A quantitative Heppes Theorem and multivariate Bernoulli distributions

TL;DR

This paper extends Heppes' theorem to multivariate Bernoulli distributions, enabling distribution determination through projections, with applications in classification and testing for known support cases.

Contribution

It introduces an extension of Heppes' theorem for finitely supported measures, specifically applied to multivariate Bernoulli distributions, facilitating distribution identification via projections.

Findings

A single projection can determine the distribution when support is known.

Extensions of Heppes' theorem are applicable to multivariate Bernoulli distributions.

The results have practical applications in classification and testing.

Abstract

Using some extensions of a theorem of Heppes on finitely supported discrete probability measures, we address the problems of classification and testing based on projections. In particular, when the support of the distributions is known in advance (as for instance for multivariate Bernoulli distributions), a single suitably chosen projection determines the distribution. Several applications of these results are considered.