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arXiv · 2410.05280

Sampling Spiked Wishart Eigenvalues

Thomas G. Brooks
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Abstract

Efficient schemes for sampling from the eigenvalues of the Wishart distribution have recently been described for both the uncorrelated central case (where the covariance matrix is $\mathbf{I}$) and the spiked Wishart with a single spike (where the covariance matrix differs from $\mathbf{I}$ in a single entry on the diagonal). Here, we generalize these schemes to the spiked Wishart with an arbitrary number of spikes. This approach also applies to the spiked pseudo-Wishart distribution. We describe how to differentiate this procedure for the purposes of stochastic gradient descent, allowing the fitting of the eigenvalue distribution to some target distribution.

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Thomas G. Brooks. 2024-09-25. Sampling Spiked Wishart Eigenvalues. https://arxiv.org/abs/2410.05280

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