Scalable Differentiable Causal Discovery in the Presence of Latent Confounders with Skeleton Posterior (Extended Version)

TL;DR

This paper introduces SPOT, a scalable framework for differentiable causal discovery that effectively incorporates skeleton posterior estimation to handle latent confounders and large datasets.

Contribution

The paper proposes a novel two-phase framework, SPOT, which estimates skeleton posteriors and guides MAG learning, improving scalability and accuracy in causal discovery with latent confounders.

Findings

SPOT outperforms existing methods on large datasets with over 50 variables.

Skeleton posterior estimation enhances causal discovery accuracy.

The framework effectively handles latent confounders in complex datasets.

Abstract

Differentiable causal discovery has made significant advancements in the learning of directed acyclic graphs. However, its application to real-world datasets remains restricted due to the ubiquity of latent confounders and the requirement to learn maximal ancestral graphs (MAGs). To date, existing differentiable MAG learning algorithms have been limited to small datasets and failed to scale to larger ones (e.g., with more than 50 variables). The key insight in this paper is that the causal skeleton, which is the undirected version of the causal graph, has potential for improving accuracy and reducing the search space of the optimization procedure, thereby enhancing the performance of differentiable causal discovery. Therefore, we seek to address a two-fold challenge to harness the potential of the causal skeleton for differentiable causal discovery in the presence of latent confounders: (1) scalable and accurate estimation of skeleton and (2) universal integration of skeleton estimation with differentiable causal discovery. To this end, we propose SPOT (Skeleton Posterior-guided OpTimization), a two-phase framework that harnesses skeleton posterior for differentiable causal discovery in the presence of latent confounders. On the contrary to a ``point-estimation'', SPOT seeks to estimate the posterior distribution of skeletons given the dataset. It first formulates the posterior inference as an instance of amortized inference problem and concretizes it with a supervised causal learning (SCL)-enabled solution to estimate the skeleton posterior. To incorporate the skeleton posterior with differentiable causal discovery, SPOT then features a skeleton posterior-guided stochastic optimization procedure to guide the optimization of MAGs. [abridged due to length limit]