High-Dimensional Discovery Under non-Gaussianity
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We consider data from graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, σ, 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 σ(u) < σ (v). The causal relationships, i.e., which other variables the linear functions depend on, can be described using a directed graph. It has been previously 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.
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