High-dimensional causal discovery under non-Gaussianity

• 成果类型: Article
• 署名作者: Wang, Y. Samuel; Drton, Mathias
• 署名单位: University of Chicago; Technical University of Munich
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asz055
• 发表日期: 2020
• 页码: 4159
• 关键词: graphs

摘要

We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, sigma, of the variables such that each observed variable Y-v is a linear function of a variable-specific error term and the other observed variables Y-u with sigma(u) < sigma(v). The causal relationships, i.e., which other variables the linear functions depend on, can be described using a directed graph. It has previously been shown that when the variable-specific error terms are non-Gaussian, the exact causal graph, as opposed to a Markov equivalence class, can be consistently estimated from observational data. We propose an algorithm that yields consistent estimates of the graph also in high-dimensional settings in which the number of variables may grow at a faster rate than the number of observations, but in which the underlying causal structure features suitable sparsity; specifically, the maximum in-degree of the graph is controlled. Our theoretical analysis is couched in the setting of log-concave error distributions.