9 papers
Dynamical mean-field limit and replica-symmetric free energy for the orthogonally-invariant SK model
Zhou Fan, Theodor Misiakiewicz, Leda Wang +1
We study a class of diffusion processes on interacting through a symmetric matrix . When eigenvectors of are Haar-uniform on the orth…
Kronecker-product random matrices and a matrix least squares problem
Zhou Fan, Renyuan Ma
We study the eigenvalue distribution and resolvent of a Kronecker-product random matrix model $A \otimes I_{n \times n}+I_{n \times n} \otimes B+Î\otimes Î\in \mathbb{C}^{n^2 \ti…
Anisotropic local law for non-separable sample covariance matrices
Zhou Fan, Renyuan Ma, Elliot Paquette +1
We establish local laws for sample covariance matrices $K = N^{-1}\sum_{i=1}^N \g_i\g_i^*$ where the random vectors $\g_1, \ldots, \g_N \in \R^n$ are independent with common covari…
High-dimensional learning dynamics of multi-pass Stochastic Gradient Descent in multi-index models
Zhou Fan, Leda Wang
We study the learning dynamics of a multi-pass, mini-batch Stochastic Gradient Descent (SGD) procedure for empirical risk minimization in high-dimensional multi-index models with i…
When does Gaussian equivalence fail and how to fix it: Non-universal behavior of random features with quadratic scaling
Garrett G. Wen, Hong Hu, Yue M. Lu +2
A major effort in modern high-dimensional statistics has been devoted to the analysis of linear predictors trained on nonlinear feature embeddings via empirical risk minimization (…
Dynamical mean-field analysis of adaptive Langevin diffusions: Replica-symmetric fixed point and empirical Bayes
Zhou Fan, Justin Ko, Bruno Loureiro +2
In many applications of statistical estimation via sampling, one may wish to sample from a high-dimensional target distribution that is adaptively evolving to the samples already s…