# Optimal Rate-Exponent Region for a Class of Hypothesis Testing Against Conditional Independence Problems

## TL;DR

This paper characterizes the optimal encoding rates and error exponents for distributed hypothesis testing against conditional independence, providing theoretical insights for both discrete and Gaussian settings.

## Contribution

It offers a new theoretical characterization of the rate-exponent region for a specific class of distributed hypothesis testing problems.

## Key findings

- Derived the optimal rate-exponent region for discrete memoryless settings.
- Extended the characterization to memoryless vector Gaussian settings.
- Provides fundamental limits for hypothesis testing with constrained error probabilities.

## Abstract

We study a class of distributed hypothesis testing against conditional independence problems. Under the criterion that stipulates minimization of the Type II error rate subject to a (constant) upper bound $\epsilon$ on the Type I error rate, we characterize the set of encoding rates and exponent for both discrete memoryless and memoryless vector Gaussian settings.