Distribution of singular values in large sample cross-covariance matrices
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915467120082944 |
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| author | Swain, Arabind Ridout, Sean Alexander Nemenman, Ilya |
| author_facet | Swain, Arabind Ridout, Sean Alexander Nemenman, Ilya |
| contents | For two large matrices ${\mathbf X}$ and ${\mathbf Y}$ with Gaussian i.i.d.\ entries and dimensions $T\times N_X$ and $T\times N_Y$, respectively, we derive the probability distribution of the singular values of $\mathbf{X}^T \mathbf{Y}$ in different parameter regimes. This extends the Marchenko-Pastur result for the distribution of eigenvalues of empirical sample covariance matrices to singular values of empirical cross-covariances. Our results will help to establish statistical significance of cross-correlations in many data-science applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05254 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distribution of singular values in large sample cross-covariance matrices Swain, Arabind Ridout, Sean Alexander Nemenman, Ilya Statistics Theory Disordered Systems and Neural Networks Data Analysis, Statistics and Probability For two large matrices ${\mathbf X}$ and ${\mathbf Y}$ with Gaussian i.i.d.\ entries and dimensions $T\times N_X$ and $T\times N_Y$, respectively, we derive the probability distribution of the singular values of $\mathbf{X}^T \mathbf{Y}$ in different parameter regimes. This extends the Marchenko-Pastur result for the distribution of eigenvalues of empirical sample covariance matrices to singular values of empirical cross-covariances. Our results will help to establish statistical significance of cross-correlations in many data-science applications. |
| title | Distribution of singular values in large sample cross-covariance matrices |
| topic | Statistics Theory Disordered Systems and Neural Networks Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2502.05254 |