  \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.
