Compositional Probabilistic and Causal Inference using Tractable Circuit Models

TL;DR

This paper introduces md-vtrees, a new structural formulation for probabilistic circuits that enables efficient, tractable inference, including causal inference tasks like backdoor adjustment, and proposes MDNets as a practical architecture.

Contribution

The paper presents md-vtrees, a novel structural framework for PCs that generalizes previous models and enables efficient algorithms for complex inference, including causal inference.

Findings

First polytime algorithms for causal inference on PCs.

Introduction of MDNets architecture using md-vtrees.

Empirical demonstration of causal inference capabilities.

Abstract

Probabilistic circuits (PCs) are a class of tractable probabilistic models, which admit efficient inference routines depending on their structural properties. In this paper, we introduce md-vtrees, a novel structural formulation of (marginal) determinism in structured decomposable PCs, which generalizes previously proposed classes such as probabilistic sentential decision diagrams. Crucially, we show how mdvtrees can be used to derive tractability conditions and efficient algorithms for advanced inference queries expressed as arbitrary compositions of basic probabilistic operations, such as marginalization, multiplication and reciprocals, in a sound and generalizable manner. In particular, we derive the first polytime algorithms for causal inference queries such as backdoor adjustment on PCs. As a practical instantiation of the framework, we propose MDNets, a novel PC architecture using md-vtrees, and empirically demonstrate their application to causal inference.