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edu.cmu.tetrad.search.utils.PurifyScoreBased Maven / Gradle / Ivy
///////////////////////////////////////////////////////////////////////////////
// For information as to what this class does, see the Javadoc, below. //
// Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, //
// 2007, 2008, 2009, 2010, 2014, 2015, 2022 by Peter Spirtes, Richard //
// Scheines, Joseph Ramsey, and Clark Glymour. //
// //
// 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 2 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, write to the Free Software //
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA //
///////////////////////////////////////////////////////////////////////////////
package edu.cmu.tetrad.search.utils;
import edu.cmu.tetrad.data.Clusters;
import edu.cmu.tetrad.data.ICovarianceMatrix;
import edu.cmu.tetrad.graph.*;
import edu.cmu.tetrad.sem.ParamType;
import edu.cmu.tetrad.sem.Parameter;
import edu.cmu.tetrad.sem.SemIm;
import edu.cmu.tetrad.sem.SemPm;
import edu.cmu.tetrad.util.MatrixUtils;
import org.apache.commons.math3.util.FastMath;
import java.util.*;
/**
* Implements a score-based Purify method.
*
* @author ricardosilva
*/
public class PurifyScoreBased implements IPurify {
private final boolean outputMessage = true;
private final TetradTest tetradTest;
private final int numVars;
private final List> forbiddenList;
// SCORE-BASED PURIFY - using BIC score function and Structural EM for
// search. Probabilistic model is Gaussian. - search operator consists only
// of adding a bi-directed edge between pairs of error variables - after
// such pairs are found, an heuristic is applied to eliminate one member of
// each pair - this methods tends to be much slower than the "tetradBased"
// ones.
double[][] Cyy, Cyz, Czz, bestCyy, bestCyz, bestCzz;
double[][] covErrors, oldCovErrors, sampleCovErrors, betas, oldBetas;
double[][] betasLat;
double[] varErrorLatent;
double[][] omega;
double[] omegaI;
double[][][] parentsResidualsCovar;
double[] iResidualsCovar;
double[][][] selectedInverseOmega;
double[][][] auxInverseOmega;
int[][] spouses;
int[] nSpouses;
int[][] parents;
int[][] parentsLat;
double[][][] parentsCov;
double[][] parentsChildCov;
double[][][] parentsLatCov;
double[][] parentsChildLatCov;
double[][][] pseudoParentsCov;
double[][] pseudoParentsChildCov;
boolean[][] parentsL;
int numObserved;
int numLatent;
int[] clusterId;
HashMap observableNames, latentNames;
SemGraph purePartitionGraph;
Graph basicGraph;
ICovarianceMatrix covarianceMatrix;
boolean[][] correlatedErrors, latentParent, observedParent;
List latentNodes, measuredNodes;
boolean modifiedGraph;
public PurifyScoreBased(TetradTest tetradTest, List> forbiddenList) {
this.tetradTest = tetradTest;
this.numVars = tetradTest.getVarNames().length;
this.forbiddenList = forbiddenList;
}
public List> purify(List> partition) {
System.out.println("*** " + partition);
List _partition = convertListToInt(partition);
printIntPartition(_partition);
SemGraph graph = scoreBasedPurify(_partition);
Graph _graph = convertSearchGraph(graph);
Clusters clusters = MimUtils.convertToClusters(_graph);
List _partition1 = new ArrayList<>();
List nodes = this.tetradTest.getVariables();
for (int i = 0; i < clusters.getNumClusters(); i++) {
List cluster = clusters.getCluster(i);
int[] _cluster = new int[cluster.size()];
for (int j = 0; j < cluster.size(); j++) {
for (int k = 0; k < nodes.size(); k++) {
Node node = nodes.get(k);
if (node.getName().equals(cluster.get(j))) {
_cluster[j] = k;
break;
}
}
}
_partition1.add(_cluster);
}
printClustering(_partition1);
return convertIntToList(_partition1);
}
public void setTrueGraph(Graph mim) {
throw new UnsupportedOperationException();
}
private void printIntPartition(List partition) {
for (int i = 0; i < partition.size(); i++) {
int[] cluster = partition.get(i);
System.out.print(i + ": ");
for (int k : cluster) {
System.out.print(k + " ");
}
System.out.println();
}
System.out.println();
}
private List convertListToInt(List> partition) {
List nodes = this.tetradTest.getVariables();
List _partition = new ArrayList<>();
for (List cluster : partition) {
int[] _cluster = new int[cluster.size()];
for (int j = 0; j < cluster.size(); j++) {
for (int k = 0; k < nodes.size(); k++) {
if (nodes.get(k).getName().equals(cluster.get(j).getName())) {
_cluster[j] = k;
}
}
}
_partition.add(_cluster);
}
return _partition;
}
private List> convertIntToList(List partition) {
List nodes = this.tetradTest.getVariables();
List> _partition = new ArrayList<>();
for (int[] cluster : partition) {
List _cluster = new ArrayList<>();
for (int k : cluster) {
_cluster.add(nodes.get(k));
}
_partition.add(_cluster);
}
return _partition;
}
private Graph convertSearchGraph(SemGraph input) {
if (input == null) {
List nodes = new ArrayList<>();
nodes.add(new GraphNode("No_model."));
return new EdgeListGraph(nodes);
}
List inputIndicators = new ArrayList<>();
List inputLatents = new ArrayList<>();
for (Node next : input.getNodes()) {
if (next.getNodeType() == NodeType.MEASURED) {
inputIndicators.add(next);
} else if (next.getNodeType() == NodeType.LATENT) {
inputLatents.add(next);
}
}
List allNodes = new ArrayList<>(inputIndicators);
allNodes.addAll(inputLatents);
Graph output = new EdgeListGraph(allNodes);
for (Node node1 : input.getNodes()) {
for (Node node2 : input.getNodes()) {
Edge edge = input.getEdge(node1, node2);
if (edge != null) {
if (node1.getNodeType() == NodeType.ERROR &&
node2.getNodeType() == NodeType.ERROR) {
Iterator ci = input.getChildren(node1).iterator();
Node indicator1 = ci.next(); //Assuming error nodes have only one children in SemGraphs...
ci = input.getChildren(node2).iterator();
Node indicator2 = ci.next(); //Assuming error nodes have only one children in SemGraphs...
if (indicator1.getNodeType() != NodeType.LATENT) {
output.setEndpoint(indicator1, indicator2,
Endpoint.ARROW);
output.setEndpoint(indicator2, indicator1,
Endpoint.ARROW);
}
} else if ((node1.getNodeType() != NodeType.LATENT ||
node2.getNodeType() != NodeType.LATENT) &&
node1.getNodeType() != NodeType.ERROR &&
node2.getNodeType() != NodeType.ERROR) {
output.setEndpoint(edge.getNode1(), edge.getNode2(),
Endpoint.ARROW);
output.setEndpoint(edge.getNode2(), edge.getNode1(),
Endpoint.TAIL);
}
}
}
}
for (int i = 0; i < inputLatents.size() - 1; i++) {
for (int j = i + 1; j < inputLatents.size(); j++) {
output.setEndpoint(inputLatents.get(i),
inputLatents.get(j), Endpoint.TAIL);
output.setEndpoint(inputLatents.get(j),
inputLatents.get(i), Endpoint.TAIL);
}
}
return output;
}
private SemGraph scoreBasedPurify(List partition) {
structuralEmInitialization(partition);
SemGraph bestGraph = this.purePartitionGraph;
System.out.println(">>>> Structural EM: initial round");
//gaussianEM(bestGraph, null);
for (int i = 0; i < this.correlatedErrors.length; i++) {
for (int j = 0; j < this.correlatedErrors.length; j++) {
this.correlatedErrors[i][j] = false;
}
}
for (int i = 0; i < this.numObserved; i++) {
for (int j = 0; j < this.numLatent; j++) {
Node latentNode = this.purePartitionGraph.getNode(
this.latentNodes.get(j).toString());
Node measuredNode = this.purePartitionGraph.getNode(
this.measuredNodes.get(i).toString());
this.latentParent[i][j] =
this.purePartitionGraph.isParentOf(latentNode, measuredNode);
}
for (int j = i; j < this.numObserved; j++) {
this.observedParent[i][j] = this.observedParent[j][i] = false;
}
}
do {
this.modifiedGraph = false;
double score = gaussianEM(bestGraph);
printlnMessage("Initial score" + score);
impurityScoreSearch(score);
if (this.modifiedGraph) {
printlnMessage(">>>> Structural EM: starting a new round");
bestGraph = updatedGraph();
}
} while (this.modifiedGraph);
boolean[][] impurities = new boolean[this.numObserved][this.numObserved];
for (int i = 0; i < this.numObserved; i++) {
List parents = bestGraph.getParents(
bestGraph.getNode(this.measuredNodes.get(i).toString()));
if (parents.size() > 1) {
boolean latent_found = false;
for (Node o : parents) {
if (o.getNodeType() == NodeType.LATENT) {
if (latent_found) {
impurities[i][i] = true;
break;
} else {
latent_found = true;
}
}
}
} else {
impurities[i][i] = false;
}
for (int j = i + 1; j < this.numObserved; j++) {
impurities[i][j] = this.correlatedErrors[i][j] ||
this.observedParent[i][j] || this.observedParent[j][i];
impurities[j][i] = impurities[i][j];
}
}
if (((TetradTestContinuous) this.tetradTest).getTestType() ==
BpcTestType.GAUSSIAN_SCORE) {
bestGraph = removeMarkedImpurities(bestGraph, impurities);
}
return bestGraph;
}
private void structuralEmInitialization(List partition) {
// Initialize semGraph
this.observableNames = new HashMap<>();
this.latentNames = new HashMap<>();
this.numObserved = 0;
this.numLatent = 0;
this.latentNodes = new ArrayList<>();
this.measuredNodes = new ArrayList<>();
this.basicGraph = new EdgeListGraph();
for (int p = 0; p < partition.size(); p++) {
int[] next = partition.get(p);
Node newLatent = new GraphNode("_L" + p);
newLatent.setNodeType(NodeType.LATENT);
this.basicGraph.addNode(newLatent);
this.latentNodes.forEach(previousLatent -> this.basicGraph.addDirectedEdge(previousLatent, newLatent));
this.latentNodes.add(newLatent);
this.latentNames.put(newLatent.toString(), this.numLatent);
this.numLatent++;
for (int j : next) {
Node newNode = new GraphNode(this.tetradTest.getVarNames()[j]);
this.basicGraph.addNode(newNode);
this.basicGraph.addDirectedEdge(newLatent, newNode);
this.observableNames.put(newNode.toString(), this.numObserved);
this.measuredNodes.add(newNode);
this.numObserved++;
}
}
if (this.numLatent + this.numObserved < 1) {
throw new IllegalArgumentException(
"Input clusters must contain at least one variable.");
}
this.clusterId = new int[this.numObserved];
int count = 0;
for (int p = 0; p < partition.size(); p++) {
int[] next = partition.get(p);
for (int i = 0; i < next.length; i++) {
this.clusterId[count++] = p;
}
}
this.purePartitionGraph = new SemGraph(this.basicGraph);
this.purePartitionGraph.setShowErrorTerms(true);
if (((TetradTestContinuous) this.tetradTest).getTestType() ==
BpcTestType.NONE) {
return;
}
//Information for graph modification
this.correlatedErrors = new boolean[this.numObserved][this.numObserved];
this.latentParent = new boolean[this.numObserved][this.numLatent];
this.observedParent = new boolean[this.numObserved][this.numObserved];
//Information for MAG expectation
this.Cyy = new double[this.numObserved][this.numObserved];
this.bestCyy = new double[this.numObserved][this.numObserved];
this.bestCyz = new double[this.numObserved][this.numLatent];
this.bestCzz = new double[this.numLatent][this.numLatent];
this.covarianceMatrix =
this.tetradTest.getCovMatrix();
String[] varNames =
this.covarianceMatrix.getVariableNames().toArray(new String[0]);
double[][] cov = this.covarianceMatrix.getMatrix().toArray();
for (int i = 0; i < cov.length; i++) {
for (int j = 0; j < cov.length; j++) {
if (this.observableNames.get(varNames[i]) != null &&
this.observableNames.get(varNames[j]) != null) {
this.Cyy[this.observableNames.get(
varNames[i])][this.observableNames
.get(varNames[j])] = cov[i][j];
}
}
}
//Information for MAG maximization
this.parents = new int[this.numObserved][];
this.spouses = new int[this.numObserved][];
this.nSpouses = new int[this.numObserved];
this.parentsLat = new int[this.numLatent][];
this.parentsL = new boolean[this.numObserved][];
this.parentsCov = new double[this.numObserved][][];
this.parentsChildCov = new double[this.numObserved][];
this.parentsLatCov = new double[this.numLatent][][];
this.parentsChildLatCov = new double[this.numLatent][];
this.pseudoParentsCov = new double[this.numObserved][][];
this.pseudoParentsChildCov = new double[this.numObserved][];
this.covErrors = new double[this.numObserved][this.numObserved];
this.oldCovErrors = new double[this.numObserved][this.numObserved];
this.sampleCovErrors = new double[this.numObserved][this.numObserved];
this.varErrorLatent = new double[this.numLatent];
this.omega = new double[this.numLatent + this.numObserved - 1][
this.numLatent + this.numObserved - 1];
this.omegaI = new double[this.numLatent + this.numObserved - 1];
this.selectedInverseOmega = new double[this.numObserved][][];
this.auxInverseOmega = new double[this.numObserved][][];
this.parentsResidualsCovar = new double[this.numObserved][][];
this.iResidualsCovar =
new double[this.numObserved + this.numLatent - 1];
this.betas =
new double[this.numObserved][this.numObserved + this.numLatent];
this.oldBetas =
new double[this.numObserved][this.numObserved + this.numLatent];
this.betasLat = new double[this.numLatent][this.numLatent];
}
private void printMessage(String message) {
if (this.outputMessage) {
System.out.print(message);
}
}
private void printlnMessage(String message) {
if (this.outputMessage) {
System.out.println(message);
}
}
private void printlnMessage() {
if (this.outputMessage) {
System.out.println();
}
}
private void printClustering(List clustering) {
for (Object o : clustering) {
int[] c = (int[]) o;
printCluster(c);
}
}
private void printCluster(int[] c) {
String[] sorted = new String[c.length];
for (int i = 0; i < c.length; i++) {
sorted[i] = this.tetradTest.getVarNames()[c[i]];
}
for (int i = 0; i < sorted.length - 1; i++) {
String min = sorted[i];
int min_idx = i;
for (int j = i + 1; j < sorted.length; j++) {
if (sorted[j].compareTo(min) < 0) {
min = sorted[j];
min_idx = j;
}
}
String temp = sorted[i];
sorted[i] = min;
sorted[min_idx] = temp;
}
for (String s : sorted) {
printMessage(s + " ");
}
printlnMessage();
}
private double gaussianEM(SemGraph semdag) {
double score, newScore = -Double.MAX_VALUE, bestScore =
-Double.MAX_VALUE;
SemPm semPm = new SemPm(semdag);
semdag.setShowErrorTerms(true);
for (int p = 0; p < this.numObserved; p++) {
System.arraycopy(this.Cyy[p], 0, this.bestCyy[p], 0, this.numObserved);
if (this.Cyz != null) {
if (this.numLatent >= 0) System.arraycopy(this.Cyz[p], 0, this.bestCyz[p], 0, this.numLatent);
}
}
if (this.Czz != null) {
for (int p = 0; p < this.numLatent; p++) {
System.arraycopy(this.Czz[p], 0, this.bestCzz[p], 0, this.numLatent);
}
}
initializeGaussianEM(semdag);
for (int i = 0; i < 3; i++) {
System.out.println("--Trial " + i);
SemIm semIm;
semIm = new SemIm(semPm);
semIm.setCovMatrix(this.covarianceMatrix);
do {
score = newScore;
gaussianExpectation(semIm);
newScore = gaussianMaximization(semIm);
if (newScore == -Double.MAX_VALUE) {
break;
}
} while (FastMath.abs(score - newScore) > 1.E-3);
System.out.println(newScore);
if (newScore > bestScore && !Double.isInfinite(newScore)) {
bestScore = newScore;
for (int p = 0; p < this.numObserved; p++) {
System.arraycopy(this.Cyy[p], 0, this.bestCyy[p], 0, this.numObserved);
if (this.numLatent >= 0) System.arraycopy(this.Cyz[p], 0, this.bestCyz[p], 0, this.numLatent);
}
for (int p = 0; p < this.numLatent; p++) {
System.arraycopy(this.Czz[p], 0, this.bestCzz[p], 0, this.numLatent);
}
}
}
for (int p = 0; p < this.numObserved; p++) {
System.arraycopy(this.bestCyy[p], 0, this.Cyy[p], 0, this.numObserved);
if (this.numLatent >= 0) System.arraycopy(this.bestCyz[p], 0, this.Cyz[p], 0, this.numLatent);
}
for (int p = 0; p < this.numLatent; p++) {
System.arraycopy(this.bestCzz[p], 0, this.Czz[p], 0, this.numLatent);
}
if (Double.isInfinite(bestScore)) {
System.out.println("* * Warning: Heywood case in this step");
return -Double.MAX_VALUE;
}
//System.exit(0);
return bestScore;
}
private void initializeGaussianEM(SemGraph semMag) {
//Build parents and spouses indices
for (int i = 0; i < this.numLatent; i++) {
Node node = this.latentNodes.get(i);
if (semMag.getParents(node).size() > 0) {
this.parentsLat[i] =
new int[semMag.getParents(node).size() - 1];
int count = 0;
for (Node parent : semMag.getParents(node)) {
if (parent.getNodeType() == NodeType.LATENT) {
this.parentsLat[i][count++] =
this.latentNames.get(
parent.getName());
}
}
this.parentsLatCov[i] =
new double[this.parentsLat[i].length][this.parentsLat[i].length];
this.parentsChildLatCov[i] =
new double[this.parentsLat[i].length];
}
}
boolean[][] correlatedErrors =
new boolean[this.numObserved][this.numObserved];
for (int i = 0; i < this.numObserved; i++) {
for (int j = 0; j < this.numObserved; j++) {
correlatedErrors[i][j] = false;
}
}
for (Edge nextEdge : semMag.getEdges()) {
if (nextEdge.getEndpoint1() == Endpoint.ARROW &&
nextEdge.getEndpoint2() == Endpoint.ARROW) {
//By construction, getNode1() and getNode2() are error nodes. They have only one child each.
Iterator it1 = semMag.getChildren(nextEdge.getNode1())
.iterator();
Node measure1 = it1.next();
Iterator it2 = semMag.getChildren(nextEdge.getNode2())
.iterator();
Node measure2 = it2.next();
correlatedErrors[this.observableNames.get(
measure1.getName())][this.observableNames
.get(measure2.getName())] = true;
correlatedErrors[this.observableNames.get(
measure2.getName())][this.observableNames.get(measure1.getName())] = true;
}
}
for (int i = 0; i < this.numObserved; i++) {
Node node = this.measuredNodes.get(i);
this.parents[i] = new int[semMag.getParents(node).size() - 1];
this.parentsL[i] = new boolean[semMag.getParents(node).size() - 1];
int count = 0;
for (Node parent : semMag.getParents(node)) {
if (parent.getNodeType() == NodeType.LATENT) {
this.parents[i][count] =
this.latentNames.get(parent.getName());
this.parentsL[i][count++] = true;
} else if (parent.getNodeType() == NodeType.MEASURED) {
this.parents[i][count] =
this.observableNames.get(
parent.getName());
this.parentsL[i][count++] = false;
}
}
int numCovar = 0;
for (int j = 0; j < correlatedErrors.length; j++) {
if (i != j && correlatedErrors[i][j]) {
numCovar++;
}
}
if (numCovar > 0) {
this.spouses[i] = new int[numCovar];
int countS = 0;
for (int j = 0; j < this.numObserved; j++) {
if (i == j) {
continue;
}
if (correlatedErrors[i][j]) {
this.spouses[i][countS++] = j;
}
}
this.nSpouses[i] = countS;
} else {
this.spouses[i] = null;
this.nSpouses[i] = 0;
}
this.parentsCov[i] =
new double[this.parents[i].length][this.parents[i].length];
this.parentsChildCov[i] = new double[this.parents[i].length];
this.pseudoParentsCov[i] =
new double[this.parents[i].length + this.nSpouses[i]][
this.parents[i].length + this.nSpouses[i]];
this.pseudoParentsChildCov[i] =
new double[this.parents[i].length + this.nSpouses[i]];
this.parentsResidualsCovar[i] = new double[this.parents[i].length][
this.numLatent + this.numObserved - 1];
this.selectedInverseOmega[i] = new double[this.nSpouses[i]][
this.numLatent + this.numObserved - 1];
this.auxInverseOmega[i] = new double[this.nSpouses[i]][
this.numLatent + this.numObserved - 1];
}
}
/**
* The expectation step for the structural EM algorithm. This is heavily based on "EM Algorithms for ML Factor
* Analysis", by Rubin and Thayer (Psychometrika, 1982)
*/
private void gaussianExpectation(SemIm semIm) {
//Get the parameters
double[][] beta =
new double[this.numLatent][this.numLatent]; //latent-to-latent coefficients
double[][] fi =
new double[this.numLatent][this.numLatent]; //latent error terms covariance
double[][] lambdaI =
new double[this.numObserved][this.numObserved]; //observed-to-indicatorcoefficients
double[][] lambdaL =
new double[this.numObserved][this.numLatent]; //latent-to-indicatorcoefficients
double[][] tau =
new double[this.numObserved][this.numObserved]; //measurement error variance
//Note: error covariance matrix tau is usually *not* diagonal, unlike the implementation of other
//structural EM algorithm such as in MimBuildScoreSearch.
for (int i = 0; i < this.numLatent; i++) {
for (int j = 0; j < this.numLatent; j++) {
beta[i][j] = 0.;
fi[i][j] = 0.;
}
}
for (int i = 0; i < this.numObserved; i++) {
for (int j = 0; j < this.numLatent; j++) {
lambdaL[i][j] = 0.;
}
}
for (int i = 0; i < this.numObserved; i++) {
for (int j = 0; j < this.numObserved; j++) {
tau[i][j] = 0.;
lambdaI[i][j] = 0.;
}
}
List parameters = semIm.getFreeParameters();
double[] paramValues = semIm.getFreeParamValues();
for (int i = 0; i < parameters.size(); i++) {
Parameter parameter = parameters.get(i);
if (parameter.getType() == ParamType.COEF) {
Node from = parameter.getNodeA();
Node to = parameter.getNodeB();
if (to.getNodeType() == NodeType.MEASURED &&
from.getNodeType() == NodeType.LATENT) {
//latent-to-indicator edge
int position1 = this.latentNames.get(from.getName());
int position2 = this.observableNames.get(to.getName());
lambdaL[position2][position1] = paramValues[i];
} else if (to.getNodeType() == NodeType.MEASURED &&
from.getNodeType() == NodeType.MEASURED) {
//indicator-to-indicator edge
int position1 =
this.observableNames.get(from.getName());
int position2 = this.observableNames.get(to.getName());
lambdaI[position2][position1] = paramValues[i];
} else if (to.getNodeType() == NodeType.LATENT) {
//latent-to-latent edge
int position1 = this.latentNames.get(from.getName());
int position2 = this.latentNames.get(to.getName());
beta[position2][position1] = paramValues[i];
}
} else if (parameter.getType() == ParamType.VAR) {
Node exo = parameter.getNodeA();
if (exo.getNodeType() == NodeType.ERROR) {
Iterator ci = semIm.getSemPm().getGraph().getChildren(exo)
.iterator();
exo = ci.next(); //Assuming error nodes have only one children in SemGraphs...
}
if (exo.getNodeType() == NodeType.LATENT) {
fi[this.latentNames.get(
exo.getName())][this.latentNames
.get(exo.getName())] = paramValues[i];
} else {
tau[this.observableNames.get(
exo.getName())][this.observableNames
.get(exo.getName())] = paramValues[i];
}
} else if (parameter.getType() == ParamType.COVAR) {
Node exo1 = parameter.getNodeA();
Node exo2 = parameter.getNodeB();
//exo1.getNodeType and exo1.getNodeType *should* be error terms of measured variables
//We will change the pointers to point to their respective indicators
exo1 = semIm.getSemPm().getGraph().getVarNode(exo1);
exo2 = semIm.getSemPm().getGraph().getVarNode(exo2);
tau[this.observableNames.get(
exo1.getName())][this.observableNames
.get(exo2.getName())] = tau[this.observableNames
.get(exo2.getName())][this.observableNames
.get(exo1.getName())] = paramValues[i];
}
}
//Fill expected sufficiente statistics accordingly to the order of
//the variables table
double[][] identity = new double[this.numLatent][this.numLatent];
for (int i = 0; i < this.numLatent; i++) {
for (int j = 0; j < this.numLatent; j++) {
if (i == j) {
identity[i][j] = 1.;
} else {
identity[i][j] = 0.;
}
}
}
double[][] identityI = new double[this.numObserved][this.numObserved];
for (int i = 0; i < this.numObserved; i++) {
for (int j = 0; j < this.numObserved; j++) {
if (i == j) {
identityI[i][j] = 1.;
} else {
identityI[i][j] = 0.;
}
}
}
double[][] iMinusB =
MatrixUtils.inverse(MatrixUtils.subtract(identity, beta));
double[][] latentImpliedCovar = MatrixUtils.product(iMinusB,
MatrixUtils.product(fi, MatrixUtils.transpose(iMinusB)));
double[][] iMinusI =
MatrixUtils.inverse(MatrixUtils.subtract(identityI, lambdaI));
double[][] indImpliedCovar = MatrixUtils.product(MatrixUtils.product(
iMinusI, MatrixUtils.sum(MatrixUtils.product(
MatrixUtils.product(lambdaL, latentImpliedCovar),
MatrixUtils.transpose(lambdaL)), tau)),
MatrixUtils.transpose(iMinusI));
double[][] loadingLatentCovar = MatrixUtils.product(iMinusI,
MatrixUtils.product(lambdaL, latentImpliedCovar));
double[][] smallDelta = MatrixUtils.product(
MatrixUtils.inverse(indImpliedCovar), loadingLatentCovar);
double[][] bigDelta = MatrixUtils.subtract(latentImpliedCovar,
MatrixUtils.product(MatrixUtils.transpose(loadingLatentCovar),
smallDelta));
this.Cyz = MatrixUtils.product(this.Cyy, smallDelta);
this.Czz = MatrixUtils.sum(
MatrixUtils.product(MatrixUtils.transpose(smallDelta), this.Cyz),
bigDelta);
}
private double gaussianMaximization(SemIm semIm) {
semIm.getSemPm().getGraph().setShowErrorTerms(true);
//SemIm realIm = getDummyExample();
//semIm = SemIm.newInstance(realIm.getEstIm());
//Fill matrices with semIm parameters
for (int i = 0; i < this.numObserved; i++) {
for (int j = 0; j < this.numObserved + this.numLatent; j++) {
this.betas[i][j] = 0.;
}
}
for (int i = 0; i < this.numLatent; i++) {
for (int j = 0; j < this.numLatent; j++) {
this.betasLat[i][j] = 0.;
}
}
for (int i = 0; i < this.numObserved; i++) {
for (int j = 0; j < this.numObserved; j++) {
this.covErrors[i][j] = 0.;
}
}
for (Parameter nextP : semIm.getFreeParameters()) {
if (nextP.getType() == ParamType.COEF) {
Node node1 = nextP.getNodeA();
Node node2 = nextP.getNodeB();
if (node1.getNodeType() == NodeType.LATENT &&
node2.getNodeType() == NodeType.LATENT) {
continue;
}
Node latent = null, observed = null;
if (node1.getNodeType() == NodeType.LATENT) {
latent = node1;
observed = node2;
} else if (node2.getNodeType() == NodeType.LATENT) {
latent = node2;
observed = node1;
}
if (latent != null) {
int index1 =
this.latentNames.get(latent.getName());
int index2 = this.observableNames.get(
observed.getName());
this.betas[index2][index1] = semIm.getParamValue(nextP);
} else {
int index1 =
this.observableNames.get(node1.getName());
int index2 =
this.observableNames.get(node2.getName());
if (semIm.getSemPm().getGraph().isParentOf(node1, node2)) {
this.betas[index2][this.numLatent + index1] =
semIm.getParamValue(nextP);
} else {
this.betas[index1][this.numLatent + index2] =
semIm.getParamValue(nextP);
}
}
} else if (nextP.getType() == ParamType.COVAR) {
Node exo1 = nextP.getNodeA();
Node exo2 = nextP.getNodeB();
//exo1.getNodeType and exo1.getNodeType *should* be error terms of measured variables
//We will change the pointers to point to their respective indicators
exo1 = semIm.getSemPm().getGraph().getVarNode(exo1);
exo2 = semIm.getSemPm().getGraph().getVarNode(exo2);
int index1 = this.observableNames.get(exo1.getName());
int index2 = this.observableNames.get(exo2.getName());
this.covErrors[index1][index2] =
this.covErrors[index2][index1] =
semIm.getParamValue(nextP);
} else if (nextP.getType() == ParamType.VAR) {
Node exo = nextP.getNodeA();
if (exo.getNodeType() == NodeType.LATENT) {
continue;
}
exo = semIm.getSemPm().getGraph().getVarNode(exo);
if (exo.getNodeType() == NodeType.MEASURED) {
int index =
this.observableNames.get(exo.getName());
this.covErrors[index][index] = semIm.getParamValue(nextP);
}
}
}
//Find estimates for the latent->latent edges and latent variances
//Assuming latents[0] is always the exogenous node in the latent layer
this.varErrorLatent[0] = this.Czz[0][0];
for (int i = 1; i < this.numLatent; i++) {
for (int j = 0; j < this.parentsLat[i].length; j++) {
this.parentsChildLatCov[i][j] =
this.Czz[i][this.parentsLat[i][j]];
for (int k = j; k < this.parentsLat[i].length; k++) {
this.parentsLatCov[i][j][k] =
this.Czz[this.parentsLat[i][j]][this.parentsLat[i][k]];
this.parentsLatCov[i][k][j] = this.parentsLatCov[i][j][k];
}
}
double[] betaL = MatrixUtils.product(
MatrixUtils.inverse(this.parentsLatCov[i]),
this.parentsChildLatCov[i]);
this.varErrorLatent[i] = this.Czz[i][i] -
MatrixUtils.innerProduct(this.parentsChildLatCov[i], betaL);
for (int j = 0; j < this.parentsLat[i].length; j++) {
this.betasLat[i][this.parentsLat[i][j]] = betaL[j];
}
}
//Initialize the covariance matrix for the parents of every observed node
for (int i = 0; i < this.numObserved; i++) {
for (int j = 0; j < this.parents[i].length; j++) {
if (this.parentsL[i][j]) {
this.parentsChildCov[i][j] =
this.Cyz[i][this.parents[i][j]];
} else {
this.parentsChildCov[i][j] =
this.Cyy[i][this.parents[i][j]];
}
for (int k = j; k < this.parents[i].length; k++) {
if (this.parentsL[i][j] && this.parentsL[i][k]) {
this.parentsCov[i][j][k] =
this.Czz[this.parents[i][j]][this.parents[i][k]];
} else if (!this.parentsL[i][j] && this.parentsL[i][k]) {
this.parentsCov[i][j][k] =
this.Cyz[this.parents[i][j]][this.parents[i][k]];
} else if (this.parentsL[i][j] && !this.parentsL[i][k]) {
this.parentsCov[i][j][k] =
this.Cyz[this.parents[i][k]][this.parents[i][j]];
} else {
this.parentsCov[i][j][k] =
this.Cyy[this.parents[i][j]][this.parents[i][k]];
}
this.parentsCov[i][k][j] = this.parentsCov[i][j][k];
}
}
}
//ICF algorithm of Drton and Richardson to find estimates for the other edges and variances/covariances
double change;
int iter = 0;
do {
for (int i = 0; i < this.covErrors.length; i++) {
if (this.covErrors.length >= 0)
System.arraycopy(this.covErrors[i], 0, this.oldCovErrors[i], 0, this.covErrors.length);
}
for (int i = 0; i < this.numObserved; i++) {
if (this.betas[i].length >= 0)
System.arraycopy(this.betas[i], 0, this.oldBetas[i], 0, this.betas[i].length);
}
for (int i = 0; i < this.numObserved; i++) {
//Build matrix Omega_{-i,-i} as defined in Drton and Richardson (2003)
for (int ii = 0; ii < this.omega.length; ii++) {
for (int j = 0; j < this.omega.length; j++) {
this.omega[ii][j] = 0.;
}
}
for (int ii = 0; ii < this.numLatent; ii++) {
this.omegaI[ii] = 0.;
this.omega[ii][ii] = this.varErrorLatent[ii];
}
for (int ii = 0; ii < this.numObserved; ii++) {
if (ii > i) {
this.omegaI[this.numLatent + ii - 1] =
this.covErrors[i][ii];
this.omega[this.numLatent + ii - 1][
this.numLatent + ii - 1] =
this.covErrors[ii][ii];
} else if (ii < i) {
this.omegaI[this.numLatent + ii] =
this.covErrors[i][ii];
this.omega[this.numLatent + ii][this.numLatent + ii] =
this.covErrors[ii][ii];
}
}
for (int ii = 0; ii < this.numObserved; ii++) {
int index_ii;
if (ii > i) {
index_ii = this.numLatent + ii - 1;
} else if (ii < i) {
index_ii = this.numLatent + ii;
} else {
continue;
}
for (int j = 0; j < this.nSpouses[ii]; j++) {
if (this.spouses[ii][j] > i) {
this.omega[index_ii][
this.numLatent + this.spouses[ii][j] - 1] =
this.covErrors[ii][this.spouses[ii][j]];
} else if (this.spouses[ii][j] < i) {
this.omega[index_ii][this.numLatent +
this.spouses[ii][j]] =
this.covErrors[ii][this.spouses[ii][j]];
}
}
}
//Find new residuals covariance matrix for every ii != i
for (int ii = 0; ii < this.numObserved; ii++) {
if (ii == i) {
continue;
}
for (int j = ii; j < this.numObserved; j++) {
if (j == i) {
continue;
}
this.sampleCovErrors[ii][j] = this.Cyy[ii][j];
for (int p = 0; p < this.parents[ii].length; p++) {
if (this.parentsL[ii][p]) {
this.sampleCovErrors[ii][j] -=
this.betas[ii][this.parents[ii][p]] *
this.Cyz[j][this.parents[ii][p]];
} else {
this.sampleCovErrors[ii][j] -= this.betas[ii][
this.numLatent + this.parents[ii][p]] *
this.Cyy[j][this.parents[ii][p]];
}
}
for (int p = 0; p < this.parents[j].length; p++) {
if (this.parentsL[j][p]) {
this.sampleCovErrors[ii][j] -=
this.betas[j][this.parents[j][p]] *
this.Cyz[ii][this.parents[j][p]];
} else {
this.sampleCovErrors[ii][j] -= this.betas[j][
this.numLatent + this.parents[j][p]] *
this.Cyy[ii][this.parents[j][p]];
}
}
for (int p1 = 0; p1 < this.parents[ii].length; p1++) {
for (int p2 = 0; p2 < this.parents[j].length; p2++) {
if (this.parentsL[ii][p1] &&
this.parentsL[j][p2]) {
this.sampleCovErrors[ii][j] +=
this.betas[ii][this.parents[ii][p1]] *
this.betas[j][this.parents[j][p2]] *
this.Czz[this.parents[ii][p1]][this.parents[j][p2]];
} else if (this.parentsL[ii][p1] &&
!this.parentsL[j][p2]) {
this.sampleCovErrors[ii][j] +=
this.betas[ii][this.parents[ii][p1]] *
this.betas[j][this.numLatent +
this.parents[j][p2]] *
this.Cyz[this.parents[j][p2]][this.parents[ii][p1]];
} else if (!this.parentsL[ii][p1] &&
this.parentsL[j][p2]) {
this.sampleCovErrors[ii][j] +=
this.betas[ii][this.numLatent +
this.parents[ii][p1]] *
this.betas[j][this.parents[j][p2]] *
this.Cyz[this.parents[ii][p1]][this.parents[j][p2]];
} else {
this.sampleCovErrors[ii][j] +=
this.betas[ii][this.numLatent +
this.parents[ii][p1]] *
this.betas[j][this.numLatent +
this.parents[j][p2]] *
this.Cyy[this.parents[ii][p1]][this.parents[j][p2]];
}
}
}
this.sampleCovErrors[j][ii] =
this.sampleCovErrors[ii][j];
}
}
//First, find the covariance of the parents of i and the residuals \epsilon_{-i}
for (int ii = 0; ii < this.parents[i].length; ii++) {
//covariance of the parent wrt every residual of latents
if (this.parentsL[i][ii]) {
this.parentsResidualsCovar[i][ii][0] =
this.Czz[this.parents[i][ii]][0];
} else {
this.parentsResidualsCovar[i][ii][0] =
this.Cyz[this.parents[i][ii]][0];
}
for (int j = 1; j < this.numLatent; j++) {
if (this.parentsL[i][ii]) {
this.parentsResidualsCovar[i][ii][j] =
this.Czz[this.parents[i][ii]][j];
for (int p = 0; p < this.parentsLat[j].length; p++) {
this.parentsResidualsCovar[i][ii][j] -=
this.betasLat[j][this.parentsLat[j][p]] *
this.Czz[this.parents[i][ii]][this.parentsLat[j][p]];
}
} else {
this.parentsResidualsCovar[i][ii][j] =
this.Cyz[this.parents[i][ii]][j];
for (int p = 0; p < this.parentsLat[j].length; p++) {
this.parentsResidualsCovar[i][ii][j] -=
this.betasLat[j][this.parentsLat[j][p]] *
this.Cyz[this.parents[i][ii]][this.parentsLat[j][p]];
}
}
}
//covariance of the parent wrt every residual of observables (except for i)
for (int j = 0; j < this.numObserved; j++) {
int index_j;
if (j < i) {
index_j = this.numLatent + j;
} else if (j > i) {
index_j = this.numLatent + j - 1;
} else {
continue;
}
if (this.parentsL[i][ii]) {
this.parentsResidualsCovar[i][ii][index_j] =
this.Cyz[j][this.parents[i][ii]];
for (int p = 0; p < this.parents[j].length; p++) {
if (this.parentsL[j][p]) {
this.parentsResidualsCovar[i][ii][index_j] -=
this.betas[j][this.parents[j][p]] *
this.Czz[this.parents[i][ii]][this.parents[j][p]];
} else {
this.parentsResidualsCovar[i][ii][index_j] -=
this.betas[j][this.numLatent +
this.parents[j][p]] *
this.Cyz[this.parents[j][p]][this.parents[i][ii]];
}
}
} else {
this.parentsResidualsCovar[i][ii][index_j] =
this.Cyy[j][this.parents[i][ii]];
for (int p = 0; p < this.parents[j].length; p++) {
if (this.parentsL[j][p]) {
this.parentsResidualsCovar[i][ii][index_j] -=
this.betas[j][this.parents[j][p]] *
this.Cyz[this.parents[i][ii]][this.parents[j][p]];
} else {
this.parentsResidualsCovar[i][ii][index_j] -=
this.betas[j][this.numLatent +
this.parents[j][p]] *
this.Cyy[this.parents[j][p]][this.parents[i][ii]];
}
}
}
}
}
//Now, find the covariance of Y_i with respect to everybody else's residuals
this.iResidualsCovar[0] =
this.Cyz[i][0]; //the first latent is exogenous
for (int j = 1; j < this.numLatent; j++) {
this.iResidualsCovar[j] = this.Cyz[i][j];
for (int p = 0; p < this.parentsLat[j].length; p++) {
this.iResidualsCovar[j] -=
this.betasLat[j][this.parentsLat[j][p]] *
this.Cyz[i][this.parentsLat[j][p]];
}
}
for (int j = 0; j < this.numObserved; j++) {
int index_j;
if (j < i) {
index_j = this.numLatent + j;
} else if (j > i) {
index_j = this.numLatent + j - 1;
} else {
continue;
}
this.iResidualsCovar[index_j] = this.Cyy[i][j];
for (int p = 0; p < this.parents[j].length; p++) {
if (this.parentsL[j][p]) {
this.iResidualsCovar[index_j] -=
this.betas[j][this.parents[j][p]] *
this.Cyz[i][this.parents[j][p]];
} else {
this.iResidualsCovar[index_j] -= this.betas[j][this.numLatent + this.parents[j][p]] *
this.Cyy[i][this.parents[j][p]];
}
}
}
//Transform it to get the covariance of parents of i and pseudo-variables Z_sp(i)
double[][] inverseOmega = MatrixUtils.inverse(this.omega);
for (int ii = 0; ii < this.nSpouses[i]; ii++) {
int sp_index;
if (this.spouses[i][ii] > i) {
sp_index = this.numLatent + this.spouses[i][ii] - 1;
} else {
sp_index = this.numLatent + this.spouses[i][ii];
}
if (this.numLatent + this.numObserved - 1 >= 0)
System.arraycopy(inverseOmega[sp_index], 0, this.selectedInverseOmega[i][ii], 0, this.numLatent + this.numObserved - 1);
}
for (int ii = 0; ii < this.nSpouses[i]; ii++) {
for (int j = 0; j < this.numLatent; j++) {
this.auxInverseOmega[i][ii][j] =
this.selectedInverseOmega[i][ii][j] *
this.varErrorLatent[j];
}
for (int j = 0; j < this.numObserved; j++) {
int index_j;
if (j > i) {
index_j = this.numLatent + j - 1;
} else if (j < i) {
index_j = this.numLatent + j;
} else {
continue;
}
this.auxInverseOmega[i][ii][index_j] = 0;
for (int k = 0; k < this.numObserved; k++) {
int index_k;
if (k > i) {
index_k = this.numLatent + k - 1;
} else if (k < i) {
index_k = this.numLatent + k;
} else {
continue;
}
this.auxInverseOmega[i][ii][index_j] +=
this.selectedInverseOmega[i][ii][index_k] *
this.sampleCovErrors[k][j];
}
}
}
for (int ii = 0; ii < this.parents[i].length; ii++) {
for (int j = ii; j < this.parents[i].length; j++) {
this.pseudoParentsCov[i][ii][j] =
this.pseudoParentsCov[i][j][ii] =
this.parentsCov[i][ii][j];
}
}
for (int ii = 0; ii < this.parents[i].length; ii++) {
for (int j = 0; j < this.nSpouses[i]; j++) {
this.pseudoParentsCov[i][ii][this.parents[i].length +
j] = 0.;
for (int k = 0;
k < this.numLatent + this.numObserved - 1; k++) {
this.pseudoParentsCov[i][ii][this.parents[i]
.length + j] +=
this.parentsResidualsCovar[i][ii][k] *
this.selectedInverseOmega[i][j][k];
}
this.pseudoParentsCov[i][this.parents[i].length +
j][ii] = this.pseudoParentsCov[i][ii][
this.parents[i].length + j];
}
}
for (int ii = 0; ii < this.nSpouses[i]; ii++) {
for (int j = ii; j < this.nSpouses[i]; j++) {
this.pseudoParentsCov[i][this.parents[i].length + ii][
this.parents[i].length + j] = 0;
for (int k = 0;
k < this.numLatent + this.numObserved - 1; k++) {
this.pseudoParentsCov[i][this.parents[i].length +
ii][this.parents[i].length + j] +=
this.auxInverseOmega[i][ii][k] *
this.selectedInverseOmega[i][j][k];
}
this.pseudoParentsCov[i][this.parents[i].length + j][
this.parents[i].length + ii] =
this.pseudoParentsCov[i][this.parents[i]
.length + ii][this.parents[i].length +
j];
if (this.pseudoParentsCov[i][this.parents[i].length +
j][this.parents[i].length + ii] == 0.) {
System.out.println("Zero here... Iter = " + iter);
iter = 1000;
break;
}
}
}
//Get the covariance of parents of i and pseudo-variables Z_sp(i) with respect to i
if (this.parents[i].length >= 0)
System.arraycopy(this.parentsChildCov[i], 0, this.pseudoParentsChildCov[i], 0, this.parents[i].length);
for (int j = 0; j < this.nSpouses[i]; j++) {
this.pseudoParentsChildCov[i][this.parents[i].length + j] =
0;
for (int k = 0;
k < this.numLatent + this.numObserved - 1; k++) {
this.pseudoParentsChildCov[i][this.parents[i].length +
j] += this.selectedInverseOmega[i][j][k] *
this.iResidualsCovar[k];
}
}
//Finally, regress Y_i on {parents} union {Z_i}
//thisI = i;
double[] params = MatrixUtils.product(
MatrixUtils.inverse(this.pseudoParentsCov[i]),
this.pseudoParentsChildCov[i]);
//Update betas and omegas (entries in covErrors)
for (int j = 0; j < this.parents[i].length; j++) {
if (this.parentsL[i][j]) {
this.betas[i][this.parents[i][j]] = params[j];
} else {
this.betas[i][this.numLatent + this.parents[i][j]] =
params[j];
}
}
for (int j = 0; j < this.nSpouses[i]; j++) {
this.covErrors[i][this.spouses[i][j]] =
this.covErrors[this.spouses[i][j]][i] =
params[this.parents[i].length + j];
if (this.spouses[i][j] > i) {
this.omegaI[this.numLatent + this.spouses[i][j] - 1] =
params[this.parents[i].length + j];
} else {
this.omegaI[this.numLatent + this.spouses[i][j]] =
params[this.parents[i].length + j];
}
}
double conditionalVar = this.Cyy[i][i] -
MatrixUtils.innerProduct(this.pseudoParentsChildCov[i],
params);
this.covErrors[i][i] = conditionalVar +
MatrixUtils.innerProduct(
MatrixUtils.product(this.omegaI, inverseOmega),
this.omegaI);
}
change = 0.;
for (int i = 0; i < this.covErrors.length; i++) {
for (int j = i; j < this.covErrors.length; j++) {
change += FastMath.abs(
this.oldCovErrors[i][j] - this.covErrors[i][j]);
}
}
for (int i = 0; i < this.numObserved; i++) {
for (int j = 0; j < this.betas[i].length; j++) {
change += FastMath.abs(this.oldBetas[i][j] - this.betas[i][j]);
}
}
iter++;
//System.out.println("Iteration = " + iter + ", change = " + change);
} while (iter < 200 && change > 0.01);
//Now, copy updated parameters back to semIm
try {
for (int i = 0; i < this.numObserved; i++) {
Node node = semIm.getSemPm().getGraph().getNode(
this.measuredNodes.get(i).toString());
Node nodeErrorTerm = semIm.getSemPm().getGraph().getExogenous(node);
for (int j = 0; j < this.parents[i].length; j++) {
Node parent;
if (this.parentsL[i][j]) {
parent = semIm.getSemPm().getGraph().getNode(
this.latentNodes.get(this.parents[i][j])
.toString());
} else {
parent = semIm.getSemPm().getGraph().getNode(
this.measuredNodes.get(this.parents[i][j])
.toString());
}
if (this.parentsL[i][j]) {
semIm.setParamValue(parent, node,
this.betas[i][this.parents[i][j]]);
} else {
semIm.setParamValue(parent, node, this.betas[i][this.numLatent + this.parents[i][j]]);
}
}
for (int j = 0; j < this.nSpouses[i]; j++) {
if (this.spouses[i][j] > i) {
Node spouse = semIm.getSemPm().getGraph().getNode(
this.measuredNodes.get(this.spouses[i][j])
.toString());
Node spouseErrorTerm = semIm.getSemPm().getGraph().getExogenous(spouse);
semIm.setParamValue(nodeErrorTerm, spouseErrorTerm,
this.covErrors[i][this.spouses[i][j]]);
}
}
}
for (int i = 0; i < this.numLatent; i++) {
Node node = semIm.getSemPm().getGraph().getNode(
this.latentNodes.get(i).toString());
if (semIm.getSemPm().getGraph().getParents(node).size() == 0) {
semIm.setParamValue(node, node, this.varErrorLatent[i]);
} else {
for (Node nextParent : semIm.getSemPm().getGraph().getParents(node)) {
if (nextParent.getNodeType() == NodeType.ERROR) {
semIm.setParamValue(nextParent, nextParent,
this.varErrorLatent[i]);
break;
}
}
for (int j = 0; j < this.parentsLat[i].length; j++) {
Node parent = semIm.getSemPm().getGraph().getNode(
this.latentNodes.get(this.parentsLat[i][j])
.toString());
semIm.setParamValue(parent, node,
this.betasLat[i][this.parentsLat[i][j]]);
}
}
}
return -semIm.getTruncLL() - 0.5 * semIm.getNumFreeParams() *
FastMath.log(this.covarianceMatrix.getSampleSize());
} catch (java.lang.IllegalArgumentException e) {
System.out.println("** Warning: " + e.toString());
return -Double.MAX_VALUE;
}
}
private SemGraph removeMarkedImpurities(SemGraph graph,
boolean[][] impurities) {
printlnMessage();
printlnMessage("** PURIFY: using marked impure pairs");
List latents = new ArrayList<>();
List partition = new ArrayList<>();
for (int i = 0; i < graph.getNodes().size(); i++) {
Node nextLatent = graph.getNodes().get(i);
if (nextLatent.getNodeType() != NodeType.LATENT) {
continue;
}
latents.add(graph.getNodes().get(i));
Iterator cit = graph.getChildren(nextLatent).iterator();
List children = new ArrayList<>();
while (cit.hasNext()) {
Node cnext = cit.next();
if (cnext.getNodeType() == NodeType.MEASURED) {
children.add(cnext);
}
}
int[] newCluster = new int[children.size()];
for (int j = 0; j < children.size(); j++) {
newCluster[j] = this.observableNames.get(
children.get(j).toString());
}
partition.add(newCluster);
}
for (int i = 0; i < impurities.length - 1; i++) {
for (int j = i + 1; j < impurities.length; j++) {
if (impurities[i][j]) {
System.out.println(this.measuredNodes.get(i).toString() + " x " +
this.measuredNodes.get(j).toString());
}
}
}
List latentCliques = new ArrayList<>();
int[] firstClique = new int[latents.size()];
for (int i = 0; i < firstClique.length; i++) {
firstClique[i] = i;
}
latentCliques.add(firstClique);
//Now, ready to purify
for (Object latentClique : latentCliques) {
int[] nextLatentList = (int[]) latentClique;
List nextPartition = new ArrayList<>();
for (int j : nextLatentList) {
nextPartition.add(partition.get(j));
}
List solution = findInducedPureGraph(nextPartition, impurities);
if (solution != null) {
System.out.println("--Solution");
for (Object o : solution) {
int[] c = (int[]) o;
for (int i : c) {
System.out.print(
this.measuredNodes.get(i).toString() + " ");
}
System.out.println();
}
printlnMessage(">> SIZE: " + sizeCluster(solution));
printlnMessage(">> New solution found!");
SemGraph graph2 = new SemGraph();
graph2.setShowErrorTerms(true);
Node[] latentsArray = new Node[solution.size()];
for (int p = 0; p < solution.size(); p++) {
int[] cluster = solution.get(p);
latentsArray[p] =
new GraphNode(ClusterUtils.LATENT_PREFIX + (p + 1));
latentsArray[p].setNodeType(NodeType.LATENT);
graph2.addNode(latentsArray[p]);
for (int i : cluster) {
Node newIndicator = new GraphNode(
this.measuredNodes.get(i).toString());
graph2.addNode(newIndicator);
graph2.addDirectedEdge(latentsArray[p], newIndicator);
}
}
for (int p = 0; p < latentsArray.length - 1; p++) {
for (int q = p + 1; q < latentsArray.length; q++) {
graph2.addDirectedEdge(latentsArray[p],
latentsArray[q]);
}
}
return graph2;
} else {
return null;
}
}
return null;
}
private List findInducedPureGraph(List partition, boolean[][] impurities) {
//Store the ID of all elements for fast access
int[][] elements = new int[sizeCluster(partition)][3];
int countElements = 0;
for (int p = 0; p < partition.size(); p++) {
int[] next = partition.get(p);
for (int j : next) {
elements[countElements][0] = j; // global ID
elements[countElements][1] = p; // set partition ID
countElements++;
}
}
//Count how many impure relations are entailed by each indicator
for (int i = 0; i < elements.length; i++) {
elements[i][2] = 0;
for (int j = 0; j < elements.length; j++) {
if (impurities[elements[i][0]][elements[j][0]]) {
elements[i][2]++; // number of impure relations
}
}
}
//Iteratively eliminate impurities till some solution (or no solution) is found
boolean[] eliminated = new boolean[this.numVars];
for (int[] element : elements) {
eliminated[element[0]] = impurities[element[0]][element[0]];
}
return buildSolution2(elements, eliminated, partition);
}
private int sizeCluster(List cluster) {
int total = 0;
for (Object o : cluster) {
int[] next = (int[]) o;
total += next.length;
}
return total;
}
private List buildSolution2(int[][] elements, boolean[] eliminated,
List partition) {
List solution = new ArrayList<>();
for (Object o : partition) {
int[] next = (int[]) o;
int[] draftArea = new int[next.length];
int draftCount = 0;
for (int j : next) {
for (int[] element : elements) {
if (element[0] == j &&
!eliminated[element[0]]) {
draftArea[draftCount++] = j;
}
}
}
if (draftCount > 0) {
int[] realCluster = new int[draftCount];
System.arraycopy(draftArea, 0, realCluster, 0, draftCount);
solution.add(realCluster);
}
}
if (solution.size() > 0) {
return solution;
} else {
return null;
}
}
private void impurityScoreSearch(double initialScore) {
double score, nextScore = initialScore;
boolean[] changed = new boolean[1];
do {
changed[0] = false;
score = nextScore;
nextScore = addImpuritySearch(score, changed);
if (changed[0]) {
changed[0] = false;
nextScore = deleteImpuritySearch(nextScore, changed);
}
} while (changed[0]);
}
private double addImpuritySearch(double initialScore, boolean[] changed) {
double score, nextScore = initialScore;
int choiceType = -1;
do {
score = nextScore;
int bestChoice1 = -1, bestChoice2 = -1;
for (int i = 0; i < this.numObserved; i++) {
//Add latent->indicator edges
//NOTE: code deactivated. Seems not to be worthy trying.
for (int j = i + 1; j < this.numObserved; j++) {
//Check if one should ignore the possibility of an impurity for this pair
if (forbiddenImpurity(this.measuredNodes.get(i).toString(),
this.measuredNodes.get(j).toString())) {
continue;
}
//indicator -> indicator edges (children of the same latent parent)
//NOTE: code deactivated. Seems not to be worthy trying.
// Here, I am not checking for cycles, and edges are considered only in one direction
//indicator <-> indicator edges
if (!this.correlatedErrors[i][j] && !this.observedParent[i][j] &&
!this.observedParent[j][i]) {
this.correlatedErrors[i][j] = this.correlatedErrors[j][i] = true;
double newScore = scoreCandidate();
System.out.println("Trying impurity " + i + " <-> " + j + " (Score = " + newScore + ")"); //System.exit(0);
if (newScore > nextScore) {
nextScore = newScore;
bestChoice1 = i;
bestChoice2 = j;
choiceType = 2;
}
this.correlatedErrors[i][j] = this.correlatedErrors[j][i] = false;
}
}
}
if (bestChoice1 != -1) {
this.modifiedGraph = true;
switch (choiceType) {
case 0:
this.latentParent[bestChoice1][bestChoice2] = true;
System.out.println(
"****************************Added impurity: " +
this.latentNodes.get(
bestChoice2).toString() +
" --> " + this.measuredNodes.get(
bestChoice1).toString() + " " +
nextScore);
break;
case 1:
this.observedParent[bestChoice1][bestChoice2] = true;
System.out.println(
"****************************Added impurity: " +
this.measuredNodes.get(
bestChoice2).toString() +
" --> " + this.measuredNodes.get(
bestChoice1).toString() + " " +
nextScore);
break;
case 2:
System.out.println(
"****************************Added impurity: " +
this.measuredNodes.get(
bestChoice1).toString() +
" <-> " + this.measuredNodes.get(
bestChoice2).toString() + " " +
nextScore);
this.correlatedErrors[bestChoice1][bestChoice2] =
this.correlatedErrors[bestChoice2][bestChoice1] =
true;
}
changed[0] = true;
}
} while (score < nextScore);
printlnMessage("End of addition round");
return score;
}
private boolean forbiddenImpurity(String name1, String name2) {
if (this.forbiddenList == null) {
return false;
}
for (Set nextPair : this.forbiddenList) {
if (nextPair.contains(name1) && nextPair.contains(name2)) {
return true;
}
}
return false;
}
private double scoreCandidate() {
SemGraph graph = updatedGraph();
initializeGaussianEM(graph);
SemPm semPm = new SemPm(graph);
SemIm semIm = new SemIm(semPm, this.covarianceMatrix);
gaussianMaximization(semIm);
try {
System.out.println("trunk ll = " + semIm.getTruncLL());
return -semIm.getTruncLL() - 0.5 * semIm.getNumFreeParams() *
FastMath.log(this.covarianceMatrix.getSampleSize());
} catch (IllegalArgumentException e) {
return -Double.MAX_VALUE;
}
}
private SemGraph updatedGraph() {
SemGraph output = new SemGraph(this.basicGraph);
output.setShowErrorTerms(true);
for (int i = 0; i < output.getNodes().size() - 1; i++) {
Node node1 = output.getNodes().get(i);
if (node1.getNodeType() != NodeType.MEASURED) {
continue;
}
for (int j = 0; j < output.getNodes().size(); j++) {
Node node2 = output.getNodes().get(j);
if (node2.getNodeType() != NodeType.LATENT) {
continue;
}
int pos1 = this.observableNames.get(
output.getNodes().get(i).toString());
int pos2 = this.latentNames.get(
output.getNodes().get(j).toString());
if (this.latentParent[pos1][pos2] &&
output.getEdge(node1, node2) == null) {
output.addDirectedEdge(node2, node1);
}
}
for (int j = i + 1; j < output.getNodes().size(); j++) {
Node node2 = output.getNodes().get(j);
if (node2.getNodeType() != NodeType.MEASURED) {
continue;
}
Node errnode1 = output.getErrorNode(output.getNodes().get(i));
Node errnode2 = output.getErrorNode(output.getNodes().get(j));
int pos1 = this.observableNames.get(
output.getNodes().get(i).toString());
int pos2 = this.observableNames.get(
output.getNodes().get(j).toString());
if (this.correlatedErrors[pos1][pos2] &&
output.getEdge(errnode1, errnode2) == null) {
output.addBidirectedEdge(errnode1, errnode2);
}
if (this.observedParent[pos1][pos2] &&
output.getEdge(node1, node2) == null) {
output.addDirectedEdge(node2, node1);
} else if (this.observedParent[pos2][pos1] &&
output.getEdge(node1, node2) == null) {
output.addDirectedEdge(node1, node2);
}
}
}
return output;
}
private double deleteImpuritySearch(double initialScore,
boolean[] changed) {
double score, nextScore = initialScore;
int choiceType = -1;
do {
score = nextScore;
int bestChoice1 = -1, bestChoice2 = -1;
for (int i = 0; i < this.numObserved - 1; i++) {
for (int j = i + 1; j < this.numObserved; j++) {
if (this.observedParent[i][j] || this.observedParent[j][i]) {
boolean directionIJ = this.observedParent[i][j];
this.observedParent[i][j] = this.observedParent[j][i] = false;
double newScore = scoreCandidate();
if (newScore > nextScore) {
nextScore = newScore;
bestChoice1 = i;
bestChoice2 = j;
choiceType = 0;
}
if (directionIJ) {
this.observedParent[i][j] = true;
} else {
this.observedParent[j][i] = true;
}
}
if (this.correlatedErrors[i][j]) {
this.correlatedErrors[i][j] = this.correlatedErrors[j][i] = false;
double newScore = scoreCandidate();
if (newScore > nextScore) {
nextScore = newScore;
bestChoice1 = i;
bestChoice2 = j;
choiceType = 1;
}
this.correlatedErrors[i][j] = this.correlatedErrors[j][i] = true;
}
}
}
if (bestChoice1 != -1) {
this.modifiedGraph = true;
switch (choiceType) {
case 0:
if (this.observedParent[bestChoice1][bestChoice2]) {
System.out.println(
"****************************Removed impurity: " +
this.measuredNodes.get(bestChoice2)
.toString() + " --> " +
this.measuredNodes.get(bestChoice1)
.toString() + " " +
nextScore);
} else {
System.out.println(
"****************************Removed impurity: " +
this.measuredNodes.get(bestChoice1)
.toString() + " --> " +
this.measuredNodes.get(bestChoice2)
.toString() + " " +
nextScore);
}
this.observedParent[bestChoice1][bestChoice2] =
this.observedParent[bestChoice2][bestChoice1] =
false;
break;
case 1:
System.out.println(
"****************************Removed impurity: " +
this.measuredNodes.get(
bestChoice1).toString() +
" <-> " + this.measuredNodes.get(
bestChoice2).toString() + " " +
nextScore);
this.correlatedErrors[bestChoice1][bestChoice2] =
this.correlatedErrors[bestChoice2][bestChoice1] =
false;
}
changed[0] = true;
}
} while (score < nextScore);
printlnMessage("End of deletion round");
return score;
}
}
