivariate sets of
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* observations (implementing {@link MutualInfoCalculatorMultiVariate}),
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* using Kraskov-Stoegbauer-Grassberger (KSG) estimation (see Kraskov et al., below).
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* The implementation is made using fast-neighbour searches with an
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* underlying k-d tree algorithm.
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* This is an abstract class to gather common functionality between the two
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* algorithms defined by Kraskov et al.
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* Two child classes {@link MutualInfoCalculatorMultiVariateKraskov1} and
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* {@link MutualInfoCalculatorMultiVariateKraskov2} then
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* actually implement the two algorithms in the Kraskov et al. paper</p>
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*
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* <p>Usage is as per the paradigm outlined for {@link MutualInfoCalculatorMultiVariate},
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* with:
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* <ul>
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* <li>For constructors see the child classes.</li>
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* <li>Further properties are defined in {@link #setProperty(String, String)}.</li>
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* <li>Computed values are in <b>nats</b>, not bits!</li>
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* </ul>
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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>Kraskov, A., Stoegbauer, H., Grassberger, P.,
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* <a href="http://dx.doi.org/10.1103/PhysRevE.69.066138">"Estimating mutual information"</a>,
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* Physical Review E 69, (2004) 066138.</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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* @author Ipek Özdemir
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*/
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public abstract class MutualInfoCalculatorMultiVariateKraskov
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extends MutualInfoMultiVariateCommon
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implements MutualInfoCalculatorMultiVariate {
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/**
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* we compute distances to the kth nearest neighbour
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*/
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protected int k = 4;
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/**
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* The norm type in use (see {@link #PROP_NORM_TYPE})
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*/
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protected int normType = EuclideanUtils.NORM_MAX_NORM;
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/**
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* Property name for the number of K nearest neighbours used in
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* the KSG algorithm in the full joint space (default 4).
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*/
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public final static String PROP_K = "k";
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/**
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* Property name for what type of norm to use between data points
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* for each marginal variable -- Options are defined by
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* {@link KdTree#setNormType(String)} and the
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* default is {@link EuclideanUtils#NORM_MAX_NORM}.
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*/
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public final static String PROP_NORM_TYPE = "NORM_TYPE";
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/**
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* Property name for a dynamics exclusion time window
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* otherwise known as Theiler window (see Kantz and Schreiber).
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* Default is 0 which means no dynamic exclusion window.
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*/
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public static final String PROP_DYN_CORR_EXCL_TIME = "DYN_CORR_EXCL";
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/**
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* Property name for the number of parallel threads to use in the
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* computation (default is to use all available)
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*/
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public static final String PROP_NUM_THREADS = "NUM_THREADS";
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/**
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* Valid property value for {@link #PROP_NUM_THREADS} to indicate
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* that all available processors should be used.
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*/
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public static final String USE_ALL_THREADS = "USE_ALL";
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/**
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* Property name for the flag to enable or disable the GPU module.
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*/
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public static final String PROP_USE_GPU = "USE_GPU";
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/**
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* Property name for the path to JIDT GPU library.
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*
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* Path must be full and contain the library filename.
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* Example: /home/johndoe/myfolder/libKraskov.so
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*/
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public static final String PROP_GPU_LIBRARY_PATH = "GPU_LIBRARY_PATH";
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/**
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* Whether we use dynamic correlation exclusion
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*/
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protected boolean dynCorrExcl = false;
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/**
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* Size of dynamic correlation exclusion window.
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*/
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protected int dynCorrExclTime = 0;
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/**
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* Number of parallel threads to use in the computation;
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* defaults to use all available.
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*/
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protected int numThreads = Runtime.getRuntime().availableProcessors();
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/**
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* Private variable to record which KSG algorithm number
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* this instance is implementing
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*/
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protected boolean isAlgorithm1 = false;
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/**
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* Whether to enable the GPU module
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*/
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protected boolean useGPU = false;
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/**
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* Path to JIDT GPU library
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*/
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protected String gpuLibraryPath = "";
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/**
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* Check whether C native code has been loaded
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*/
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protected boolean cudaLibraryLoaded = false;
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/**
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* protected k-d tree data structure (for fast nearest neighbour searches)
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* representing the joint source-dest space
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*/
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protected KdTree kdTreeJoint;
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/**
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* protected data structure (for fast nearest neighbour searches)
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* representing the source space
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*/
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protected NearestNeighbourSearcher nnSearcherSource;
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/**
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* protected data structure (for fast nearest neighbour searches)
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* representing the dest space
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*/
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protected NearestNeighbourSearcher nnSearcherDest;
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/**
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* Constant for digamma(k), with k the number of nearest neighbours selected
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*/
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protected double digammaK;
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/**
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* Constant for digamma(N), with N the number of samples.
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*/
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protected double digammaN;
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/**
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* Construct an instance of the KSG MI calculator
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*/
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public MutualInfoCalculatorMultiVariateKraskov() {
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super();
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// Switch on adding noise to the data by default for the KSG estimator
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addNoise = true;
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noiseLevel = (double) 1e-8;
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}
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@Override
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public void initialise(int sourceDimensions, int destDimensions) {
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kdTreeJoint = null;
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nnSearcherSource = null;
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nnSearcherDest = null;
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super.initialise(sourceDimensions, destDimensions);
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}
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/**
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* Sets properties for the KSG MI calculator.
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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>Valid property names, and what their
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* values should represent, include:</p>
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* <ul>
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* <li>{@link #PROP_K} -- number of k nearest neighbours to use in joint kernel space
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* in the KSG algorithm (default is 4).</li>
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* <li>{@link #PROP_NORM_TYPE} -- normalization type to apply to
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* working out the norms between the points in each marginal space.
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* Options are defined by {@link KdTree#setNormType(String)} -
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* default is {@link EuclideanUtils#NORM_MAX_NORM}.</li>
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* <li>{@link #PROP_DYN_CORR_EXCL_TIME} -- a dynamics exclusion time window,
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* also known as Theiler window (see Kantz and Schreiber);
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* default is 0 which means no dynamic exclusion window.</li>
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* <li>{@link #PROP_NUM_THREADS} -- the integer number of parallel threads
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* to use in the computation. Can be passed as a string "USE_ALL"
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* to use all available processors on the machine.
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* Default is "USE_ALL".
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* <li>any valid properties for {@link MutualInfoMultiVariateCommon#setProperty(String, String)}.</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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* @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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public void setProperty(String propertyName, String propertyValue) throws Exception {
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boolean propertySet = true;
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if (propertyName.equalsIgnoreCase(PROP_K)) {
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k = Integer.parseInt(propertyValue);
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} else if (propertyName.equalsIgnoreCase(PROP_NORM_TYPE)) {
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normType = KdTree.validateNormType(propertyValue);
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} else if (propertyName.equalsIgnoreCase(PROP_DYN_CORR_EXCL_TIME)) {
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dynCorrExclTime = Integer.parseInt(propertyValue);
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dynCorrExcl = (dynCorrExclTime > 0);
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} else if (propertyName.equalsIgnoreCase(PROP_NUM_THREADS)) {
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if (propertyValue.equalsIgnoreCase(USE_ALL_THREADS)) {
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numThreads = Runtime.getRuntime().availableProcessors();
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} else { // otherwise the user has passed in an integer:
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numThreads = Integer.parseInt(propertyValue);
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}
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} else if (propertyName.equalsIgnoreCase(PROP_USE_GPU)) {
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useGPU = Boolean.parseBoolean(propertyValue);
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} else if (propertyName.equalsIgnoreCase(PROP_GPU_LIBRARY_PATH)) {
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gpuLibraryPath = propertyValue;
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} else {
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// No property was set here
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propertySet = false;
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// try the superclass:
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super.setProperty(propertyName, propertyValue);
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}
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if (debug && propertySet) {
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System.out.println(this.getClass().getSimpleName() + ": Set property " + propertyName +
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" to " + propertyValue);
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}
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}
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/**
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* Get property values for the calculator.
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*
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* <p>Valid property names, and what their
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* values should represent, are the same as those for
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* {@link #setProperty(String, String)}</p>
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*
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* <p>Unknown property values are responded to with a null return value.</p>
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*
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* @param propertyName name of the property
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* @return current value of the property
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* @throws Exception for invalid property values
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*/
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public String getProperty(String propertyName)
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throws Exception {
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if (propertyName.equalsIgnoreCase(PROP_K)) {
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return Integer.toString(k);
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} else if (propertyName.equalsIgnoreCase(PROP_NORM_TYPE)) {
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return KdTree.convertNormTypeToString(normType);
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} else if (propertyName.equalsIgnoreCase(PROP_DYN_CORR_EXCL_TIME)) {
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return Integer.toString(dynCorrExclTime);
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} else if (propertyName.equalsIgnoreCase(PROP_NUM_THREADS)) {
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return Integer.toString(numThreads);
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} else if (propertyName.equalsIgnoreCase(PROP_USE_GPU)) {
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return Boolean.toString(useGPU);
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} else if (propertyName.equalsIgnoreCase(PROP_GPU_LIBRARY_PATH)) {
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return gpuLibraryPath;
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} else {
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// try the superclass:
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return super.getProperty(propertyName);
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}
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}
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/* (non-Javadoc)
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* @see infodynamics.measures.continuous.MutualInfoMultiVariateCommon#finaliseAddObservations()
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*/
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@Override
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public void finaliseAddObservations() throws Exception {
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// Allow the parent to generate the data for us first
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super.finaliseAddObservations();
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if (totalObservations <= k + 2*dynCorrExclTime) {
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throw new Exception("There are less observations provided (" +
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totalObservations +
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") than required for the number of nearest neighbours parameter (" +
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k + ") and any dynamic correlation exclusion (" + dynCorrExclTime + ")");
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}
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// Set the constants:
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digammaK = MathsUtils.digamma(k);
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digammaN = MathsUtils.digamma(totalObservations);
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}
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/**
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* {@inheritDoc}
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*
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* @return the average MI in nats (not bits!)
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*/
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public double computeAverageLocalOfObservations() throws Exception {
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// Compute the MI
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double startTime = Calendar.getInstance().getTimeInMillis();
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lastAverage = computeFromObservations(false, null)[0];
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miComputed = true;
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if (debug) {
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Calendar rightNow2 = Calendar.getInstance();
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long endTime = rightNow2.getTimeInMillis();
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System.out.println("Calculation time: " + ((endTime - startTime)/1000.0) + " sec" );
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}
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return lastAverage;
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}
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/**
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* {@inheritDoc}
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*
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* @return the MI under the new ordering, in nats (not bits!).
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*/
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public double computeAverageLocalOfObservations(int[] reordering) throws Exception {
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if (reordering == null) {
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return computeAverageLocalOfObservations();
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}
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// Save internal variables pertaining to the original order for
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// later reinstatement:
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// (don't need to save and reinstate kdTreeSource, since we're not
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// altering the source data order).
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KdTree originalKdTreeJoint = kdTreeJoint;
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kdTreeJoint = null; // So that it is rebuilt for the new ordering
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NearestNeighbourSearcher originalKdTreeDest = nnSearcherDest;
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nnSearcherDest = null; // So that it is rebuilt for the new ordering
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double[][] originalData2 = destObservations;
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// Generate a new re-ordered data2
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destObservations = MatrixUtils.extractSelectedTimePointsReusingArrays(originalData2, reordering);
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// Compute the MI
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double newMI = computeFromObservations(false, null)[0];
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// restore original variables:
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destObservations = originalData2;
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kdTreeJoint = originalKdTreeJoint;
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nnSearcherDest = originalKdTreeDest;
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return newMI;
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}
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/**
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* <p>Computes the local values of the MI,
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* for each valid observation in the previously supplied observations
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* (with PDFs computed using all of the previously supplied observation sets).</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[][], double[][])},
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* then the return value is a single time-series of local
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* channel measure values corresponding to these samples.</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[][], 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.</p>
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*
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* @return the "time-series" of local MIs in nats
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* @throws Exception
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*/
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public double[] computeLocalOfPreviousObservations() throws Exception {
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double[] localValues = computeFromObservations(true, null);
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lastAverage = MatrixUtils.mean(localValues);
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miComputed = true;
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return localValues;
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}
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@Override
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public double[] computeLocalUsingPreviousObservations(double[][] states1, double[][] states2) throws Exception {
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// Do normalisation of the incoming data if required:
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double[][] states1ToUse, states2ToUse;
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if (normalise) {
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states1ToUse = MatrixUtils.normaliseIntoNewArray(states1, sourceMeansBeforeNorm, sourceStdsBeforeNorm, 0, states1.length-timeDiff);
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states2ToUse = MatrixUtils.normaliseIntoNewArray(states2, destMeansBeforeNorm, destStdsBeforeNorm, timeDiff, states2.length-timeDiff);
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} else {
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if (timeDiff > 0) {
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states1ToUse = MatrixUtils.selectRows(states1, 0, states1.length-timeDiff);
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states2ToUse = MatrixUtils.selectRows(states2, 0, states2.length-timeDiff);
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} else {
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states1ToUse = states1;
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states2ToUse = states2;
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}
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}
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// And call the algorithm:
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double[] localValues = computeFromObservations(true,
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new double[][][]{states1ToUse, states2ToUse});
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return localValues;
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}
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/**
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* This protected method handles the multiple threads which
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* computes either the average or local MI (over parts of the total
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* observations), computing the x and y
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* distances between all tuples in time.
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*
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* <p>The method returns:<ol>
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* <li>for (returnLocals == false), an array of size 1,
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* containing the average MI </li>
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* <li>for local MIs (returnLocals == true), the array of local MI values</li>
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* </ol>
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*
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* @param returnLocals whether to return an array or local values, or else
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* sums of these values
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* @param newObservations set to null for computing for the observation set for the PDF, or pass in a new set
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* of observations to compute the average/locals for (using the existing observations to construct the PDF)
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* @return either the average MI, or array of local MI value, in nats not bits
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* @throws Exception
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*/
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protected double[] computeFromObservations(boolean returnLocals, double[][][] newObservations) throws Exception {
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int N = sourceObservations.length; // number of observations for the PDFs
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double[] returnValues = null;
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// How many time points are we averaging over?
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int numTimePointsToComputeFor = (newObservations == null) ?
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N : newObservations[0].length;
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if (useGPU && (newObservations != null)) {
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System.out.println("Cannot use GPU for estimation based on new observations -- falling back to CPU calculation...");
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}
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if (useGPU && (newObservations == null)) {
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returnValues = gpuComputeFromObservations(0, N, returnLocals);
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} else if (numThreads == 1) {
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// Single-threaded implementation:
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ensureKdTreesConstructed();
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if (newObservations == null) {
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returnValues = partialComputeFromObservations(0, numTimePointsToComputeFor, returnLocals);
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} else {
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returnValues = partialComputeFromNewObservations(0, numTimePointsToComputeFor,
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newObservations[0], newObservations[1], returnLocals);
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}
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} else {
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// We're going multithreaded:
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ensureKdTreesConstructed();
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if (returnLocals) {
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// We're computing local MI
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returnValues = new double[numTimePointsToComputeFor];
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} else {
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// We're computing average MI
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returnValues = new double[MiKraskovThreadRunner.RETURN_ARRAY_LENGTH_MI];
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}
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// Distribute the observations to the threads for the parallel processing
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int lTimesteps = numTimePointsToComputeFor / numThreads; // each thread gets the same amount of data
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int res = numTimePointsToComputeFor % numThreads; // the first thread gets the residual data
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if (debug) {
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System.out.printf("Computing Kraskov MI with %d threads (%d timesteps each, plus %d residual)\n",
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numThreads, lTimesteps, res);
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}
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Thread[] tCalculators = new Thread[numThreads];
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MiKraskovThreadRunner[] runners = new MiKraskovThreadRunner[numThreads];
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for (int t = 0; t < numThreads; t++) {
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int startTime = (t == 0) ? 0 : lTimesteps * t + res;
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int numTimesteps = (t == 0) ? lTimesteps + res : lTimesteps;
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if (debug) {
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System.out.println(t + ".Thread: from " + startTime +
|
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" to " + (startTime + numTimesteps)); // Trace Message
|
|
}
|
|
runners[t] = new MiKraskovThreadRunner(this, startTime, numTimesteps, newObservations, 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 MI; 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 MI, keep the running sums of digammas and counts
|
|
MatrixUtils.addInPlace(returnValues, runners[t].getReturnValues(), MiKraskovThreadRunner.RETURN_ARRAY_LENGTH_MI);
|
|
}
|
|
}
|
|
}
|
|
|
|
// Finalise the results:
|
|
if (returnLocals) {
|
|
return returnValues;
|
|
} else {
|
|
// Compute the average number of points within eps_x and eps_y
|
|
double averageDiGammas = returnValues[MiKraskovThreadRunner.INDEX_SUM_DIGAMMAS] / (double) numTimePointsToComputeFor;
|
|
double avNx = returnValues[MiKraskovThreadRunner.INDEX_SUM_NX] / (double) numTimePointsToComputeFor;
|
|
double avNy = returnValues[MiKraskovThreadRunner.INDEX_SUM_NY] / (double) numTimePointsToComputeFor;
|
|
if (debug) {
|
|
System.out.println(String.format("Average n_x=%.3f, Average n_y=%.3f", avNx, avNy));
|
|
}
|
|
|
|
// Use digamma(N) normally, unless we're looking at new observations:
|
|
double digammaNToUse = (newObservations == null) ? digammaN : MathsUtils.digamma(totalObservations+1);
|
|
|
|
// Finalise the average result, depending on which algorithm we are implementing:
|
|
if (isAlgorithm1) {
|
|
return new double[] { digammaK - averageDiGammas + digammaNToUse };
|
|
} else {
|
|
return new double[] { digammaK - (1.0 / (double)k) - averageDiGammas + digammaNToUse };
|
|
}
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Use the same nearest neighbour searches to return a KL-based
|
|
* conditional entropy, sharing the neighbour search radius.
|
|
* With reference to the KSG paper, this takes the KL-based estimator for H(X) (eqn 22) and adds it to the negative of MI.
|
|
* It should also be noted that if the variables are normalised, this changes the absolute values of the entropies,
|
|
* and they become relative to normalised variables.
|
|
* Since this is a side-method for this estimator, it is currently is only implemented single threaded on CPU.
|
|
* It should also be considered experimental - this will eventually be moved to its own estimator.
|
|
*
|
|
* @return the average conditional entropy of variable1 given variable2 in nats (not bits!)
|
|
*/
|
|
public double computeAverageConditionalEntropy() throws Exception {
|
|
// Compute the MI
|
|
double startClockTime = Calendar.getInstance().getTimeInMillis();
|
|
double conditionalEntropy = 0.0;
|
|
conditionalEntropy = computeFromObservations(false, null)[0];
|
|
|
|
int N = sourceObservations.length; // number of observations for the PDFs
|
|
|
|
// Single-threaded implementation:
|
|
ensureKdTreesConstructed();
|
|
double avDigammaCond = 0;
|
|
double avLog2xkNNDist = 0;
|
|
for (int t = 0; t < N; t++) {
|
|
// For this sample only:
|
|
double[] returnValues = partialComputeFromObservations(t, 1, false);
|
|
int n_y = (int) returnValues[MiKraskovThreadRunner.INDEX_SUM_NY];
|
|
if (isAlgorithm1) {
|
|
avDigammaCond += MathsUtils.digamma(n_y+1);
|
|
} else {
|
|
avDigammaCond += MathsUtils.digamma(n_y);
|
|
}
|
|
double doublekNNDist = returnValues[MiKraskovThreadRunner.INDEX_SUM_2X_NEIGH_DIST];
|
|
avLog2xkNNDist += Math.log(doublekNNDist);
|
|
}
|
|
avDigammaCond /= (double) N;
|
|
avLog2xkNNDist *= (double) dimensionsSource / (double) N;
|
|
if (isAlgorithm1) {
|
|
conditionalEntropy = -digammaK + avDigammaCond + avLog2xkNNDist;
|
|
} else {
|
|
conditionalEntropy = -digammaK + (1.0 / (double)k) + avDigammaCond + avLog2xkNNDist;
|
|
}
|
|
|
|
if (debug) {
|
|
Calendar rightNow2 = Calendar.getInstance();
|
|
long endTime = rightNow2.getTimeInMillis();
|
|
System.out.println("Calculation time: " + ((endTime - startClockTime)/1000.0) + " sec" );
|
|
}
|
|
return conditionalEntropy;
|
|
}
|
|
|
|
/**
|
|
* 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>The method returns:<ol>
|
|
* <li>for average MIs (returnLocals == false), the relevant sums of digamma(n_x+1) and digamma(n_y+1)
|
|
* for a partial set of the observations</li>
|
|
* <li>for local MIs (returnLocals == true), the array of local MI 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) and digamma(n_y+1), then
|
|
* sum of n_x and finally sum of n_y (these latter two are for debugging purposes).
|
|
* @throws Exception
|
|
*/
|
|
protected abstract double[] partialComputeFromObservations(
|
|
int startTimePoint, int numTimePoints, boolean returnLocals) throws Exception;
|
|
|
|
/**
|
|
* 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.
|
|
* In particular, this method differs from {@link #partialComputeFromObservations(int, int, boolean)}
|
|
* because it operates on a new set of observations (using the old set of observations for
|
|
* constructing the search spaces and PDFs)
|
|
*
|
|
* <p>The method returns:<ol>
|
|
* <li>for average MIs (returnLocals == false), the relevant sums of digamma(n_x+1), digamma(n_y+1)
|
|
* for a partial set of the observations</li>
|
|
* <li>for local MIs (returnLocals == true), the array of local MI values</li>
|
|
* </ol>
|
|
*
|
|
* @param startTimePoint start time for the partial set we examine
|
|
* @param numTimePoints number of time points (including startTimePoint to examine)
|
|
* @param newVar1Observations new time series of observations for variable 1
|
|
* @param newVar2Observations new time series of observations for variable 2
|
|
* @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) and digamma(n_y+1), then
|
|
* sum of n_x and finally sum of n_y (these latter two are for debugging purposes).
|
|
* @throws Exception
|
|
*/
|
|
protected abstract double[] partialComputeFromNewObservations(
|
|
int startTimePoint, int numTimePoints,
|
|
double[][] newVar1Observations, double[][] newVar2Observations,
|
|
boolean returnLocals) throws Exception;
|
|
|
|
/**
|
|
* Protected method to be used internally for GPU implementations.
|
|
* This method serves the same purpose as partialComputeFromObservations,
|
|
* but for GPU computation. Each algorithm must override this method
|
|
* and implement a GPU routine to calculate all values in a single call
|
|
* to the GPU code.
|
|
*/
|
|
protected double[] gpuComputeFromObservations(int startTimePoint,
|
|
int numTimePoints, boolean returnLocals, int nb_surrogates,
|
|
int[][] newOrderings) throws Exception {
|
|
|
|
if (debug) {
|
|
System.out.println("Start GPU calculation");
|
|
}
|
|
|
|
ensureCudaLibraryLoaded();
|
|
|
|
boolean useMaxNorm;
|
|
|
|
if ( normType == EuclideanUtils.NORM_MAX_NORM) {
|
|
useMaxNorm = true;
|
|
} else if ( normType == EuclideanUtils.NORM_EUCLIDEAN || normType == EuclideanUtils.NORM_EUCLIDEAN_SQUARED) {
|
|
useMaxNorm = false;
|
|
} else {
|
|
throw new Exception("Only max and square norms are implemented. Abort.");
|
|
}
|
|
|
|
double[] res;
|
|
|
|
try {
|
|
if (debug) {
|
|
System.out.printf("Calling GPU calculation with returnLocals=%b and nb_surrogates=%d\n", returnLocals, nb_surrogates);
|
|
}
|
|
res = MIKraskov(totalObservations, sourceObservations, dimensionsSource,
|
|
destObservations, dimensionsDest, k, dynCorrExclTime, returnLocals, useMaxNorm,
|
|
isAlgorithm1, nb_surrogates, null!=newOrderings, newOrderings);
|
|
if (debug) {
|
|
System.out.println("GPU calculation finished successfully. Returning results");
|
|
}
|
|
} catch (Throwable e) {
|
|
System.out.println("WARNING. Error in GPU code. Reverting back to CPU.");
|
|
e.printStackTrace();
|
|
res = partialComputeFromObservations(0, totalObservations, returnLocals);
|
|
}
|
|
|
|
return res;
|
|
}
|
|
|
|
|
|
/**
|
|
* FIXME
|
|
*/
|
|
protected double[] gpuComputeFromObservations(int startTimePoint,
|
|
int numTimePoints, boolean returnLocals) throws Exception {
|
|
return gpuComputeFromObservations(startTimePoint, numTimePoints, returnLocals, 0, null);
|
|
}
|
|
|
|
/**
|
|
* FIXME
|
|
*/
|
|
protected double[] gpuComputeFromObservations(int startTimePoint,
|
|
int numTimePoints, boolean returnLocals, int[][] newOrderings) throws Exception {
|
|
return gpuComputeFromObservations(startTimePoint, numTimePoints,
|
|
returnLocals, newOrderings.length, newOrderings);
|
|
}
|
|
|
|
/**
|
|
* Native method to calculate MI in GPU.
|
|
*/
|
|
private native double[] MIKraskov(
|
|
int N, double[][] source, int dimx, double[][] dest, int dimy,
|
|
int k, int theiler, boolean returnLocals, boolean useMaxNorm,
|
|
boolean isAlgorithm1, int nb_surrogates, boolean orderingsGiven,
|
|
int[][] newOrderings);
|
|
|
|
/**
|
|
* 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(new int[] {dimensionsSource, dimensionsDest},
|
|
new double[][][] {sourceObservations, destObservations},
|
|
observationSetIndices, observationTimePoints);
|
|
kdTreeJoint.setNormType(normType);
|
|
}
|
|
if (nnSearcherSource == null) {
|
|
nnSearcherSource = NearestNeighbourSearcher.create(sourceObservations,
|
|
observationSetIndices, observationTimePoints);
|
|
nnSearcherSource.setNormType(normType);
|
|
}
|
|
if (nnSearcherDest == null) {
|
|
nnSearcherDest = NearestNeighbourSearcher.create(destObservations,
|
|
observationSetIndices, observationTimePoints);
|
|
nnSearcherDest.setNormType(normType);
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Internal method to ensure that the Cuda native library has been correctly
|
|
* loaded.
|
|
*
|
|
* @throws Exception if library not found or unable to load
|
|
*/
|
|
protected void ensureCudaLibraryLoaded() throws Exception {
|
|
|
|
if (!cudaLibraryLoaded) {
|
|
|
|
try {
|
|
if (gpuLibraryPath.length() < 1) {
|
|
NativeUtils.loadLibraryFromJar("/cuda/libKraskov.so");
|
|
} else {
|
|
System.load(gpuLibraryPath);
|
|
}
|
|
} catch (Throwable e) {
|
|
String errmsg = "GPU library not found. To compile GPU code set the enablegpu flag to true in build.xml, or run `ant gpu jar`.";
|
|
errmsg += "\nFor more information see the JIDT GPU wiki page: https://github.com/jlizier/jidt/wiki/GPU";
|
|
if (gpuLibraryPath.length() > 0) {
|
|
errmsg += "\n\nGPU library was not found in the path provided. Provide full path including library file name.";
|
|
errmsg += "\nExample: /home/johndoe/myfolder/libKraskov.so";
|
|
}
|
|
throw new Exception(errmsg);
|
|
}
|
|
|
|
cudaLibraryLoaded = true;
|
|
|
|
}
|
|
}
|
|
|
|
/**
|
|
* {@inheritDoc}
|
|
*/
|
|
@Override
|
|
public EmpiricalMeasurementDistribution computeSignificance(int numPermutationsToCheck)
|
|
throws Exception {
|
|
if (useGPU) {
|
|
double[] res = gpuComputeFromObservations(0, totalObservations, false, numPermutationsToCheck, null);
|
|
return new EmpiricalMeasurementDistribution(
|
|
MatrixUtils.select(res, 1, res.length - 1), res[0]);
|
|
} else {
|
|
return super.computeSignificance(numPermutationsToCheck);
|
|
}
|
|
}
|
|
|
|
/**
|
|
* {@inheritDoc}
|
|
*/
|
|
@Override
|
|
public EmpiricalMeasurementDistribution computeSignificance(int[][] newOrderings)
|
|
throws Exception {
|
|
if (useGPU) {
|
|
double[] res = gpuComputeFromObservations(0, totalObservations, false, newOrderings.length, newOrderings);
|
|
return new EmpiricalMeasurementDistribution(
|
|
MatrixUtils.select(res, 1, res.length - 1), res[0]);
|
|
} else {
|
|
return super.computeSignificance(newOrderings);
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Compute the prediction error in one variable from the k nearest neighbours (kNNs) of the observation
|
|
* of the other variable.
|
|
* The kNNs of the variable to predict from are formed from the supplied norm type within that variable.
|
|
* The number of kNNs to use here is the current property value set for {@link #PROP_K}.
|
|
* The prediction error is a sum of absolute errors for each dimension within the variable to predict
|
|
*
|
|
* @param predictFirstVariable true for predicting the first variable (Source) or
|
|
* false for predicting the second variable (destination)
|
|
* @return array of prediction errors for each dimension of the predicted variable
|
|
* @throws Exception
|
|
*/
|
|
public double[] computePredictionErrorsFromObservations(boolean predictFirstVariable) throws Exception {
|
|
return computePredictionErrorsFromObservations(predictFirstVariable, k);
|
|
}
|
|
|
|
/**
|
|
* Compute the prediction error in one variable from the k nearest neighbours (kNNs) of the observation
|
|
* of the other variable.
|
|
* The kNNs of the variable to predict from are formed from the supplied norm type within that variable.
|
|
* The prediction error is a sum of absolute errors for each dimension within the variable to predict
|
|
*
|
|
* @param predictFirstVariable true for predicting the first variable (Source) or
|
|
* false for predicting the second variable (destination)
|
|
* @param kNNs number of nearest neighbours to use
|
|
* @return array of prediction errors for each dimension of the predicted variable
|
|
* @throws Exception
|
|
*/
|
|
public double[] computePredictionErrorsFromObservations(boolean predictFirstVariable, int kNNs) throws Exception {
|
|
int N = sourceObservations.length; // number of observations
|
|
|
|
double[] totalErrors = null;
|
|
|
|
ensureKdTreesConstructed();
|
|
|
|
if (numThreads == 1) {
|
|
// Single-threaded implementation:
|
|
totalErrors = partialComputePredictionErrorFromObservations(0, N, kNNs, predictFirstVariable);
|
|
} else {
|
|
// We're going multithreaded:
|
|
totalErrors = new double[predictFirstVariable ? dimensionsSource : dimensionsDest];
|
|
|
|
// Distribute the observations to the threads for the parallel processing
|
|
int lTimesteps = N / numThreads; // each thread gets the same amount of data
|
|
int res = N % numThreads; // the first thread gets the residual data
|
|
if (debug) {
|
|
System.out.printf("Computing prediction errors for variable %d from variable %d with %d threads (%d timesteps each, plus %d residual)\n",
|
|
predictFirstVariable ? 1 : 2, predictFirstVariable ? 2 : 1,
|
|
numThreads, lTimesteps, res);
|
|
}
|
|
Thread[] tCalculators = new Thread[numThreads];
|
|
MiKraskovPredictionThreadRunner[] runners = new MiKraskovPredictionThreadRunner[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 MiKraskovPredictionThreadRunner(this, startTime,
|
|
numTimesteps, kNNs, predictFirstVariable);
|
|
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) {
|
|
tCalculators[t].join();
|
|
}
|
|
// Now we add in the data from this completed thread:
|
|
MatrixUtils.addInPlace(totalErrors, runners[t].getReturnValues());
|
|
}
|
|
}
|
|
|
|
// Finalise the results:
|
|
if (debug) {
|
|
System.out.printf("Total prediction error from variable %d to variable %d=",
|
|
predictFirstVariable ? 2 : 1, predictFirstVariable ? 1 : 2);
|
|
MatrixUtils.printArray(System.out, 3, totalErrors);
|
|
}
|
|
return totalErrors;
|
|
}
|
|
|
|
/**
|
|
* 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 MiKraskovThreadRunner implements Runnable {
|
|
protected MutualInfoCalculatorMultiVariateKraskov miCalc;
|
|
protected int myStartTimePoint;
|
|
protected int numberOfTimePoints;
|
|
protected double[][][] newObservations;
|
|
protected boolean computeLocals;
|
|
|
|
protected double[] returnValues = null;
|
|
protected Exception problem = null;
|
|
|
|
public static final int INDEX_SUM_DIGAMMAS = 0;
|
|
public static final int INDEX_SUM_NX = 1;
|
|
public static final int INDEX_SUM_NY = 2;
|
|
public static final int INDEX_SUM_2X_NEIGH_DIST = 3; // Not used by GPU, and only read for conditional entropy
|
|
public static final int RETURN_ARRAY_LENGTH_MI = 3;
|
|
public static final int RETURN_ARRAY_LENGTH = 4;
|
|
|
|
public MiKraskovThreadRunner(
|
|
MutualInfoCalculatorMultiVariateKraskov miCalc,
|
|
int myStartTimePoint, int numberOfTimePoints,
|
|
double[][][] newObservations,
|
|
boolean computeLocals) {
|
|
this.miCalc = miCalc;
|
|
this.myStartTimePoint = myStartTimePoint;
|
|
this.numberOfTimePoints = numberOfTimePoints;
|
|
this.computeLocals = computeLocals;
|
|
this.newObservations = newObservations;
|
|
}
|
|
|
|
/**
|
|
* Return the values from this part of the data,
|
|
* or throw any exception that was encountered by the
|
|
* thread.
|
|
*
|
|
* @return the relevant return values from this part of the data
|
|
* @throws Exception an exception previously encountered by this thread.
|
|
*/
|
|
public double[] getReturnValues() throws Exception {
|
|
if (problem != null) {
|
|
throw problem;
|
|
}
|
|
return returnValues;
|
|
}
|
|
|
|
/**
|
|
* Start the thread for the given parameters
|
|
*/
|
|
public void run() {
|
|
try {
|
|
if (newObservations == null) {
|
|
// Computing on existing observations
|
|
returnValues = miCalc.partialComputeFromObservations(
|
|
myStartTimePoint, numberOfTimePoints, computeLocals);
|
|
} else {
|
|
// Computing on new observations
|
|
returnValues = miCalc.partialComputeFromNewObservations(
|
|
myStartTimePoint, numberOfTimePoints,
|
|
newObservations[0], newObservations[1],
|
|
computeLocals);
|
|
}
|
|
} catch (Exception e) {
|
|
// Store the exception for later retrieval
|
|
problem = e;
|
|
return;
|
|
}
|
|
}
|
|
}
|
|
// end class MiKraskovThreadRunner
|
|
|
|
/**
|
|
* Private class to handle multi-threading of the prediction from
|
|
* k nearest neighbours.
|
|
* Each instance calls partialComputePredictionErrorFromObservations()
|
|
* 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 MiKraskovPredictionThreadRunner implements Runnable {
|
|
protected MutualInfoCalculatorMultiVariateKraskov miCalc;
|
|
protected int myStartTimePoint;
|
|
protected int numberOfTimePoints;
|
|
protected int kNNs;
|
|
protected boolean predictFirstVariable;
|
|
|
|
protected double[] returnValues = null;
|
|
protected Exception problem = null;
|
|
|
|
public MiKraskovPredictionThreadRunner(
|
|
MutualInfoCalculatorMultiVariateKraskov miCalc,
|
|
int myStartTimePoint, int numberOfTimePoints,
|
|
int kNNs, boolean predictFirstVariable) {
|
|
this.miCalc = miCalc;
|
|
this.myStartTimePoint = myStartTimePoint;
|
|
this.numberOfTimePoints = numberOfTimePoints;
|
|
this.kNNs = kNNs;
|
|
this.predictFirstVariable = predictFirstVariable;
|
|
}
|
|
|
|
/**
|
|
* Return the sum of prediction errors from this part of the data,
|
|
* or throw any exception that was encountered by the
|
|
* thread.
|
|
*
|
|
* @return sum of prediction errors from this part of the data, for
|
|
* each of the dimensions of the relevant variable
|
|
* @throws Exception an exception previously encountered by this thread.
|
|
*/
|
|
public double[] getReturnValues() throws Exception {
|
|
if (problem != null) {
|
|
throw problem;
|
|
}
|
|
return returnValues;
|
|
}
|
|
|
|
/**
|
|
* Start the thread for the given parameters
|
|
*/
|
|
public void run() {
|
|
try {
|
|
returnValues = miCalc.partialComputePredictionErrorFromObservations(
|
|
myStartTimePoint, numberOfTimePoints, kNNs, predictFirstVariable);
|
|
} catch (Exception e) {
|
|
// Store the exception for later retrieval
|
|
problem = e;
|
|
return;
|
|
}
|
|
}
|
|
}
|
|
// end class MiKraskovPredictionThreadRunner
|
|
|
|
/**
|
|
* Protected method to be used internally for threaded implementations.
|
|
* This method implements the guts of examining prediction errors in one variable
|
|
* from the k nearest neighbours of the other.
|
|
* It is intended to be called by one thread to work on that specific
|
|
* sub-set of the data.
|
|
*
|
|
* @param startTimePoint start time for the partial set we examine
|
|
* @param numTimePoints number of time points (including startTimePoint to examine)
|
|
* @param kNNs number of nearest neighbours to use
|
|
* @param predictFirstVariable whether to use the second variable to predict the first (true)
|
|
* or first variable to predict the second (false)
|
|
* @return an array of the sum of square prediction errors for each dimension within the predicted
|
|
* variable.
|
|
* @throws Exception
|
|
*/
|
|
protected double[] partialComputePredictionErrorFromObservations(
|
|
int startTimePoint, int numTimePoints, int kNNs, boolean predictFirstVariable) throws Exception {
|
|
|
|
double startTime = Calendar.getInstance().getTimeInMillis();
|
|
|
|
double[] totalErrors = new double[predictFirstVariable ? dimensionsSource : dimensionsDest];
|
|
|
|
for (int t = startTimePoint; t < startTimePoint + numTimePoints; t++) {
|
|
// Find the k nearest neighbours for the relevant predictor variable
|
|
if (predictFirstVariable) {
|
|
// First variable value to predict:
|
|
double[] sourceValueToPredict = sourceObservations[t];
|
|
// Find kNNs of second variable
|
|
PriorityQueue<NeighbourNodeData> nnPQ =
|
|
nnSearcherDest.findKNearestNeighbours(kNNs, t, dynCorrExclTime);
|
|
double[] predictedValue = new double[dimensionsSource];
|
|
for (NeighbourNodeData kthNnData : nnPQ) {
|
|
// Retrieve the source value this corresponds to
|
|
double[] neighbourSourceValue = sourceObservations[kthNnData.sampleIndex];
|
|
// And include it's contribution in the prediction
|
|
for (int d = 0; d < dimensionsSource; d++) {
|
|
predictedValue[d] += neighbourSourceValue[d];
|
|
}
|
|
}
|
|
// Now add in the square prediction errors from the prediction:
|
|
for (int d = 0; d < dimensionsSource; d++) {
|
|
predictedValue[d] /= (double) kNNs;
|
|
totalErrors[d] += (sourceValueToPredict[d] - predictedValue[d]) *
|
|
(sourceValueToPredict[d] - predictedValue[d]);
|
|
}
|
|
} else { // predict second variable
|
|
// Second variable value to predict:
|
|
double[] destValueToPredict = destObservations[t];
|
|
// Find kNNs of first variable
|
|
PriorityQueue<NeighbourNodeData> nnPQ =
|
|
nnSearcherSource.findKNearestNeighbours(kNNs, t, dynCorrExclTime);
|
|
double[] predictedValue = new double[dimensionsDest];
|
|
for (NeighbourNodeData kthNnData : nnPQ) {
|
|
// Retrieve the dest value this corresponds to
|
|
double[] neighbourDestValue = destObservations[kthNnData.sampleIndex];
|
|
// And include it's contribution in the prediction
|
|
for (int d = 0; d < dimensionsDest; d++) {
|
|
predictedValue[d] += neighbourDestValue[d];
|
|
}
|
|
}
|
|
// Now add in the square prediction errors from the prediction:
|
|
for (int d = 0; d < dimensionsDest; d++) {
|
|
predictedValue[d] /= (double) kNNs;
|
|
totalErrors[d] += (destValueToPredict[d] - predictedValue[d]) *
|
|
(destValueToPredict[d] - predictedValue[d]);
|
|
}
|
|
}
|
|
}
|
|
|
|
if (debug) {
|
|
Calendar rightNow2 = Calendar.getInstance();
|
|
long endTime = rightNow2.getTimeInMillis();
|
|
System.out.println("Subset " + startTimePoint + ":" +
|
|
(startTimePoint + numTimePoints) + " Calculation time: " +
|
|
((endTime - startTime)/1000.0) + " sec" );
|
|
}
|
|
|
|
return totalErrors;
|
|
}
|
|
|
|
/**
|
|
* Debug method to return the k nearest neighbour distances that
|
|
* would be utilised for each sample point here.
|
|
* Note that this is specifically the max-norm across the two variables, which is used for both
|
|
* variables in the range searches in algorithm 1 (although algorithm 2 would use the max distance
|
|
* for each variable within the kNNs in their separate range searches).
|
|
*
|
|
* @param startTimePoint
|
|
* @param numTimePoints
|
|
* @return
|
|
* @throws Exception
|
|
*/
|
|
public double[] kNNDistances(int startTimePoint, int numTimePoints) throws Exception {
|
|
|
|
double[] kNNdistances = new double[numTimePoints];
|
|
|
|
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();
|
|
|
|
kNNdistances[t - startTimePoint] = kthNnData.distance;
|
|
}
|
|
return kNNdistances;
|
|
}
|
|
|
|
|
|
/**
|
|
* Debug method to return the k nearest neighbour distances that
|
|
* would be utilised in {@link #computeLocalUsingPreviousObservations(double[][], double[][])}
|
|
* for a cross MI.
|
|
* Note that this is specifically the max-norm across the two variables, which is used for both
|
|
* variables in the range searches in algorithm 1 (although algorithm 2 would use the max distance
|
|
* for each variable within the kNNs in their separate range searches).
|
|
*
|
|
* @param startTimePoint
|
|
* @param numTimePoints
|
|
* @param newVar1Observations
|
|
* @param newVar2Observations
|
|
* @return
|
|
* @throws Exception
|
|
*/
|
|
public double[] kNNDistancesForNewSamples(int startTimePoint, int numTimePoints,
|
|
double[][] newVar1Observations, double[][] newVar2Observations) throws Exception {
|
|
|
|
double[] kNNdistances = new double[numTimePoints];
|
|
|
|
for (int t = startTimePoint; t < startTimePoint + numTimePoints; t++) {
|
|
// Compute eps for this time step by
|
|
// finding the kth closest neighbour for the new sample:
|
|
PriorityQueue<NeighbourNodeData> nnPQ =
|
|
kdTreeJoint.findKNearestNeighbours(k,
|
|
new double[][] {newVar1Observations[t], newVar2Observations[t]});
|
|
// First element in the PQ is the kth NN,
|
|
// and epsilon = kthNnData.distance
|
|
NeighbourNodeData kthNnData = nnPQ.poll();
|
|
|
|
kNNdistances[t - startTimePoint] = kthNnData.distance;
|
|
}
|
|
return kNNdistances;
|
|
}
|
|
|
|
}
|