Optimal Transport for Structure Learning Under Missing Data
Vy Vo He Zhao Trung Le Edwin V. Bonilla Dinh Phung
Causal discovery in the presence of missing data introduces a chicken-and-egg
dilemma. While the goal is to recover the true causal structure, robust
imputation requires considering the dependencies or preferably causal relations
among variables. Merely filling in missing values with existing imputation
methods and subsequently applying structure learning on the complete data is
empirical shown to be sub-optimal. To this end, we propose in this paper a
score-based algorithm, based on optimal transport, for learning causal
structure from missing data. This optimal transport viewpoint diverges from
existing score-based approaches that are dominantly based on EM. We project
structure learning as a density fitting problem, where the goal is to find the
causal model that induces a distribution of minimum Wasserstein distance with
the distribution over the observed data. Through extensive simulations and
real-data experiments, our framework is shown to recover the true causal graphs
more effectively than the baselines in various simulations and real-data
experiments. Empirical evidences also demonstrate the superior scalability of
our approach, along with the flexibility to incorporate any off-the-shelf
causal discovery methods for complete data.