Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Zero-suppressed BDDs for set manipulation in combinatorial problems
DAC '93 Proceedings of the 30th international Design Automation Conference
Artificial Intelligence - special issue on computational tradeoffs under bounded resources
Using ROBDDs for Inference in Bayesian Networks with Troubleshooting as an Example
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
A differential approach to inference in Bayesian networks
Journal of the ACM (JACM)
Compiling Bayesian networks with local structure
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Compressing probabilistic Prolog programs
Machine Learning
Variational Bayes via propositionalized probability computation in PRISM
Annals of Mathematics and Artificial Intelligence
New advances in logic-based probabilistic modeling by PRISM
Probabilistic inductive logic programming
Don't fear optimality: sampling for probabilistic-logic sequence models
ILP'09 Proceedings of the 19th international conference on Inductive logic programming
Compiling bayesian networks for parameter learning based on shared BDDs
AI'11 Proceedings of the 24th international conference on Advances in Artificial Intelligence
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Compiling Bayesian networks (BNs) is a hot topic within probabilistic modeling and processing. In this paper, we propose a new method for compiling BNs into Multi-Linear Functions (MLFs) based on Zero-suppressed Binary Decision Diagrams (ZBDDs), which are a graph-based representation of combinatorial item sets. Our method differs from the original approach of Darwiche et al., which encodes BNs into Conjunctive Normal Forms (CNFs) and then translates CNFs into factored MLFs. Our approach directly translates a BN into a set of factored MLFs using a ZBDD-based symbolic probability calculation. The MLF may have exponential computational complexity, but our ZBDD-based data structure provides a compact factored form of the MLF, and arithmetic operations can be executed in a time almost linear with the ZBDD size. In our method, it is not necessary to generate the MLF for the whole network, as we can extract MLFs for only part of the network related to the query, avoiding unnecessary calculation of redundant MLF terms. We present experimental results for some typical benchmark examples. Although our algorithm is simply based on the mathematical definition of probability calculation, performance is competitive to existing state-of-the-art methods.