Adversarial data augmentation has shown promise for training robust deep neural networks
against unforeseen data shifts or corruptions. However, it is difficult to define heuristics to …

Estimation of mutual information from observed samples is a basic primitive in machine
learning, useful in several learning tasks including correlation mining, information …

The field of property testing originated in work on program checking, and has evolved into
an established and very active research area. In this work, we survey the developments of …

We propose a general methodology for the construction and analysis of essentially minimax
estimators for a wide class of functionals of finite dimensional parameters, and elaborate on …

We show that a class of statistical properties of distributions, which includes such practically
relevant properties as entropy, the number of distinct elements, and distance metrics …

Estimating mutual information from independent identically distributed samples drawn from
an unknown joint density function is a basic statistical problem of broad interest with …

Abstract Le Cam's method, Fano's inequality, and Assouad's lemma are three widely used
techniques to prove lower bounds for statistical estimation tasks. We propose their …

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 …

There is a folkloric belief that a depth-$\Theta (m) $ quantum circuit is needed to estimate the
trace of the product of $ m $ density matrices (ie, a multivariate trace), a subroutine crucial to …

We consider the problem of estimating the support size of a discrete distribution whose
minimum nonzero mass is at least 1 k. Under the independent sampling model, we show …