The Necessity of Bounded Treewidth for Efficient Inference in Bayesian Networks
نویسندگان
چکیده
Algorithms for probabilistic inference in Bayesian networks are known to have running times that are worst-case exponential in the size of the network. For networks with a moralised graph of bounded treewidth, however, these algorithms take a time which is linear in the network’s size. In this paper, we show that under the assumption of the Exponential Time Hypothesis (ETH), small treewidth of the moralised graph actually is a necessary condition for a Bayesian network to render inference efficient by an algorithm accepting arbitrary instances. We thus show that no algorithm can exist that performs inference on arbitrary Bayesian networks of unbounded treewidth in polynomial time, unless the ETH fails.
منابع مشابه
Learning Optimal Bounded Treewidth Bayesian Networks via Maximum Satisfiability
Bayesian network structure learning is the well-known computationally hard problem of finding a directed acyclic graph structure that optimally describes given data. A learned structure can then be used for probabilistic inference. While exact inference in Bayesian networks is in general NP-hard, it is tractable in networks with low treewidth. This provides good motivations for developing algor...
متن کاملBayesian Inference in Treewidth-Bounded Graphical Models Without Indegree Constraints
We present new polynomial time algorithms for inference problems in Bayesian networks (BNs) when restricted to instances that satisfy the following two conditions: they have bounded treewidth and the conditional probability table (CPT) at each node is specified concisely using an r-symmetric function for some constant r. Our polynomial time algorithms work directly on the unmoralized graph. Our...
متن کاملApproximate Structure Learning for Large Bayesian Networks
We present approximate structure learning algorithms for Bayesian networks. We discuss on the two main phases of the task: the preparation of the cache of the scores and structure optimization, both with bounded and unbounded treewidth. We improve on state-ofthe-art methods that rely on an ordering-based search by sampling more effectively the space of the orders. This allows for a remarkable i...
متن کاملA Fully Polynomial Time Approximation Scheme for Updating Credal Networks of Bounded Treewidth and Number of Variable States
Credal networks lift the precise probability assumption of Bayesian networks, enabling a richer representation of uncertainty in the form of closed convex sets of probability measures. The increase in expressiveness comes at the expense of higher computational costs. In this paper we present a new algorithm which is an extension of the wellknown variable elimination algorithm for computing post...
متن کاملPhase Transition of Tractability in Constraint Satisfaction and Bayesian Network Inference
Identifying tractable subclasses and design ing efficient algorithms for these tractable classes are important topics in the study of constraint satisfaction and Bayesian network inference problems. In this paper we inves tigate the asymptotic average behavior of a typical tractable subclass characterized by the treewidth of the problems. We show that the property of having a bounded treewidt...
متن کامل