Publication Date:
2019-10-25
Description:
Summary 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.
Print ISSN:
0006-3444
Electronic ISSN:
1464-3510
Topics:
Biology
,
Mathematics
,
Medicine
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