The Missing Mass Problem

TL;DR

This paper establishes precise bounds on the expected missing mass for various distributions, providing insights into extremal cases and extending results to metric spaces, which could impact statistical estimation and learning theory.

Contribution

It offers tight bounds on the expected missing mass and characterizes extremal distributions, extending the analysis to totally bounded metric spaces.

Findings

Tight bounds on expected missing mass for finite and countably infinite spaces.

Characterization of extremal distributions for missing mass.

Extension of results to totally bounded metric spaces.

Abstract

We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally bounded metric spaces that may be of independent interest.