Score-Based Causal Discovery of Latent Variable Causal Models

TL;DR

This paper introduces score-based methods for identifying causal structures involving latent variables, providing theoretical guarantees and unifying existing approaches with experimental validation.

Contribution

It develops score-based causal discovery techniques with identifiability guarantees for models with latent variables, addressing limitations of constraint-based methods.

Findings

Score-based methods achieve score equivalence and consistency.

The methods provide a unified view of existing structural assumptions.

Experimental results demonstrate effectiveness of the proposed approaches.

Abstract

Identifying latent variables and the causal structure involving them is essential across various scientific fields. While many existing works fall under the category of constraint-based methods (with e.g. conditional independence or rank deficiency tests), they may face empirical challenges such as testing-order dependency, error propagation, and choosing an appropriate significance level. These issues can potentially be mitigated by properly designed score-based methods, such as Greedy Equivalence Search (GES) (Chickering, 2002) in the specific setting without latent variables. Yet, formulating score-based methods with latent variables is highly challenging. In this work, we develop score-based methods that are capable of identifying causal structures containing causally-related latent variables with identifiability guarantees. Specifically, we show that a properly formulated scoring function can achieve score equivalence and consistency for structure learning of latent variable causal models. We further provide a characterization of the degrees of freedom for the marginal over the observed variables under multiple structural assumptions considered in the literature, and accordingly develop both exact and continuous score-based methods. This offers a unified view of several existing constraint-based methods with different structural assumptions. Experimental results validate the effectiveness of the proposed methods.