HAMILTON-JACOBI EQUATIONS FOR NONSYMMETRIC MATRIX INFERENCE

• 成果类型: Article
• 署名作者: Chen, Hong-Bin
• 署名单位: New York University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1739
• 发表日期: 2022
• 页码: 2540-2567
• 关键词: formula; LIMITS

摘要

We study the high-dimensional limit of the free energy associated with the inference problem of a rank-one nonsymmetric matrix. The matrix is expressed as the outer product of two vectors, not necessarily independent. The distributions of the two vectors are only assumed to have scaled bounded supports. We bound the difference between the free energy and the solution to a suitable Hamilton-Jacobi equation in terms of two much simpler quantities: concentration rate of this free energy, and the convergence rate of a simpler free energy in a decoupled system. To demonstrate the versatility of this approach, we apply our result to the i.i.d. case and the spherical case. By plugging in estimates of the two simpler quantities, we identify the limits and obtain convergence rates.