Compositional Probabilistic and Causal Inference using Tractable Circuit Models
This work addresses the need for efficient causal inference in probabilistic modeling, offering a novel method that generalizes prior approaches.
The paper tackled the problem of performing advanced probabilistic and causal inference efficiently by introducing md-vtrees, a structural formulation for tractable probabilistic circuits, resulting in the first polytime algorithms for queries like backdoor adjustment.
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.