Spectral methods have emerged as a simple yet surprisingly effective approach for
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …

We study the scaling limits of stochastic gradient descent (SGD) with constant step-size in
the high-dimensional regime. We prove limit theorems for the trajectories of summary …

Over the last decade or so, Approximate Message Passing (AMP) algorithms have become
extremely popular in various structured high-dimensional statistical problems. Although the …

We study the problem of estimating the trace of a matrix A that can only be accessed through
matrix-vector multiplication. We introduce a new randomized algorithm, Hutch++, which …

These notes survey and explore an emerging method, which we call the low-degree
method, for understanding statistical-versus-computational tradeoffs in high-dimensional …

Many high-dimensional statistical inference problems are believed to possess inherent
computational hardness. Various frameworks have been proposed to give rigorous …

A precise high-dimensional asymptotic theory for boosting and minimum-l1-norm
interpolated classifiers Page 1 The Annals of Statistics 2022, Vol. 50, No. 3, 1669–1695 …

Complex systems are high-dimensional nonlinear dynamical systems with heterogeneous
interactions among their constituents. To make interpretable predictions about their large …

Computational barriers to estimation from low-degree polynomials Page 1 The Annals of
Statistics 2022, Vol. 50, No. 3, 1833–1858 https://doi.org/10.1214/22-AOS2179 © Institute of …

Researchers currently use a number of approaches to predict and substantiate information-
computation gaps in high-dimensional statistical estimation problems. A prominent …