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 0rthodontist Dec8-06 12:32 PM

Bayes net inference

I don't understand this simple algorithm from Russel & Norvig for computing a distribution of X given certain observed values e:

Code:

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} u E u Y /* Y = hidden variables */                 Q(X) <- a distribution over X, initially empty         for each value xi of X do                 extend e with value xi for X                 Q(xi) <- Enumerate-All(Vars[bn], e)         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 the sum over y of P(y | parents(Y)) * Enumerate-All(Rest(vars), ey)                         where ey is e extended with Y = y
I am having trouble understanding exactly what Enumerate-All does. Specifically I do not understand how P(y | parents(Y)) is computed. We don't know the values that the parents of Y take, do we?

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