Enumeration-Ask.md

ENUMERATION-ASK

AIMA3e

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 x_i of X do
   Q(x_i) ← ENUMERATE-ALL(bn.VARS, e_xi)
     where e_xi is e extended with X = x_i
 return NORMALIZE(Q(X))

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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), e_y)
     where e_y is e extended with Y = y

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