Decomposing Gaussians with unknown covariance

A Dharamshi, A Neufeld, L L Gao, J Bien and D Witten

Biometrika, 2026, vol. 113, issue 1, asaf057.

Abstract: Common workflows in machine learning and statistics rely on the ability to partition the information in a dataset into independent portions. Recent work has shown that this may be possible even when conventional sample splitting is not, such as when the number of samples, , is one or when observations are not independent and identically distributed. In the case of multivariate Gaussian data, these alternatives to sample splitting require knowledge of the covariance matrix. In many important problems, such as in spatial or longitudinal data analysis and in graphical modelling, the covariance matrix may be unknown and even of primary interest. Therefore, in this work we develop new approaches for decomposing multivariate Gaussians with unknown covariance. First, we present a general algorithm that encompasses all previous decomposition methods for Gaussian data as special cases and which can further handle the case of unknown covariance. It yields a new and more flexible alternative to sample splitting when . When , we prove that it is impossible to partition the information in a multivariate Gaussian into independent portions without knowing the covariance matrix. Hence, we use the general algorithm to decompose a single multivariate Gaussian with unknown covariance into dependent parts with tractable conditional distributions and demonstrate their use for inference and validation. The proposed decomposition strategy extends naturally to Gaussian processes. In simulations and for electroencephalography data, we apply these decompositions to the tasks of model selection and post-selection inference in settings where alternative strategies are unavailable.

Keywords: Correlated data; Model validation; Multivariate Gaussian; Randomization; Sample splitting; Selective inference (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1093/biomet/asaf057 (application/pdf)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:oup:biomet:v:113:y:2026:i:1:p:asaf057.

Ordering information: This journal article can be ordered from
https://academic.oup.com/journals

Access Statistics for this article

Biometrika is currently edited by Paul Fearnhead

More articles in Biometrika from Biometrika Trust Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK.
Bibliographic data for series maintained by Oxford University Press ().