Learning inference friendly Bayesian networks: using incremental compilation
Authors
Pedersen, Søren ; Karlsen, Martin
Term
2. term
Education
Publication year
2008
Abstract
Dette projekt undersøger strukturlæring i Bayesianske netværk—modeller, der beskriver variabler og deres sandsynlige sammenhænge. Vi ser på, hvordan den valgte læringsmetode påvirker modellens kompleksitet under inferens. Vi gennemgår junction tree-metoden til udbredelse af sandsynligheder og beskriver, hvordan et netværk kompileres til et junction tree. Analysen viser, at størrelsen på klikerne (grupper af variabler i træet) er en væsentlig kilde til kompleksitet. For at håndtere dette foreslår vi en scorefunktion, der afvejer modellens tilpasning (log-likelihood) mod kompleksitet målt som den samlede størrelse af kliker, styret af en vægtparameter. Metoden bruger inkrementel kompilering, så kandidatnetværk ikke kræver re-triangulering af hele junction tree. Vi sammenligner denne score med standard BIC (Bayesian Information Criterion), også med en vægtparameter, og måler præcision og inferenstid. Resultaterne viser, at det at medtage junction tree-størrelse i scoren kan give netværk, der er hurtigere til inferens og i nogle tilfælde forbliver brugbare, hvor BIC-lærte netværk bliver for komplekse.
This project investigates structural learning in Bayesian networks—models that represent variables and their probabilistic relationships. We focus on how the chosen learning method affects model complexity during inference. We study the junction tree approach for propagating probabilities, outlining how a network is compiled into a junction tree. Our analysis shows that the size of the cliques (groups of variables in the tree) is a key source of complexity. To address this, we propose a scoring function that balances goodness of fit (log-likelihood) against complexity measured by the combined size of cliques, controlled by a weighting parameter. The method uses incremental compilation so candidate networks do not require re-triangulating the entire junction tree. We evaluate this score against standard BIC (Bayesian Information Criterion) scoring, also with a weighting parameter, measuring precision and inference time. Results indicate that incorporating junction tree size in the score can yield networks that infer faster and, in some cases, remain usable where BIC-learned networks become too complex.
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