Given a set of $n$ random $d$-dimensional boolean vectors with the promise that two of them are $\rho$-correlated with each other, how quickly can one find the two correlated vectors? We present a surprising and simple algorithm which, for any constant $\epsilon>0$ runs in (expected) time $d n^{\frac{3 \omega}{4}+\epsilon} poly(\frac{1}{\rho})< ... more >>>

We introduce a new approach to characterizing the unobserved portion of a distribution, which provides sublinear-sample additive estimators for a class of properties that includes entropy and distribution support size. Together with the lower bounds proven in the companion paper [29], this settles the longstanding question of the sample complexities ... more >>>

We prove two new multivariate central limit theorems; the first relates the sum of independent distributions to the multivariate Gaussian of corresponding mean and covariance, under the earthmover distance matric (also known as the Wasserstein metric). We leverage this central limit theorem to prove a stronger but more specific central ... more >>>