An EM Algorithm on BDDs with Order Encoding for Logic-based Probabilistic Models
Masakazu Ishihata (Tokyo Institute of Technology), Yoshitaka Kameya
(Tokyo Institute of Technology), Taisuke Sato (Tokyo Institute of Technology),
and Shin-ichi Minato (Hokkaido University);
JMLR W&P 13:161-176, 2010.
Logic-based probabilistic models (LBPMs) enable us to handle various
problems in the real world thanks to the expressive power of logic.
However, most of LBPMs have restrictions to realize efficient probability
computation and learning. We propose an EM algorithm working
on BDDs with order encoding for LBPMs. A notable advantage of our
algorithm over existing approaches is that it copes with multi-valued
random variables without restrictions. The complexity of our algorithm
is proportional to the size of the BDD. In the case of hidden
Markov models (HMMs), the complexity is the same as that specialized
for HMMs. As an example to eliminate restrictions of existing
approaches, we utilize our algorithm to give diagnoses for failure in a
logic circuit involving stochastic error gates.