2013/11/27 by Ervin Tánczos, Rui Castro, Tánczos, Ervin +2 · 1 citation
Computer Science · Engineering · Mathematics · #Distributed Sensor Networks and Detection Algorithms #FOS: Mathematics #Machine Learning and Algorithms #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1311.7118
arxiv created 2013/11/27 · openalex publication_date 2013/11/27 · arxiv updated 2013/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In many practical settings one can sequentially and adaptively guide the collection of future data, based on information extracted from data collected previously. These sequential data collection procedures are known by different names, such as sequential experimental design, active learning or adaptive sensing/sampling. The intricate relation between data analysis and acquisition in adaptive sensing paradigms can be extremely powerful, and often allows for reliable signal estimation and detection in situations where non-adaptive sensing would fail dramatically. In this work we investigate the problem of estimating the support of a structured sparse signal from coordinate-wise observations under the adaptive sensing paradigm. We present a general procedure for support set estimation that is optimal in a variety of cases and shows that through the use of adaptive sensing one can: (i) mitigate the effect of observation noise when compared to non-adaptive sensing and, (ii) capitalize on structural information to a much larger extent than possible with non-adaptive sensing. In addition to a general procedure to perform adaptive sensing in structured settings we present both performance upper bounds, and corresponding lower bounds for both sensing paradigms.