aima.core.probability.bayes.approx

Class LikelihoodWeighting

java.lang.Object

aima.core.probability.bayes.approx.LikelihoodWeighting

All Implemented Interfaces:

BayesSampleInference

public class LikelihoodWeighting
extends java.lang.Object
implements BayesSampleInference

Artificial Intelligence A Modern Approach (3rd Edition): page 534.

 function LIKELIHOOD-WEIGHTING(X, e, bn, N) returns an estimate of P(X|e)
   inputs: X, the query variable
           e, observed values for variables E
           bn, a Bayesian network specifying joint distribution P(X1,...,Xn)
           N, the total number of samples to be generated
   local variables: W, a vector of weighted counts for each value of X, initially zero
   
   for j = 1 to N do
       x,w <- WEIGHTED-SAMPLE(bn,e)
       W[x] <- W[x] + w where x is the value of X in x
   return NORMALIZE(W)
 --------------------------------------------------------------------------------------
 function WEIGHTED-SAMPLE(bn, e) returns an event and a weight
   
    w <- 1; x <- an event with n elements initialized from e
    foreach variable Xi in X1,...,Xn do
        if Xi is an evidence variable with value xi in e
            then w <- w * P(Xi = xi | parents(Xi))
            else x[i] <- a random sample from P(Xi | parents(Xi))
    return x, w
 

Figure 14.15 The likelihood-weighting algorithm for inference in Bayesian networks. In WEIGHTED-SAMPLE, each nonevidence variable is sampled according to the conditional distribution given the values already sampled for the variable's parents, while a weight is accumulated based on the likelihood for each evidence variable.

Note: The implementation has been extended to handle queries with multiple variables.

Author:

Ciaran O'Reilly, Ravi Mohan

Constructor Summary

Constructors

Constructor and Description
LikelihoodWeighting()
LikelihoodWeighting(Randomizer r)

Method Summary

Modifier and Type	Method and Description
CategoricalDistribution	ask(RandomVariable[] X, AssignmentProposition[] observedEvidence, BayesianNetwork bn, int N)
CategoricalDistribution	likelihoodWeighting(RandomVariable[] X, AssignmentProposition[] e, BayesianNetwork bn, int N) The LIKELIHOOD-WEIGHTING algorithm in Figure 14.15.
Pair<java.util.Map<RandomVariable,java.lang.Object>,java.lang.Double>	weightedSample(BayesianNetwork bn, AssignmentProposition[] e) The WEIGHTED-SAMPLE function in Figure 14.15.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

LikelihoodWeighting

public LikelihoodWeighting()

LikelihoodWeighting

public LikelihoodWeighting(Randomizer r)

Method Detail

likelihoodWeighting

public CategoricalDistribution likelihoodWeighting(RandomVariable[] X,
                                                   AssignmentProposition[] e,
                                                   BayesianNetwork bn,
                                                   int N)

The LIKELIHOOD-WEIGHTING algorithm in Figure 14.15. For answering queries given evidence in a Bayesian Network.

Parameters:

X - the query variables

e - observed values for variables E

bn - a Bayesian network specifying joint distribution P(X₁,...,X_n)

N - the total number of samples to be generated

Returns:

an estimate of P(X|e)

weightedSample

public Pair<java.util.Map<RandomVariable,java.lang.Object>,java.lang.Double> weightedSample(BayesianNetwork bn,
                                                                                            AssignmentProposition[] e)

The WEIGHTED-SAMPLE function in Figure 14.15.

Parameters:

e - observed values for variables E

bn - a Bayesian network specifying joint distribution P(X₁,...,X_n)

Returns:

return x, w - an event with its associated weight.

ask

public CategoricalDistribution ask(RandomVariable[] X,
                                   AssignmentProposition[] observedEvidence,
                                   BayesianNetwork bn,
                                   int N)

Specified by:

ask in interface BayesSampleInference

Parameters:

X - the query variables.

observedEvidence - observed values for variables E.

bn - a Bayes net with variables {X} ∪ E ∪ Y /* Y = hidden variables

N - the total number of samples to be generated

Returns:

an estimate of P(X|e).