An efficient search-and-score algorithm for ancestral graphs using multivariate information scores
This addresses the problem of causal discovery with latent variables for researchers in statistics and machine learning, representing an incremental improvement over existing methods.
The researchers tackled the problem of learning ancestral graphs with latent variables by developing a greedy search-and-score algorithm that uses multivariate information scores over ac-connected subsets. The result was a computationally efficient method that outperformed state-of-the-art causal discovery methods on challenging benchmark datasets.
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.