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

TL;DR

This paper introduces a novel approach for probabilistic inference in mixed discrete-continuous domains by leveraging knowledge compilation with sentential decision diagrams, improving scalability and handling non-linear constraints.

Contribution

It proposes using sentential decision diagrams for WMI, enabling scalable inference and the ability to handle certain non-linear constraints, advancing the state-of-the-art.

Findings

Competitive performance with existing WMI systems

Handles a specific class of non-linear constraints

Scales better in hybrid probabilistic inference tasks

Abstract

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.