Abstract
Bayesian networks (BN) are a popular representation for reasoning under uncertainty. The analysis of many real-world use cases, that in principle can be modeled by BNs, suffers however from the computational complexity of inference. Inference methods based on Weighted Model Counting (WMC) reduce the cost of inference by exploiting patterns exhibited by the probabilities associated with BN nodes. However, these methods require a computationally intensive compilation step in search of these patterns, which effectively prohibits the handling of larger BNs. In this paper, we propose a solution to this problem by extending WMC methods with a framework called Compositional Weighted Model Counting (CWMC). CWMC reduces compilation cost by partitioning a BN into a set of subproblems, thereby scaling the application of state-of-the-art innovations in WMC to scenarios where inference cost could previously not be amortized over compilation cost. The framework supports various target representations that are less or equally succinct as decision-DNNF. At the same time, its inference time complexity O(nexp(w)), where n is the number of variables and w is the tree-width, is comparable to mainstream algorithms based on variable elimination, clustering and conditioning.
Highlights
The field of probabilistic inference has made considerable progress in the past three decades with the development of novel probabilistic graphical models, such as Bayesian networks (BNs) and chain graphs [10]
The current article proposes Compositional Weighted Model Counting (CWMC), a framework for probabilistic inference that partitions the compilation into subproblems, which are recomposed in the inference query
We introduce Compositional Weighted Model Counting (CWMC), which combines Compositional Framework (CF) and WMC
Summary
The field of probabilistic inference has made considerable progress in the past three decades with the development of novel probabilistic graphical models, such as Bayesian networks (BNs) and chain graphs [10]. Various symbolic formalisms have been proposed for KC, e.g., [34],[29] and [44], which all have different characteristics in terms of compilation effort and query times Because this symbolic approach represents local structure concisely, like the decision tree in Fig. 1c and the diagrams [45, Th.3], KC is generally seen as a method that renders many practical reasoning problems tractable [33]. The current article proposes Compositional Weighted Model Counting (CWMC), a framework for probabilistic inference that partitions the compilation into subproblems, which are recomposed in the inference query. It builds upon, and extends [15]. Empirical evaluation shows that both compilation and inference cost are reduced while employing CWMC, sometimes by multiple orders of magnitude (Section 8)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
