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

Let A∈\mathbbR^n*n be a symmetric random matrix with independent and identically
distributed (iid) Gaussian entries above the diagonal. We consider the problem of …

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

Optimization of mean-field spin glasses Page 1 The Annals of Probability 2021, Vol. 49, No. 6,
2922–2960 https://doi.org/10.1214/21-AOP1519 © Institute of Mathematical Statistics, 2021 …

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 …

Clustering is a fundamental primitive in unsupervised learning which gives rise to a rich
class of computationally-challenging inference tasks. In this work, we focus on the canonical …

Given a random $ n\times n $ symmetric matrix $\boldsymbol W $ drawn from the Gaussian
orthogonal ensemble (GOE), we consider the problem of certifying an upper bound on the …

Given a graph and an integer k, Densest k-Subgraph is the algorithmic task of finding the
subgraph on k vertices with the maximum number of edges. This is a fundamental problem …

The Sum-of-Squares (SoS) hierarchy of semidefinite programs is a powerful algorithmic
paradigm which captures state-of-the-art algorithmic guarantees for a wide array of …