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Compressed Hypothesis Testing: To Mix or Not to Mix? by Cho, Myung; Xu, Weiyu; Lai, Lifeng is a scholarly article available to read on EtoBox.

What is Compressed Hypothesis Testing: To Mix or Not to Mix? about?

In this paper, we study the problem of determining $k$ anomalous random variables that have different probability distributions from the rest $(n-k)$ random variables. Instead of sampling each individual random variable separately as in the conventional hypothesis testing, we propose to perform hypothesis testing using mixed observations that are functions of multiple random variables. We characterize the error exponents for correctly identifying the $k$ anomalous random variables under fixed time-invariant mixed observations, random time-varying mixed observations, and deterministic time-varying mixed observations. For our error exponent characterization, we introduce the notions of inner conditional Chernoff information and outer conditional Chernoff information. It is demonstrated that mixed observations can strictly improve the error exponents of hypothesis testing, over separate observations of individual random variables. We further characterize the optimal sensing vector maximizing the error exponents, which leads to explicit constructions of the optimal mixed observations in special cases of hypothesis testing for Gaussian random variables. These results show that mixed obs

Author

Cho, Myung; Xu, Weiyu; Lai, Lifeng

Published

2016

Language

EN