Scalable Differentiable Causal Discovery in the Presence of Latent Confounders with Skeleton Posterior (Extended Version)
This work addresses a scalability bottleneck in causal discovery for real-world applications, offering a novel method to handle latent confounders more efficiently.
The paper tackles the challenge of scaling differentiable causal discovery to larger datasets with latent confounders by proposing SPOT, a two-phase framework that uses skeleton posterior estimation to improve accuracy and reduce search space, achieving state-of-the-art results on datasets with up to 100 variables.
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]