Neyman-Pearson Test for Zero-Rate Multiterminal Hypothesis Testing

TL;DR

This paper introduces a Neyman-Pearson-like test for zero-rate multiterminal hypothesis testing, demonstrating its superior performance over previous methods in finite blocklength and large deviation regimes using information-spectrum and information geometry techniques.

Contribution

It proposes a new Neyman-Pearson-like test for zero-rate multiterminal hypothesis testing, with proven optimality in finite and asymptotic regimes, advancing the understanding of non-asymptotic performance.

Findings

Proposed test outperforms Hoeffding-like test at short block lengths.

Achieves optimal trade-off between type I and type II exponents in large deviation regime.

Optimal up to second-order term of type II error exponent when type I error is non-vanishing.

Abstract

The problem of zero-rate multiterminal hypothesis testing is revisited from the perspective of information-spectrum approach and finite blocklength analysis. A Neyman-Pearson-like test is proposed and its non-asymptotic performance is clarified; for a short block length, it is numerically determined that the proposed test is superior to the previously reported Hoeffding-like test proposed by Han-Kobayashi. For a large deviation regime, it is shown that our proposed test achieves an optimal trade-off between the type I and type II exponents presented by Han-Kobayashi. Among the class of symmetric (type based) testing schemes, when the type I error probability is non-vanishing, the proposed test is optimal up to the second-order term of the type II error exponent; the latter term is characterized in terms of the variance of the projected relative entropy density. The information geometry method plays an important role in the analysis as well as the construction of the test.