aima.core.probability.bayes.exact

Class EnumerationAsk

java.lang.Object

aima.core.probability.bayes.exact.EnumerationAsk

All Implemented Interfaces:

BayesInference

public class EnumerationAsk
extends java.lang.Object
implements BayesInference

Artificial Intelligence A Modern Approach (3rd Edition): Figure 14.9, page 525.

 function ENUMERATION-ASK(X, e, bn) returns a distribution over X
   inputs: X, the query variable
           e, observed values for variables E
           bn, a Bayes net with variables {X} ∪ E ∪ Y /* Y = hidden variables //
           
   Q(X) <- a distribution over X, initially empty
   for each value xi of X do
       Q(xi) <- ENUMERATE-ALL(bn.VARS, exi)
          where exi is e extended with X = xi
   return NORMALIZE(Q(X))
   
 ---------------------------------------------------------------------------------------------------
 
 function ENUMERATE-ALL(vars, e) returns a real number
   if EMPTY?(vars) then return 1.0
   Y <- FIRST(vars)
   if Y has value y in e
       then return P(y | parents(Y)) * ENUMERATE-ALL(REST(vars), e)
       else return ∑y P(y | parents(Y)) * ENUMERATE-ALL(REST(vars), ey)
           where ey is e extended with Y = y
 

Figure 14.9 The enumeration algorithm for answering queries on Bayesian networks.

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

Author:

Ciaran O'Reilly

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
protected class	EnumerationAsk.ObservedEvidence

Constructor Summary

Constructors

Constructor and Description
EnumerationAsk()

Method Summary

Modifier and Type	Method and Description
CategoricalDistribution	ask(RandomVariable[] X, AssignmentProposition[] observedEvidence, BayesianNetwork bn)
protected double	enumerateAll(java.util.List<RandomVariable> vars, EnumerationAsk.ObservedEvidence e)
CategoricalDistribution	enumerationAsk(RandomVariable[] X, AssignmentProposition[] observedEvidence, BayesianNetwork bn) The ENUMERATION-ASK algorithm in Figure 14.9 evaluates expression trees (Figure 14.8) using depth-first recursion.

Methods inherited from class java.lang.Object

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

Constructor Detail

EnumerationAsk

public EnumerationAsk()

Method Detail

enumerationAsk

public CategoricalDistribution enumerationAsk(RandomVariable[] X,
                                              AssignmentProposition[] observedEvidence,
                                              BayesianNetwork bn)

The ENUMERATION-ASK algorithm in Figure 14.9 evaluates expression trees (Figure 14.8) using depth-first recursion.

Parameters:

X - the query variables.

observedEvidence - observed values for variables E.

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

Returns:

a distribution over the query variables.

ask

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

Specified by:

ask in interface BayesInference

Parameters:

X - the query variables.

observedEvidence - observed values for variables E.

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

Returns:

a distribution over the query variables.

enumerateAll

protected double enumerateAll(java.util.List<RandomVariable> vars,
                              EnumerationAsk.ObservedEvidence e)