We focus on the task of learning a single index model $\sigma (w^\star\cdot x) $ with respect
to the isotropic Gaussian distribution in $ d $ dimensions. Prior work has shown that the …

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 …

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

Mathematics in Zurich has a long and distinguished tradition, in which the writing of lecture
notes volumes and research monographs plays a prominent part. The Zurich Lectures in …

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

Inference problems with conjectured statistical-computational gaps are ubiquitous
throughout modern statistics, computer science, statistical physics and discrete probability …

Despite the non-convex optimization landscape, over-parametrized shallow networks are
able to achieve global convergence under gradient descent. The picture can be radically …

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 …

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 …