Ordering-Based Causal Structure Learning in the Presence of Latent Variables
This work addresses causal inference in complex systems with hidden variables, offering a novel algorithmic improvement over existing constraint-based methods.
The paper tackles the problem of learning causal graphs with latent confounders by proposing a score-based approach, proving that under weaker assumptions than faithfulness, the sparsest independence map is Markov equivalent to the true model, and demonstrating that their greedy algorithm outperforms state-of-the-art methods like FCI and FCI+ on synthetic data.
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 score-based 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 \emph{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.