Adaptive sensing performance lower bounds for sparse signal detection and support estimation

Abstract

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A performance guarantee for adaptive estimation of sparse signals

“…Future work will consider the extension of the techniques in this paper to estimation loss functions other than MSE, to analogous policies for adaptive spectrum sensing [10], to other tasks such as signal support recovery, and to direct analysis of policies with more than two stages. In addition, it would be desirable to determine fundamental limits on adaptive sensing, along the lines of [12], [13], for the problem considered in this work.…”

Detection of Correlations With Adaptive Sensing

“…The behavior of the minimax risk has been analyzed for various class choices C [1], [7], [11], [22]. Detection and estimation in this model has been analyzed under adaptive sensing in [13] and [19], where it is shown that, perhaps surprisingly, all sufficiently symmetric classes C lead to the same almost matching necessary and sufficient conditions for detection. This is quite different from the non-adaptive version of the problem where size and structure of C influence, in a significant way, possibilities of detection (see [1]).…”

“…Here, in order to bound the maximum KL divergence, we will take an approach similar to [13] for detection-of-means under adaptive sensing, although our setup differs slightly. In [13], the testing procedures measure a single coordinate at a time, while we need multiple measures per step in order to capture correlations. We have the following necessary condition.…”

“…This phenomenon is akin to what was observed in the context of detection-of-means under adaptive sensing, where the lower bounds are the same provided the classes of contaminated components are symmetric. In this setting, it was shown in addition in [13] that the condition in the lower bound is essentially sufficient and therefore, unlike in the non-adaptive counterpart of the problem, knowledge of the structure of C does not make the detection problem any easier. However, the problem of detection of correlations considered here seems to be more subtle in that one lacks matching upper bounds for all cases.…”

“…More precisely, data is collected in a sequential and adaptive way, where data collected at earlier stages informs the collection of data in future stages. Adaptive sensing has been studied in the context of other detection and estimation problems, such as in detection of a shift in the mean of a Gaussian vector [13], [19], in compressed sensing [6], [13], [18], in experimental design, optimization with Gaussian processes [36], and in active learning [15]. Adaptive sensing procedures are quite flexible, as the data collection procedure can be "steered" to ensure most collected data provides important information.…”