Bayes-optimal limits in structured PCA, and how to reach them. (arXiv:2210.01237v1 [cs.IT])

We study the paradigmatic spiked matrix model of principal components
analysis, where the rank-one signal is corrupted by additive noise. While the
noise is typically taken from a Wigner matrix with independent entries, here
the potential acting on the eigenvalues has a quadratic plus a quartic
component. The quartic term induces strong correlations between the matrix
elements, which makes the setting relevant for applications but analytically
challenging. Our work provides the first characterization of the Bayes-optimal
limits for inference in …

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