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

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 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.

To appear in AISTATS 2020

References in corpus (9)

• A Transformational Characterization of Equivalent Bayesian Network Structures
• Geometry of the faithfulness assumption in causal inference
• ${\ell }_0$-penalized maximum likelihood for sparse directed acyclic graphs
• Enumerating Markov Equivalence Classes of Acyclic Digraph Models
• Strong Faithfulness and Uniform Consistency in Causal Inference
• Markov properties for mixed graphs
• Adjacency-Faithfulness and Conservative Causal Inference
• Parameter and Structure Learning in Nested Markov Models
• A Transformational Characterization of Markov Equivalence for Directed Acyclic Graphs with Latent Variables

Cited by in corpus (2)

• Computably Continuous Reinforcement-Learning Objectives are PAC-learnable
• Bayesian network structure learning with causal effects in the presence of latent variables