Learning causal structures using hidden compact representation

Abstract

Learning causal structures from observational data is of great challenge and interest in many disciplines. Various methods have demonstrated their effectiveness for causal structure learning on different types of data, but most of them are suffered from the indeterminacy of Markov equivalence classes, especially on discrete data. A recent breakthrough formulates the problem as finding a hidden compact representation (HCR) with lower cardinality to distinguish the correct causal direction. However, method based on the HCR model is only applicable in bivariate cases. In this paper, we generalize the HCR model to multivariate cases and provide an effective likelihood-based algorithm for causal structure learning in presence of hidden compact representation. Our theoretical results show that under some weak technique conditions about the underlying causal mechanism, causal directions are still identifiable even in multivariate cases. Our empirical studies demonstrate the effectiveness of proposed methods on various types of data and structures.