On Identifying a Massive Number of Distributions

TL;DR

This paper investigates the problem of identifying numerous underlying distributions from observed sequences, providing asymptotic bounds on the probability of error as both the number of distributions and sequences grow with the observation length.

Contribution

It introduces asymptotic bounds on distribution identification error when the number of distributions and sequences increases with blocklength.

Findings

Derived asymptotic upper bounds on error probability.

Established matching lower bounds on identification accuracy.

Abstract

Finding the underlying probability distributions of a set of observed sequences under the constraint that each sequence is generated i.i.d by a distinct distribution is considered. The number of distributions, and hence the number of observed sequences, are let to grow with the observation blocklength $n$. Asymptotically matching upper and lower bounds on the probability of error are derived.