Original title:
Representations of Bayesian Networks by Low-Rank Models
Authors:
Tichavský, Petr ; Vomlel, Jiří Document type: Papers Conference/Event: International Conference on Probabilistic Graphical Models, Praha (CZ), 20180911
Year:
2018
Language:
eng Abstract:
Conditional probability tables (CPTs) of discrete valued random variables may achieve high dimensions and Bayesian networks deﬁned as the product of these CPTs may become intractable by conventional methods of BN inference because of their dimensionality. In many cases, however, these probability tables constitute tensors of relatively low rank. Such tensors can be written in the so-called Kruskal form as a sum of rank-one components. Such representation would be equivalent to adding one artiﬁcial parent to all random variables and deleting all edges between the variables. The most difﬁcult task is to ﬁnd such a representation given a set of marginals or CPTs of the random variables under consideration. In the former case, it is a problem of joint canonical polyadic (CP) decomposition of a set of tensors. The latter ﬁtting problem can be solved in a similar manner. We apply a recently proposed alternating direction method of multipliers (ADMM), which assures that the model has a probabilistic interpretation, i.e., that all elements of all factor matrices are nonnegative. We perform experiments with several well-known Bayesian networks.\n\n
Keywords:
canonical polyadic tensor decomposition; conditional probability tables; marginal probability tables Project no.: GA17-00902S (CEP) Funding provider: GA ČR Host item entry: Proceedings of Machine Learning Research