Journal article
Hypothesis Testing for Subset Identification: A Linear Measurement Scheme
IEEE transactions on signal processing, Vol.73, pp.4605-4621
2025
DOI: 10.1109/TSP.2025.3622365
Abstract
In this paper, we propose the concept of compressed hypothesis testing to perform hypothesis testing using a small number of linear sketching measurements, namely observations that are functions of multiple random variables. In particular, we investigate the problem of identifying <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula> anomalous random variables that follow different probability distributions from the remaining <inline-formula><tex-math notation="LaTeX">(n \text{-} k)</tex-math></inline-formula> random variables, where <inline-formula><tex-math notation="LaTeX">k < n</tex-math></inline-formula>. Instead of individually sampling each random variable, as typically done in conventional hypothesis testing, we propose a novel approach using sketching observations which are functions of multiple random variables. We analyze the error exponents for accurately detecting the <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula> anomalous random variables under various observation models: fixed time-invariant sketching observations, random time-varying sketching observations, and deterministic time-varying sketching observations. In characterizing the error exponents under sketching observations, we introduce "inner conditional Chernoff information" and "outer conditional Chernoff information." Our findings demonstrate that sketching observations can significantly enhance the error exponents in hypothesis testing compared to separate observations of individual random variables. These results show the potential of sketching observations in reducing the required number of samples for hypothesis testing applications, e.g., anomaly detection in network tomography. To address large-scale hypothesis testing challenges, we additionally propose two efficient decoding algorithms: a LASSO-based approach and a message-passing-based method. Through numerical experiments, we demonstrate the advantages of our proposed concepts and methods compared to conventional hypothesis testing, which samples each random variable separately, with a real-world application in network tomography.
Details
- Title: Subtitle
- Hypothesis Testing for Subset Identification: A Linear Measurement Scheme
- Creators
- Myung Cho - California State University, NorthridgeWeiyu Xu - University of IowaZiqing Lu - University of IowaLifeng Lai - University of California, Davis
- Resource Type
- Journal article
- Publication Details
- IEEE transactions on signal processing, Vol.73, pp.4605-4621
- DOI
- 10.1109/TSP.2025.3622365
- ISSN
- 1053-587X
- eISSN
- 1941-0476
- Publisher
- IEEE
- Number of pages
- 16
- Language
- English
- Electronic publication date
- 10/15/2025
- Date published
- 2025
- Academic Unit
- Electrical and Computer Engineering
- Record Identifier
- 9985019031202771
Metrics
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