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anytimeExactBeliefPropagation.ModelGenerator Maven / Gradle / Ivy
package anytimeExactBeliefPropagation;
import static com.sri.ai.expresso.helper.Expressions.apply;
import static com.sri.ai.expresso.helper.Expressions.makeSymbol;
import static com.sri.ai.expresso.helper.Expressions.parse;
import static com.sri.ai.grinder.helper.GrinderUtil.getIndexExpressionsOfFreeVariablesIn;
import static com.sri.ai.grinder.sgdpllt.library.FunctorConstants.EQUAL;
import static com.sri.ai.grinder.sgdpllt.library.FunctorConstants.IF_THEN_ELSE;
import static com.sri.ai.grinder.sgdpllt.library.FunctorConstants.SUM;
import static com.sri.ai.grinder.sgdpllt.library.FunctorConstants.TIMES;
import static com.sri.ai.util.Util.in;
import static com.sri.ai.util.Util.println;
import static java.lang.Math.min;
import java.util.ArrayList;
import java.util.Collection;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Random;
import java.util.Set;
import com.google.common.annotations.Beta;
import com.sri.ai.expresso.api.Expression;
import com.sri.ai.expresso.api.IndexExpressionsSet;
import com.sri.ai.expresso.api.IntensionalSet;
import com.sri.ai.expresso.api.Type;
import com.sri.ai.expresso.core.DefaultExtensionalMultiSet;
import com.sri.ai.expresso.helper.Expressions;
import com.sri.ai.grinder.sgdpllt.api.Context;
import com.sri.ai.grinder.sgdpllt.api.Theory;
import com.sri.ai.grinder.sgdpllt.library.bounds.Bound;
import com.sri.ai.grinder.sgdpllt.library.bounds.Bounds;
import com.sri.ai.grinder.sgdpllt.library.bounds.DefaultExtensionalBound;
import com.sri.ai.util.base.Pair;
import com.sri.ai.util.base.Triple;
import com.sri.ai.util.collect.ManyToManyRelation;
import anytimeExactBeliefPropagation.Model.Model;
import anytimeExactBeliefPropagation.Model.Node.FactorNode;
import anytimeExactBeliefPropagation.Model.Node.VariableNode;
/**
* A class that provides a handful number of graphical models, under the form of {@link Set}s of {@link Expression}s
*
* TODO Add "seeds" for repeatability
* TODO for binary query nodes, add max-min probability of truth
*
* @author Gabriel Azevedo Ferreira
*/
@Beta
public class ModelGenerator {
private static Expression randomNumberGenerator() {
Random randomGenerator = new Random();
return makeSymbol(randomGenerator.nextInt(9));
}
private static Expression generateProbability(Context context,int i, Expression... listOfVariables) {
if (listOfVariables.length == 0 ) {
return null;
}
Expression result = makeSymbol(0);// randomNumberGenerator();
Expression variable = listOfVariables[i];
// listOfVariables.remove(0);
Type type = context.getTypeOfRegisteredSymbol(variable);
Iterator iteratorToValuesInType = type.iterator();
if (listOfVariables.length == i+1) {
for (Expression value : in(iteratorToValuesInType)) {
Expression varEqualsValue = apply(EQUAL,variable,value);
Expression randProbability = randomNumberGenerator();
result = apply(IF_THEN_ELSE,varEqualsValue, randProbability, result);
}
}
else{
for (Expression value : in(iteratorToValuesInType)) {
Expression varEqualsValue = apply(EQUAL,variable,value);
Expression randProbability = generateProbability(context, i+1, listOfVariables);
result = apply(IF_THEN_ELSE,varEqualsValue, randProbability, result);
}
}
return result;
}
/**
* Generates a random factor (a non normalized probability distribution) over a set of variables
* @param context
* @param listOfVariables
* @return
*/
public static Expression generateProbability(Context context, Expression... listOfVariables) {
return generateProbability(context, 0, listOfVariables);
}
/**
* Generates an Ising model with random probabilities
* @param nLines
* @param nCols
* @param context
* @param possibleValues
* Example: Boolean, 1..6
* @return
*/
public static Triple,Context,Expression> IsingModel(int nLines, int nCols, Context context, Expression possibleValues) {
Set factorsInModel = new HashSet();
Expression[][] a = new Expression[nLines][nCols];
for (int i = 0; i < nLines; i++) {
for (int j = 0; j < nCols; j++) {
a[i][j] = makeSymbol("A_"+i+"_"+j);
context = context.extendWithSymbolsAndTypes(a[i][j],possibleValues);
}
}
for (int i = 0; i < nLines; i++) {
for (int j = 0; j < nCols; j++) {
if (j < nCols - 1) {
Expression fHor = generateProbability(context, a[i][j], a[i][j+1]);
factorsInModel.add(fHor);
}
if (i < nLines-1) {
Expression fVer = generateProbability(context, a[i][j], a[i+1][j]);
factorsInModel.add(fVer);
}
}
}
Triple,Context,Expression> result = new Triple<>(factorsInModel,context,a[0][0]);
return result;
}
/**
* Generates a random model with a given number of variables
*
* @param nVariables
* @param nFactors
* @param context
* @param possibleValues
* @return
*/
public static Triple,Context,Expression> randomModel(int nVariables, int nFactors, Context context, Expression possibleValues) {
Set factorsInModel = new HashSet();
Expression[] a = new Expression[nVariables];
for (int i = 0; i < nVariables; i++) {
a[i]= makeSymbol("A_"+i);
context = context.extendWithSymbolsAndTypes(a[i],possibleValues);
}
Random rand = new Random();
for (int i = 0; i < nFactors; i++) {
int n = rand.nextInt(min(15,nVariables));
Expression[] varOfF = new Expression[n];
for (int j = 0; j < varOfF.length; j++) {
varOfF[j] = a[rand.nextInt(nVariables)];
}
Expression f = generateProbability(context, varOfF);
factorsInModel.add(f);
}
Triple,Context,Expression> result = new Triple<>(factorsInModel,context,a[0]);
return result;
}
/**
* Creates a model that looks like a queue of factors and variables
* Q - F - V - F -...- F - V
* @param nVariables
* @param context
* @param possibleValues
* @return
*/
public static Triple,Context,Expression> lineModel(int nVariables, Context context, Expression possibleValues) {
Set factorsInModel = new HashSet();
Expression[] a = new Expression[nVariables];
for (int i = 0; i < nVariables; i++) {
a[i]= makeSymbol("A_"+i);
context = context.extendWithSymbolsAndTypes(a[i],possibleValues);
}
for (int i = 0; i < a.length - 1; i++) {
Expression factor = generateProbability(context, a[i],a[i+1]);
factorsInModel.add(factor);
}
Triple,Context,Expression> result = new Triple<>(factorsInModel,context,a[0]);
return result;
}
/**
* creates a tree with n children per node
* @param depth
* @param numberOfChildren
* @param context
* @param possibleValues
* @return
*/
public static Triple,Context,Expression> nTreeModel(int depth , int numberOfChildren, Context context, Expression possibleValues) {
Set factorsInModel = new HashSet();
int nCols = 1;
for (int i = 0; i < depth; i++) {
nCols *= numberOfChildren;
}
Expression[][] a = new Expression[depth][nCols];
for (int i = 0; i < depth; i++) {
for (int j = 0; j < nCols; j++) {
a[i][j]= makeSymbol("A_" + i + "_" + j);
context = context.extendWithSymbolsAndTypes(a[i][j],possibleValues);
}
}
int colMax = 1;
for (int i = 0; i < depth - 1; i++) {
for (int j = 0; j < colMax; j++) {
for (int k = j * numberOfChildren; k < (j+1) * numberOfChildren; k++) {
Expression factor = generateProbability(context, a[i][j],a[i+1][k]);
factorsInModel.add(factor);
}
}
colMax*=numberOfChildren;
}
Triple,Context,Expression> result = new Triple<>(factorsInModel,context,a[0][0]);
return result;
}
/**
* Lifited variabble Elimination
* this method just creates the inference equation and asks SGDPLL to solve it
* @param m
* @return
*/
public static Expression lveCalculation(Model m) {
return LVECalculation(m.getEntireGraph().getBs(),m.getQuery().getValue(),m.getContext(),m.getTheory());
}
public static Expression LVECalculation(Collection factorNodes, Expression query, Context context, Theory theory) {
Set factorExpressions = new HashSet<>();
for (FactorNode f : factorNodes) {
factorExpressions.add(f.getValue());
}
Expression product = apply(TIMES, factorExpressions);
Set freevariables = Expressions.freeVariables(product, context);
freevariables.remove(query);
ArrayList varToSumOut = new ArrayList<>();
varToSumOut.addAll(freevariables);
Expression variablesToBeSummedOut = new DefaultExtensionalMultiSet(varToSumOut);
IndexExpressionsSet indices = getIndexExpressionsOfFreeVariablesIn(variablesToBeSummedOut, context);
Expression setOfFactorInstantiations = IntensionalSet.makeMultiSet(
indices,
product,// head
makeSymbol(true)// No Condition
);
Expression sumOnPhi = apply(SUM, setOfFactorInstantiations);
Expression evaluation = theory.evaluate(sumOnPhi, context);
Expression result = Bounds.normalizeSingleExpression(evaluation, theory, context);
return result;
}
public static void printModel(Model m, boolean entire) {
ManyToManyRelation graph = entire ? m.getEntireGraph() : m.getExploredGraph();
for (Pair e : in(graph.iterator())) {
println(e.second.getValue() + " -> " + e.first.getValue());
}
}
public static void printFactors(Set factorsInModel) {
for (FactorNode e : factorsInModel) {
println(e.getValue());
}
}
public static void printModel(Set factorsInModel) {
for (Expression e : factorsInModel) {
println(e);
}
}
public static Pair maxMinProbability(Bound b,Model m) {
Context context = m.getContext();
Theory theory = m.getTheory();
Expression query = m.getQuery().getValue();
Type type = context.getTypeOfRegisteredSymbol(query);
if (type.getName().equals("Boolean")) {
double maxProbabilityOfTrue = -1;
double minProbabilityOfTrue = 10;
if (b.isExtensionalBound()) {
DefaultExtensionalBound extensionalBound = (DefaultExtensionalBound) b;
List listOfElements = extensionalBound.getArguments();
for (Expression distribution : listOfElements) {
// replace and evaluate
Expression replacingQueryByTrue = distribution.replaceAllOccurrences(query, parse("true"), context);
Expression evaluating = theory.evaluate(replacingQueryByTrue, context);
// convert to double
double value = evaluating.doubleValue();
// update max and min
if (value > maxProbabilityOfTrue) {
maxProbabilityOfTrue = value;
}
if (value < minProbabilityOfTrue) {
minProbabilityOfTrue = value;
}
}
Pair result = new Pair<>(minProbabilityOfTrue,maxProbabilityOfTrue);
return result;
}
else if (b.isIntensionalBound()) {
}
}
return null;
}
}
