Probabilistic sentential decision diagrams
Doga Kisa, Guy Van den Broeck, Arthur Choi, Adnan Y. Darwiche · Lirias · 2014
We propose the Probabilistic Sentential Decision Dia-gram (PSDD): A complete and canonical representation of probability distributions defined over the models of a given propositional theory. Each parameter of a PSDD can be viewed as the (conditional) probability of mak-ing a decision in a corresponding Sentential Decision Diagram (SDD). The SDD itself is a recently proposed complete and canonical representation of propositional theories. We explore a number of interesting properties of PSDDs, including the independencies that underlie them. We show that the PSDD is a tractable represen-tation. We further show how the parameters of a PSDD can be efficiently estimated, in closed form, from com-plete data. We empirically evaluate the quality of PS-DDs learned from data, when we have knowledge, a priori, of the domain logical constraints.