We give a brief survey of the literature on the empirical estimation of entropy, differential
entropy, relative entropy, mutual information and related information measures. While those …

We consider the problem of estimating the L 1 distance between two discrete probability
measures P and Q from empirical data in a nonasymptotic and large alphabet setting. When …

In recent years, with the continuous breakthrough of computer vision technology, the
accuracy of object detection and target recognition has been improved by leaps and …

Consider a finite sample from an unknown distribution over a countable alphabet. The
occupancy probability (OP) refers to the total probability of symbols that appear exactly k …

The mean of an unknown variance-$\sigma^ 2$ distribution $ f $ can be estimated from $ n $
samples with variance $\frac {\sigma^ 2}{n} $ and nearly corresponding subgaussian rate …

Abstract We present\emph {Local Moment Matching (LMM)}, a unified methodology for
symmetric functional estimation and distribution estimation under Wasserstein distance. We …

Estimating the number of distinct values (NDV) in a column is useful for many tasks in
database systems, such as columnstore compression and data profiling. In this work, we …

With the recent progress of science and the development of society, the development of
artificial intelligence technology and robot theory have become increasingly mature …

Estimating symmetric properties of a distribution, eg support size, coverage, entropy,
distance to uniformity, are among the most fundamental problems in algorithmic statistics …

We study three fundamental statistical-learning problems: distribution estimation, property
estimation, and property testing. We establish the profile maximum likelihood (PML) …