10 Mar 2004
CS 3243 - Uncertainty
18
Inference
by enumeration, contd.
Typically, we are interested in
the posterior joint distribution of the query variables Y
given specific values e for the evidence variables E
Let the hidden variables be H = X - Y - E
Then the required summation
of joint entries is done by summing out the hidden variables:
P(Y | E = e) = αP(Y,E = e) = αΣhP(Y,E= e, H = h)
nThe terms in the summation are joint entries because Y, E and H together exhaust the set of random variables
nObvious problems:
1.Worst-case time
complexity O(dn) where d is the
largest arity
2.Space complexity O(dn) to store the joint
distribution
3.How to find the
numbers for O(dn) entries?