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Titel:

High-dimensional causal discovery under non-Gaussianity

Dokumenttyp:
Zeitschriftenaufsatz
Autor(en):
Wang, Y Samuel; Drton, Mathias
Abstract:
We consider 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 Yv is a linear function of a variable-specific error term and the other observed variables Yu 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 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.
Dewey Dezimalklassifikation:
510 Mathematik
Zeitschriftentitel:
Biometrika
Jahr:
2020
Band / Volume:
107
Jahr / Monat:
2020-03
Quartal:
1. Quartal
Monat:
Mar
Heft / Issue:
1
Seitenangaben Beitrag:
41–59
Sprache:
en
Volltext / DOI:
doi:10.1093/biomet/asz055
Verlag / Institution:
Oxford University Press (OUP)
Print-ISSN:
0006-3444
E-ISSN:
0006-34441464-3510
Publikationsdatum:
01.03.2020
Semester:
WS 19-20
Format:
Text
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