Causal Structural Learning Via Local Graphs

Abstract

We consider the problem of learning causal structures in sparse high-dimensional settings that may be subject to the presence of (potentially many) unmeasured confounders, as well as selection bias. Based on the structure found in common families of large random networks and examining the representation of local structures in linear structural equation models (SEM), we propose a new local notion of sparsity for consistent structure learning in the presence of latent and selection variables, and develop a new version of the Fast Causal Inference (FCI) algorithm with reduced computational and sample complexity, which we refer to as local FCI (lFCI). The new notion of sparsity allows the presence of highly connected hub nodes, which are common in real-world networks, but problematic for existing methods. Our numerical experiments indicate that the lFCI algorithm achieves state-of-the-art performance across many classes of large random networks, and its performance is superior to that of existing methods for networks containing hub nodes.

References in corpus (11)

• Extended Bayesian Information Criteria for Gaussian Graphical Models
• Estimating high-dimensional directed acyclic graphs with the PC-algorithm
• Ising models on locally tree-like graphs
• High-dimensional structure estimation in Ising models: Local separation criterion
• Markov equivalence for ancestral graphs
• Binary Models for Marginal Independence
• Fast and Adaptive Sparse Precision Matrix Estimation in High Dimensions
• High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion
• Ising models on power-law random graphs
• Learning Sparse Causal Models is not NP-hard
• Generalized Score Matching for Non-Negative Data

Cited by in corpus (2)

• Causal Discovery with Unobserved Confounding and non-Gaussian Data
• Causal Discovery in High-Dimensional Point Process Networks with Hidden Nodes