We raise the question of approximating compressibility of a string with respect to a fixed compression scheme, in sublinear time. We study this question in detail for two popular lossless compression schemes: run-length encoding (RLE) and Lempel-Ziv (LZ), and present algorithms and lower bounds for approximating compressibility with respect to ... 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 >>>

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 >>>