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///////////////////////////////////////////////////////////////////////////////
// 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.sem;
import edu.cmu.tetrad.data.CovarianceMatrix;
import edu.cmu.tetrad.data.DataSet;
import edu.cmu.tetrad.data.ICovarianceMatrix;
import edu.cmu.tetrad.graph.Graph;
import edu.cmu.tetrad.graph.Node;
import edu.cmu.tetrad.graph.NodeType;
import edu.cmu.tetrad.util.*;
import org.apache.commons.math3.util.FastMath;
import java.io.IOException;
import java.io.ObjectInputStream;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.TreeSet;
/**
* Estimates a SemIm given a CovarianceMatrix and a SemPm. (A DataSet may be substituted for the CovarianceMatrix.) Uses
* regression to do the estimation, so this is only for DAG models. But the DAG model may be reset on the fly and the
* estimation redone. Variables whose parents have not changed will not be reestimated. Intended to speed up estimation
* for algorithm that require repeated estimation of DAG models over the same variables. Assumes all variables are
* measured.
*
* @author josephramsey
*/
public final class DagScorer implements TetradSerializable, Scorer {
private static final long serialVersionUID = 23L;
private final ICovarianceMatrix covMatrix;
private final Matrix edgeCoef;
private final Matrix errorCovar;
private final List variables;
private final Matrix sampleCovar;
private DataSet dataSet;
private Graph dag;
private Matrix implCovarMeasC;
private double logDetSample;
private double fml = Double.NaN;
/**
* Constructs a new SemEstimator that uses the specified optimizer.
*
* @param dataSet a DataSet, all of whose variables are contained in the given SemPm. (They are identified by
* name.)
*/
public DagScorer(DataSet dataSet) {
this(new CovarianceMatrix(dataSet));
this.dataSet = dataSet;
}
/**
* Constructs a new SemEstimator that uses the specified optimizer.
*
* @param covMatrix a covariance matrix, all of whose variables are contained in the given SemPm. (They are
* identified by name.)
*/
public DagScorer(ICovarianceMatrix covMatrix) {
if (covMatrix == null) {
throw new NullPointerException(
"CovarianceMatrix must not be null.");
}
this.variables = covMatrix.getVariables();
this.covMatrix = covMatrix;
int m = this.getVariables().size();
this.edgeCoef = new Matrix(m, m);
this.errorCovar = new Matrix(m, m);
this.sampleCovar = covMatrix.getMatrix();
}
/**
* Generates a simple exemplar of this class to test serialization.
*/
public static Scorer serializableInstance() {
return new DagScorer(CovarianceMatrix.serializableInstance());
}
/**
* Runs the estimator on the data and SemPm passed in through the constructor. Returns the fml score of the
* resulting model.
*/
public double score(Graph dag) {
List changedNodes = getChangedNodes(dag);
for (Node node : changedNodes) {
int i1 = indexOf(node);
getErrorCovar().set(i1, i1, 0);
for (int _j = 0; _j < getVariables().size(); _j++) {
getEdgeCoef().set(_j, i1, 0);
}
if (node.getNodeType() != NodeType.MEASURED) {
continue;
}
int idx = indexOf(node);
List parents = new ArrayList<>(dag.getParents(node));
for (int i = 0; i < parents.size(); i++) {
Node nextParent = parents.get(i);
if (nextParent.getNodeType() == NodeType.ERROR) {
parents.remove(nextParent);
break;
}
}
double variance = getSampleCovar().get(idx, idx);
if (parents.size() > 0) {
Vector nodeParentsCov = new Vector(parents.size());
Matrix parentsCov = new Matrix(parents.size(), parents.size());
for (int i = 0; i < parents.size(); i++) {
int idx2 = indexOf(parents.get(i));
nodeParentsCov.set(i, getSampleCovar().get(idx, idx2));
for (int j = i; j < parents.size(); j++) {
int idx3 = indexOf(parents.get(j));
parentsCov.set(i, j, getSampleCovar().get(idx2, idx3));
parentsCov.set(j, i, getSampleCovar().get(idx3, idx2));
}
}
Vector edges = parentsCov.inverse().times(nodeParentsCov);
for (int i = 0; i < edges.size(); i++) {
int idx2 = indexOf(parents.get(i));
this.edgeCoef.set(idx2, indexOf(node), edges.get(i));
}
variance -= nodeParentsCov.dotProduct(edges);
}
this.errorCovar.set(i1, i1, variance);
}
this.dag = dag;
this.fml = Double.NaN;
return getFml();
}
private int indexOf(Node node) {
for (int i = 0; i < getVariables().size(); i++) {
if (node.getName().equals(this.getVariables().get(i).getName())) {
return i;
}
}
throw new IllegalArgumentException("Dag must have the same nodes as the data.");
}
private List getChangedNodes(Graph dag) {
if (this.dag == null) {
return dag.getNodes();
}
if (!new HashSet<>(this.getVariables()).equals(new HashSet<>(dag.getNodes()))) {
System.out.println(new TreeSet<>(dag.getNodes()));
System.out.println(new TreeSet<>(this.variables));
throw new IllegalArgumentException("Dag must have the same nodes as the data.");
}
List changedNodes = new ArrayList<>();
for (Node node : dag.getNodes()) {
if (!new HashSet<>(this.dag.getParents(node)).equals(new HashSet<>(dag.getParents(node)))) {
changedNodes.add(node);
}
}
return changedNodes;
}
public ICovarianceMatrix getCovMatrix() {
return this.covMatrix;
}
/**
* @return a string representation of the Sem.
*/
public String toString() {
return "\nSemEstimator";
}
/**
* The value of the maximum likelihood function for the getModel the model (Bollen 107). To optimize, this should be
* minimized.
*/
public double getFml() {
if (!Double.isNaN(this.fml)) {
return this.fml;
}
Matrix implCovarMeas; // Do this once.
try {
implCovarMeas = implCovarMeas();
} catch (Exception e) {
e.printStackTrace();
return Double.NaN;
}
Matrix sampleCovar = sampleCovar();
double logDetSigma = logDet(implCovarMeas);
double traceSSigmaInv = traceABInv(sampleCovar, implCovarMeas);
double logDetSample = logDetSample();
int pPlusQ = getMeasuredNodes().size();
double fml = logDetSigma + traceSSigmaInv - logDetSample - pPlusQ;
if (FastMath.abs(fml) < 0) {
fml = 0.0;
}
this.fml = fml;
return fml;
}
private Matrix sampleCovar() {
return getSampleCovar();
}
private Matrix implCovarMeas() {
computeImpliedCovar();
return this.implCovarMeasC;
}
/**
* @return BIC score, calculated as chisq - dof. This is equal to getFullBicScore() up to a constant.
*/
public double getBicScore() {
int dof = getDof();
return getChiSquare() - dof * FastMath.log(getSampleSize());
}
/**
* @return the chi square value for the model.
*/
public double getChiSquare() {
return (getSampleSize() - 1) * getFml();
}
/**
* @return the p-value for the model.
*/
public double getPValue() {
return 1.0 - ProbUtils.chisqCdf(getChiSquare(), getDof());
}
/**
* Adds semantic checks to the default deserialization method. This method must have the standard signature for a
* readObject method, and the body of the method must begin with "s.defaultReadObject();". Other than that, any
* semantic checks can be specified and do not need to stay the same from version to version. A readObject method of
* this form may be added to any class, even if Tetrad sessions were previously saved out using a version of the
* class that didn't include it. (That's what the "s.defaultReadObject();" is for. See J. Bloch, Effective Java, for
* help.
*/
private void readObject
(ObjectInputStream
s)
throws IOException, ClassNotFoundException {
s.defaultReadObject();
if (getCovMatrix() == null) {
throw new NullPointerException();
}
}
/**
* Computes the implied covariance matrices of the Sem. There are two:
* implCovar contains the covariances of all the variables and
* implCovarMeas contains covariance for the measured variables
* only.
*/
private void computeImpliedCovar() {
// Note. Since the sizes of the temp matrices in this calculation
// never change, we ought to be able to reuse them.
Matrix implCovarC = MatrixUtils.impliedCovar(edgeCoef().transpose(), errCovar());
// Submatrix of implied covar for measured vars only.
int size = getMeasuredNodes().size();
this.implCovarMeasC = new Matrix(size, size);
for (int i = 0; i < size; i++) {
for (int j = 0; j < size; j++) {
this.implCovarMeasC.set(i, j, implCovarC.get(i, j));
}
}
}
private Matrix errCovar() {
return getErrorCovar();
}
private Matrix edgeCoef() {
return getEdgeCoef();
}
private double logDet(Matrix matrix2D) {
return FastMath.log(matrix2D.det());
}
private double traceAInvB(Matrix A, Matrix B) {
// Note that at this point the sem and the sample covar MUST have the
// same variables in the same order.
Matrix inverse = A.inverse();
Matrix product = inverse.times(B);
double trace = product.trace();
// double trace = MatrixUtils.trace(product);
if (trace < -1e-8) {
throw new IllegalArgumentException("Trace was negative: " + trace);
}
return trace;
}
private double traceABInv(Matrix A, Matrix B) {
// Note that at this point the sem and the sample covar MUST have the
// same variables in the same order.
try {
Matrix product = A.times(B.inverse());
double trace = product.trace();
if (trace < -1e-8) {
throw new IllegalArgumentException("Trace was negative: " + trace);
}
return trace;
} catch (Exception e) {
System.out.println(B);
throw new RuntimeException(e);
}
}
private double logDetSample() {
if (this.logDetSample == 0.0 && sampleCovar() != null) {
double det = sampleCovar().det();
this.logDetSample = FastMath.log(det);
}
return this.logDetSample;
}
public DataSet getDataSet() {
return this.dataSet;
}
public int getNumFreeParams() {
return this.dag.getEdges().size() + this.dag.getNodes().size();
}
public int getDof() {
return (this.dag.getNodes().size() * (this.dag.getNodes().size() + 1)) / 2 - getNumFreeParams();
}
public int getSampleSize() {
return this.covMatrix.getSampleSize();
}
public List getMeasuredNodes() {
return this.getVariables();
}
public Matrix getSampleCovar() {
return this.sampleCovar;
}
public Matrix getEdgeCoef() {
return this.edgeCoef;
}
public Matrix getErrorCovar() {
return this.errorCovar;
}
public List getVariables() {
return this.variables;
}
public SemIm getEstSem() {
SemPm pm = new SemPm(this.dag);
if (this.dataSet != null) {
return new SemEstimator(this.dataSet, pm, new SemOptimizerRegression()).estimate();
} else if (this.covMatrix != null) {
return new SemEstimator(this.covMatrix, pm, new SemOptimizerRegression()).estimate();
} else {
throw new IllegalStateException();
}
}
}
