abstract bibtex

Learning a Bayesian network structure from data is a well-motivated but computationally hard task. We present an algorithm that computes the exact posterior probability of a subnetwork, e.g., a directed edge; a modiﬁed version of the algorithm ﬁnds one of the most probable network structures. This algorithm runs in time O(n2n + nk+1C(m)), where n is the number of network variables, k is a constant maximum in-degree, and C(m) is the cost of computing a single local marginal conditional likelihood for m data instances. This is the ﬁrst algorithm with less than super-exponential complexity with respect to n. Exact computation allows us to tackle complex cases where existing Monte Carlo methods and local search procedures potentially fail. We show that also in domains with a large number of variables, exact computation is feasible, given suitable a priori restrictions on the structures; combining exact and inexact methods is also possible. We demonstrate the applicability of the presented algorithm on four synthetic data sets with 17, 22, 37, and 100 variables.

@article{koivisto_exact_nodate, title = {Exact {Bayesian} {Structure} {Discovery} in {Bayesian} {Networks}}, abstract = {Learning a Bayesian network structure from data is a well-motivated but computationally hard task. We present an algorithm that computes the exact posterior probability of a subnetwork, e.g., a directed edge; a modiﬁed version of the algorithm ﬁnds one of the most probable network structures. This algorithm runs in time O(n2n + nk+1C(m)), where n is the number of network variables, k is a constant maximum in-degree, and C(m) is the cost of computing a single local marginal conditional likelihood for m data instances. This is the ﬁrst algorithm with less than super-exponential complexity with respect to n. Exact computation allows us to tackle complex cases where existing Monte Carlo methods and local search procedures potentially fail. We show that also in domains with a large number of variables, exact computation is feasible, given suitable a priori restrictions on the structures; combining exact and inexact methods is also possible. We demonstrate the applicability of the presented algorithm on four synthetic data sets with 17, 22, 37, and 100 variables.}, language = {en}, author = {Koivisto, Mikko and Sood, Kismat}, pages = {25} }

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