A fast score-based search algorithm for maximal ancestral graphs using entropy
Zhongyi Hu, Robin Evans
TL;DR
This work tackles learning maximal ancestral graphs (MAGs) from data by replacing unstable BIC-based scoring with an entropy-based imset score grounded in the refined Markov property (ROMP). It develops a polynomial-time, greedy search over Markov equivalence classes using partial ancestral graphs (PAGs) and a novel branching strategy for discriminating paths, under Meek-like MAG conjecture assumptions. The proposed score S_G^r = -2N⟨δ_V − u_G^r, ŜH⟩ + d log N, together with ROMP and controlled head-size, yields a decomposable, consistent objective and scalable MEC navigation. Empirical results on simulated linear Gaussian MAGs show superior edge-accuracy and competitive BIC gaps compared to BIC-based and constraint-based baselines, illustrating practical benefits for causal discovery in the presence of latent confounders. The approach highlights a path toward efficient, principled MAG learning with principled handling of equivalence classes and finite-sample corrections.
Abstract
\emph{Maximal ancestral graph} (MAGs) is a class of graphical model that extend the famous \emph{directed acyclic graph} in the presence of latent confounders. Most score-based approaches to learn the unknown MAG from empirical data rely on BIC score which suffers from instability and heavy computations. We propose to use the framework of imsets \citep{studeny2006probabilistic} to score MAGs using empirical entropy estimation and the newly proposed \emph{refined Markov property} \citep{hu2023towards}. Our graphical search procedure is similar to \citet{claassen2022greedy} but improved from our theoretical results. We show that our search algorithm is polynomial in number of nodes by restricting degree, maximal head size and number of discriminating paths. In simulated experiment, our algorithm shows superior performance compared to other state of art MAG learning algorithms.