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 …

In the noisy tensor completion problem we observe m entries (whose location is chosen
uniformly at random) from an unknown n_1\times n_2\times n_3 tensor T. We assume that T …

Recently, research in unsupervised learning has gravitated towards exploring statistical-
computational gaps induced by sparsity. A line of work initiated in Berthet and Rigollet …

This paper establishes a statistical versus computational trade-offfor solving a basic high-
dimensional machine learning problem via a basic convex relaxation method. Specifically …

This chapter provides a survey of the common techniques for determining the sharp
statistical and computational limits in high-dimensional statistical problems with planted …

Analyzing concentration of large random matrices is a common task in a wide variety of
fields. Given independent random variables, several tools are available to bound the norms …

The problem of finding large cliques in random graphs and its “planted” variant, where one
wants to recover a clique of size ω> log (n) added to an Erdős-Rényi graph G∼ G (n, 1/2) …

We study a semidefinite programming (SDP) relaxation of the maximum likelihood
estimation for exactly recovering a hidden community of cardinality K from an n\times n …

We prove that with high probability over the choice of a random graph $ G $ from the Erd\H
{o} sR\'enyi distribution $ G (n, 1/2) $, a natural $ n^{O (\varepsilon^ 2\log n)} $-time, degree …

In this paper, we derive nearly tight probabilistic norm bounds for a class of random matrices
we call graph matrices. While the classical case of symmetric matrices with independent …