ProDAG: Projected Variational Inference for Directed Acyclic Graphs

TL;DR

ProDAG introduces a Bayesian variational inference method for DAG learning that efficiently quantifies uncertainty and outperforms existing methods in accuracy and uncertainty estimation.

Contribution

It develops a novel projection-based variational inference framework that directly supports sparse DAGs, enabling better uncertainty quantification in DAG learning.

Findings

ProDAG outperforms state-of-the-art methods in accuracy.

ProDAG provides more reliable uncertainty quantification.

The method efficiently handles the combinatorial nature of DAG constraints.

Abstract

Directed acyclic graph (DAG) learning is a central task in structure discovery and causal inference. Although the field has witnessed remarkable advances over the past few years, it remains statistically and computationally challenging to learn a single (point estimate) DAG from data, let alone provide uncertainty quantification. We address the difficult task of quantifying graph uncertainty by developing a Bayesian variational inference framework based on novel, provably valid distributions that have support directly on the space of sparse DAGs. These distributions, which we use to define our prior and variational posterior, are induced by a projection operation that maps an arbitrary continuous distribution onto the space of sparse weighted acyclic adjacency matrices. While this projection is combinatorial, it can be solved efficiently using recent continuous reformulations of acyclicity constraints. We empirically demonstrate that our method, ProDAG, can outperform state-of-the-art alternatives in both accuracy and uncertainty quantification.