Component Caching in Hybrid Domains with Piecewise Polynomial Densities

Counting the models of a propositional formula is an important problem: for example, it serves as the backbone of probabilistic inference by weighted model counting. A key algorithmic insight is component caching (CC), in which disjoint components of a formula, generated dynamically during a DPLL search, are cached so that they only have to be solved once. In the recent years, driven by SMT technology and probabilistic inference in hybrid domains, there is an increasing interest in counting the models of linear arithmetic sentences. To date, however, solvers for these are block-clause implementations, which are nonviable on large problem instances. In this paper, as a first step in extending CC to hybrid domains, we show how propositional CC systems can be leveraged when limited to piecewise polynomial densities. Our experiments demonstrate a large gap in performance when compared to existing approaches based on a variety of block-clause strategies

Scaling up Probabilistic Inference in Linear and Non-Linear Hybrid Domains by Leveraging Knowledge Compilation.

Weighted model integration (WMI) extends weighted model counting (WMC) in providing a computational abstraction for probabilistic inference in mixed discrete-continuous domains. WMC has emerged as an assembly language for state-of-the-art reasoning in Bayesian networks, factor graphs, probabilistic programs and probabilistic databases. In this regard, WMI shows immense promise to be much more widely applicable, especially as many real-world applications involve attribute and feature spaces that are continuous and mixed. Nonetheless, state-of-the-art tools for WMI are limited and less mature than their propositional counterparts. In this work, we propose a new implementation regime that leverages propositional knowledge compilation for scaling up inference. In particular, we use sentential decision diagrams, a tractable representation of Boolean functions, as the underlying model counting and model enumeration scheme. Our regime performs competitively to state-of-the-art WMI systems but is also shown to handle a specific class of non-linear constraints over non-linear potentials.Comment: In proceedings of ICAART, 2020. A version also appears in AAAI Workshop: Statistical Relational Artificial Intelligence (StarAI), 202

Probabilistic Inference in Hybrid Domains by Weighted Model Integration

Weighted model counting (WMC) on a propositional knowledge base is an effective and general approach to probabilistic inference in a variety of formalisms, includ-ing Bayesian and Markov Networks. However, an in-herent limitation of WMC is that it only admits the in-ference of discrete probability distributions. In this pa-per, we introduce a strict generalization of WMC called weighted model integration that is based on annotating Boolean and arithmetic constraints, and combinations thereof. This methodology is shown to capture discrete, continuous and hybrid Markov networks. We then con-sider the task of parameter learning for a fragment of the language. An empirical evaluation demonstrates the ap-plicability and promise of the proposal.