In this review article we discuss connections between the physics of disordered systems,
phase transitions in inference problems, and computational hardness. We introduce two …

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 …

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 …

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

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

In this paper, we propose a general framework for tensor singular value decomposition
(tensor singular value decomposition (SVD)), which focuses on the methodology and theory …

We use the Sum of Squares method to develop new efficient algorithms for learning well-
separated mixtures of Gaussians and robust mean estimation, both in high dimensions, that …

We develop efficient algorithms for estimating low-degree moments of unknown distributions
in the presence of adversarial outliers and design a new family of convex relaxations for k …

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

We study planted problems-finding hidden structures in random noisy inputs-through the
lens of the sum-of-squares semidefinite programming hierarchy (SoS). This family of …