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- Title:
High-dimensional causal discovery under non-Gaussianity
- Document type:
- Zeitschriftenaufsatz
- Author(s):
- 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 Decimal Classification:
- 510 Mathematik
- Journal title:
- Biometrika
- Year:
- 2020
- Journal volume:
- 107
- Year / month:
- 2020-03
- Quarter:
- 1. Quartal
- Month:
- Mar
- Journal issue:
- 1
- Pages contribution:
- 41–59
- Language:
- en
- Fulltext / DOI:
- doi:10.1093/biomet/asz055
- Publisher:
- Oxford University Press (OUP)
- Print-ISSN:
- 0006-3444
- E-ISSN:
- 0006-34441464-3510
- Date of publication:
- 01.03.2020
- Semester:
- WS 19-20
- Format:
- Text
BibTeX