Thinning a Wishart Random Matrix Article Swipe

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Ameer Dharamshi , Anna Neufeld , Lucy L. Gao , Daniela Witten , Jacob Bien ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2502.09957

Recent work has explored data thinning, a generalization of sample splitting that involves decomposing a (possibly matrix-valued) random variable into independent components. In the special case of a $n \times p$ random matrix with independent and identically distributed $N_p(μ, Σ)$ rows, Dharamshi et al. (2024a) provides a comprehensive analysis of the settings in which thinning is or is not possible: briefly, if $Σ$ is unknown, then one can thin provided that $n>1$. However, in some situations a data analyst may not have direct access to the data itself. For example, to preserve individuals' privacy, a data bank may provide only summary statistics such as the sample mean and sample covariance matrix. While the sample mean follows a Gaussian distribution, the sample covariance follows (up to scaling) a Wishart distribution, for which no thinning strategies have yet been proposed. In this note, we fill this gap: we show that it is possible to generate two independent data matrices with independent $N_p(μ, Σ)$ rows, based only on the sample mean and sample covariance matrix. These independent data matrices can either be used directly within a train-test paradigm, or can be used to derive independent summary statistics. Furthermore, they can be recombined to yield the original sample mean and sample covariance.

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Wishart distribution Thinning Matrix (chemical analysis) Mathematics Statistics Chemistry Geography Chromatography Multivariate statistics Forestry

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2502.09957
PDF: https://arxiv.org/pdf/2502.09957
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4407632472

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DOI: https://doi.org/10.48550/arxiv.2502.09957

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Title: Thinning a Wishart Random Matrix

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Type: preprint

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Language: en

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Publication year: 2025

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Publication date: 2025-02-14

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Authors: Ameer Dharamshi, Anna Neufeld, Lucy L. Gao, Daniela Witten, Jacob Bien

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Landing page: https://arxiv.org/abs/2502.09957

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PDF URL: https://arxiv.org/pdf/2502.09957

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Concepts: Wishart distribution, Thinning, Matrix (chemical analysis), Mathematics, Statistics, Chemistry, Geography, Chromatography, Multivariate statistics, Forestry

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