{"ID":2893853,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.12019","arxiv_id":"2507.12019","title":"The Role of Rank in Mismatched Low-Rank Symmetric Matrix Estimation","abstract":"We investigate the performance of a Bayesian statistician tasked with recovering a rank-\\(k\\) signal matrix \\(\\bS \\bS^{\\top} \\in \\mathbb{R}^{n \\times n}\\), corrupted by element-wise additive Gaussian noise. This problem lies at the core of numerous applications in machine learning, signal processing, and statistics. We derive an analytic expression for the asymptotic mean-square error (MSE) of the Bayesian estimator under mismatches in the assumed signal rank, signal power, and signal-to-noise ratio (SNR), considering both sphere and Gaussian signals. Additionally, we conduct a rigorous analysis of how rank mismatch influences the asymptotic MSE. Our primary technical tools include the spectrum of Gaussian orthogonal ensembles (GOE) with low-rank perturbations and asymptotic behavior of \\(k\\)-dimensional spherical integrals.","short_abstract":"We investigate the performance of a Bayesian statistician tasked with recovering a rank-\\(k\\) signal matrix \\(\\bS \\bS^{\\top} \\in \\mathbb{R}^{n \\times n}\\), corrupted by element-wise additive Gaussian noise. This problem lies at the core of numerous applications in machine learning, signal processing, and statistics. We...","url_abs":"https://arxiv.org/abs/2507.12019","url_pdf":"https://arxiv.org/pdf/2507.12019v1","authors":"[\"Panpan Niu\",\"Yuhao Liu\",\"Teng Fu\",\"Jie Fan\",\"Chaowen Deng\",\"Zhongyi Huang\"]","published":"2025-07-16T08:24:44Z","proceeding":"cs.IT","tasks":"[\"cs.IT\",\"eess.SP\"]","methods":"[]","has_code":false}