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pl:prolog:pllib:belief_networks [2019/06/27 15:50] (aktualna) |
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| + | ====== Belief networks ====== | ||
| + | {{tag>networks interpreter}} | ||
| + | ===== Description ===== | ||
| + | An interpreter for belief networks. | ||
| + | |||
| + | **Source**: PROLOG programming for artificial intelligence, 3rd Edition, Harlow, 2001, ISBN 0-201-40375-7. | ||
| + | ===== Download ===== | ||
| + | Program source code: {{belief_networks.pl}} | ||
| + | ===== Listing ===== | ||
| + | <code prolog> | ||
| + | % Figure 15.11 An interpreter for belief networks. | ||
| + | |||
| + | :- op( 900, fy, not). | ||
| + | |||
| + | % not Goal): negation as failure; | ||
| + | % Note: This is often available as a built-in predicate, | ||
| + | % often written as prefix operator "\+", e.g. \+ likes(mary,snakes) | ||
| + | |||
| + | not Goal :- | ||
| + | Goal, !, fail | ||
| + | ; | ||
| + | true. | ||
| + | |||
| + | % Reasoning in belief networks | ||
| + | |||
| + | % Belief network is represented by relations: | ||
| + | % parent( ParentNode, Node) | ||
| + | % p( Node, ParentStates, Prob) | ||
| + | % where Prob is conditional probability of Node given | ||
| + | % values of parent variables ParentStates, for example: | ||
| + | % p( alarm, [ burglary, not earthquake], 0.99) | ||
| + | % p( Node, Prob) | ||
| + | % probability of node without parents | ||
| + | |||
| + | |||
| + | % prob( Event, Condition, P): | ||
| + | % probability of Event, given Cond, is P; | ||
| + | % Event is a variable, its negation, or a list | ||
| + | % of simple events representing their conjunction | ||
| + | |||
| + | prob( [X | Xs], Cond, P) :- !, % Probability of conjunction | ||
| + | prob( X, Cond, Px), | ||
| + | prob( Xs, [X | Cond], PRest), | ||
| + | P is Px * PRest. | ||
| + | |||
| + | prob( [], _, 1) :- !. % Empty conjunction | ||
| + | |||
| + | prob( X, Cond, 1) :- | ||
| + | member( X, Cond), !. % Cond implies X | ||
| + | |||
| + | prob( X, Cond, 0) :- | ||
| + | member( not X, Cond), !. % Cond implies X is false | ||
| + | |||
| + | prob( not X, Cond, P) :- !, % Probability of negation | ||
| + | prob( X, Cond, P0), | ||
| + | P is 1 - P0. | ||
| + | |||
| + | % Use Bayes rule if condition involves a descendant of X | ||
| + | |||
| + | prob( X, Cond0, P) :- | ||
| + | delete( Y, Cond0, Cond), | ||
| + | predecessor( X, Y), !, % Y is a descendant of X | ||
| + | prob( X, Cond, Px), | ||
| + | prob( Y, [X | Cond], PyGivenX), | ||
| + | prob( Y, Cond, Py), | ||
| + | P is Px * PyGivenX / Py. % Assuming Py > 0 | ||
| + | |||
| + | % Cases when condition does not involve a descendant | ||
| + | |||
| + | prob( X, Cond, P) :- | ||
| + | p( X, P), !. % X a root cause - its probability given | ||
| + | |||
| + | prob( X, Cond, P) :- !, | ||
| + | findall( (CONDi,Pi), p(X,CONDi,Pi), CPlist), % Conditions on parents | ||
| + | sum_probs( CPlist, Cond, P). | ||
| + | |||
| + | % sum_probs( CondsProbs, Cond, WeigthedSum) | ||
| + | % CondsProbs is a list of conditions and corresponding probabilities, | ||
| + | % WeightedSum is weighted sum of probabilities of Conds given Cond | ||
| + | |||
| + | sum_probs( [], _, 0). | ||
| + | |||
| + | sum_probs( [ (COND1,P1) | CondsProbs], COND, P) :- | ||
| + | prob( COND1, COND, PC1), | ||
| + | sum_probs( CondsProbs, COND, PRest), | ||
| + | P is P1 * PC1 + PRest. | ||
| + | |||
| + | predecessor( X, not Y) :- !, % Negated variable Y | ||
| + | predecessor( X, Y). | ||
| + | |||
| + | predecessor( X, Y) :- | ||
| + | parent( X, Y). | ||
| + | |||
| + | predecessor( X, Z) :- | ||
| + | parent( X, Y), | ||
| + | predecessor( Y, Z). | ||
| + | |||
| + | member( X, [X | _]). | ||
| + | |||
| + | member( X, [_ | L]) :- | ||
| + | member( X, L). | ||
| + | |||
| + | delete( X, [X | L], L). | ||
| + | |||
| + | delete( X, [Y | L], [Y | L2]) :- | ||
| + | delete( X, L, L2). | ||
| + | </code> | ||
| + | ===== Comments ===== | ||
