Ordering-Based Causal Structure Learning in the Presence of Latent Variables

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Daniel Bernstein, Basil Saeed, Chandler Squires, Caroline Uhler ;
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:4098-4108, 2020.

Abstract

We consider the task of learning a causal graph in the presence of latent confounders given i.i.d.samples from the model. While current algorithms for causal structure discovery in the presence of latent confounders are constraint-based, we here propose a hybrid approach. We prove that under assumptions weaker than faithfulness, any sparsest independence map (IMAP) of the distribution belongs to the Markov equivalence class of the true model. This motivates the Sparsest Poset formulation - that posets can be mapped to minimal IMAPs of the true model such that the sparsest of these IMAPs is Markov equivalent to the true model. Motivated by this result, we propose a greedy algorithm over the space of posets for causal structure discovery in the presence of latent confounders and compare its performance to the current state-of-the-art algorithms FCI and FCI+ on synthetic data.

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