Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.09957 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909958929383424 |
|---|---|
| author | Dharamshi, Ameer Neufeld, Anna Gao, Lucy L. Witten, Daniela Bien, Jacob |
| author_facet | Dharamshi, Ameer Neufeld, Anna Gao, Lucy L. Witten, Daniela Bien, Jacob |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09957 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Thinning a Wishart Random Matrix Dharamshi, Ameer Neufeld, Anna Gao, Lucy L. Witten, Daniela Bien, Jacob Methodology Machine Learning 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. |
| title | Thinning a Wishart Random Matrix |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2502.09957 |