STOC

We investigate the statistical task of closeness (or equivalence) testing for multidimensional distributions. Specifically, given sample access to two unknown distributions p, q on ^d, we want to distinguish between the case that p=q versus ||p−q||_Ak > є, ...

Approximate message passing (AMP) is a family of iterative algorithms that generalize matrix power iteration. AMP algorithms are known to optimally solve many average-case optimization problems. In this paper, we show that a large class of AMP algorithms ...

The planted clique conjecture states that no polynomial-time algorithm can find a hidden clique of size k ≪ √n in an n-vertex Erdős–Rényi random graph with a k-clique planted. In this paper, we prove the equivalence among many (in fact, most) variants of ...

We study the problem of robust community recovery: efficiently recovering communities in sparse stochastic block models in the presence of adversarial corruptions. In the absence of adversarial corruptions, there are efficient algorithms when the signal-...

We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This setting ...