Detection of a planted dense subgraph in a random graph is a fundamental...
We study the computational complexity of two related problems: recoverin...
Planted dense cycles are a type of latent structure that appears in many...
Random graph models with community structure have been studied extensive...
We consider the problem of estimating an unknown parameter vector
θ∈ℝ^n,...
Suppose we are given an n-dimensional order-3 symmetric tensor T ∈
(ℝ^n)...
Given independent standard Gaussian points v_1, …, v_n in dimension
d, f...
We study the group testing problem where the goal is to identify a set o...
Many high-dimensional statistical inference problems are believed to pos...
Clustering is a fundamental primitive in unsupervised learning which giv...
We consider the problem of finding a near ground state of a p-spin model...
Recovering a planted vector v in an n-dimensional random subspace of
ℝ^N...
Montanari and Richard (2015) asked whether a natural semidefinite progra...
We study the algorithmic task of finding a large independent set in a sp...
We study the problem of efficiently refuting the k-colorability of a gra...
One fundamental goal of high-dimensional statistics is to detect or reco...
We study a variant of the sparse PCA (principal component analysis) prob...
In compressed sensing, the restricted isometry property (RIP) on M × N
s...
We study statistical and computational limits of clustering when the mea...
We consider the problem of finding nearly optimal solutions of optimizat...
A conjecture of Hopkins (2018) posits that for certain high-dimensional
...
These notes survey and explore an emerging method, which we call the
low...
We study the computational cost of recovering a unit-norm sparse princip...
For the tensor PCA (principal component analysis) problem, we propose a ...
Given a random n × n symmetric matrix W drawn from the
Gaussian orthogo...
A tensor network is a diagram that specifies a way to "multiply" a colle...
A central problem of random matrix theory is to understand the eigenvalu...
In these notes we describe heuristics to predict computational-to-statis...
Motivated by geometric problems in signal processing, computer vision, a...
We study the statistical limits of both detecting and estimating a rank-...
Various alignment problems arising in cryo-electron microscopy, communit...
A central problem of random matrix theory is to understand the eigenvalu...
The stochastic block model is one of the oldest and most ubiquitous mode...