Score-Based Causal Discovery of Latent Variable Causal Models

• URL: http://arxiv.org/abs/2605.20396v1
• Date: Tue, 19 May 2026 18:44:43 GMT
• Title: Score-Based Causal Discovery of Latent Variable Causal Models
• Abstract summary: We show that a properly formulated scoring function can achieve score equivalence and consistency for structure learning of latent variable causal models.<n>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.
• Score: 44.676955616247334
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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