Consider the problem of estimating the Shannon entropy of a distribution over k elements from n independent samples. We show that the minimax mean-square error is within the universal multiplicativeâ€¦ (More)

Resolving a conjecture of Abbe, Bandeira, and Hall, the authors have recently shown that the semidefinite programming (SDP) relaxation of the maximum likelihood estimator achieves the sharp thresholdâ€¦ (More)

The binary symmetric stochastic block model deals with a random graph of n vertices partitioned into two equal-sized clusters, such that each pair of vertices is independently connected withâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

2016

Estimating the number of unseen species is an important problem in many scientific endeavors. Its most popular formulation, introduced by Fisher et al. [Fisher RA, Corbet AS, Williams CB (1943) Jâ€¦ (More)

Compressed sensing of simultaneously sparse and low-rank matrices enables recovery of sparse signals from a few linear measurements of their bilinear form. One important question is how manyâ€¦ (More)

Self-recalibration of the relative pose in a vision system plays a very important role in many applications and much research has been conducted on this issue over the years. However, most existingâ€¦ (More)

We study the problem of recovering a hidden community of cardinality <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> from an <inline-formula> <tex-mathâ€¦ (More)