An efficient search-and-score algorithm for ancestral graphs using multivariate information scores

TL;DR

This paper introduces a fast greedy search-and-score algorithm for ancestral graphs that uses multivariate information scores, improving causal discovery efficiency and accuracy on benchmark datasets.

Contribution

The paper presents a novel two-step greedy algorithm leveraging local information scores for ancestral graphs, enhancing computational efficiency and outperforming existing methods.

Findings

Outperforms state-of-the-art causal discovery methods on benchmarks.

Uses multivariate information scores over ac-connected subsets.

Efficiently handles ancestral graphs with latent variables.

Abstract

We propose a greedy search-and-score algorithm for ancestral graphs, which include directed as well as bidirected edges, originating from unobserved latent variables. The normalized likelihood score of ancestral graphs is estimated in terms of multivariate information over relevant ``ac-connected subsets'' of vertices, C, that are connected through collider paths confined to the ancestor set of C. For computational efficiency, the proposed two-step algorithm relies on local information scores limited to the close surrounding vertices of each node (step 1) and edge (step 2). This computational strategy, although restricted to information contributions from ac-connected subsets containing up to two-collider paths, is shown to outperform state-of-the-art causal discovery methods on challenging benchmark datasets.