Sequential Testing for Sparse Recovery

Malloy, Matthew; Nowak, Robert

doi:10.1109/tit.2014.2363846

Cited by 35 publications

(56 citation statements)

References 32 publications

(64 reference statements)

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“…Proof: Define ℓ (θ (1) and ℓ (θ (1) ,ϕ) m (t) instead of ℓ m (t) and ℓ m (t), respectively. Again, since ℓ (θ (1) ,ϕ) m (t) has zero mean for all t > τ M L , all the three terms can be bounded as done in (44).…”

Section: (51)mentioning

confidence: 99%

Searching for Anomalies Over Composite Hypotheses

Hemo

Gafni

Cohen

et al. 2020

IEEE Trans. Signal Process.

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The problem of detecting anomalies in multiple processes is considered. We consider a composite hypothesis case, in which the measurements drawn when observing a process follow a common distribution with an unknown parameter (vector), whose value lies in normal or abnormal parameter spaces, depending on its state. The objective is a sequential search strategy that minimizes the expected detection time subject to an error probability constraint. We develop a deterministic search algorithm with the following desired properties. First, when no additional side information on the process states is known, the proposed algorithm is asymptotically optimal in terms of minimizing the detection delay as the error probability approaches zero. Second, when the parameter value under the null hypothesis is known and equal for all normal processes, the proposed algorithm is asymptotically optimal as well, with better detection time determined by the true null state. Third, when the parameter value under the null hypothesis is unknown, but is known to be equal for all normal processes, the proposed algorithm is consistent in terms of achieving error probability that decays to zero with the detection delay. Finally, an explicit upper bound on the error probability under the proposed algorithm is established for the Bar Hemo, Tomer Gafni and Kobi Cohen are with the

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Section: (51)mentioning

confidence: 99%

Searching for Anomalies Over Composite Hypotheses

Hemo

Gafni

Cohen

et al. 2020

IEEE Trans. Signal Process.

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show abstract

“…The sequential test that we use to examine the identity of a queried component is based on the ideas of distilled sensing introduced and analyzed in Haupt et al (2011) and the Sequential Thresholding procedure of Malloy and Nowak (2014). The distilled sensing algorithm is designed to recover the support of a sparse signal (whose active components remain the same during the sampling process).…”

Section: Algorithm 1: Detection Algorithmmentioning

confidence: 99%

Are there needles in a moving haystack? Adaptive sensing for detection of dynamically evolving signals

Castro¹,

Tánczos²

2019

Bernoulli

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In this paper we investigate the problem of detecting dynamically evolving signals. We model the signal as an n dimensional vector that is either zero or has s non-zero components. At each time step t ∈ N the non-zero components change their location independently with probability p. The statistical problem is to decide whether the signal is a zero vector or in fact it has non-zero components. This decision is based on m noisy observations of individual signal components collected at times t = 1, . . . , m. We consider two different sensing paradigms, namely adaptive and non-adaptive sensing. For non-adaptive sensing the choice of components to measure has to be decided before the data collection process started, while for adaptive sensing one can adjust the sensing process based on observations collected earlier. We characterize the difficulty of this detection problem in both sensing paradigms in terms of the aforementioned parameters, with special interest to the speed of change of the active components. In addition we provide an adaptive sensing algorithm for this problem and contrast its performance to that of non-adaptive detection algorithms.

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“…The procedure presented in [26] has essentially the same performance as this one, and is also a coordinate-wise method that it is based on sequential thresholding. However, it is parameter adaptive and agnostic about s for a wide range of values.…”

Section: Corollary 1 (S-sets) Consider the Setting Of Proposition 2mentioning

confidence: 99%

Adaptive Sensing for Estimation of Structured Sparse Signals

Castro

Tánczos

2015

IEEE Trans. Inform. Theory

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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.

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Sequential Testing for Sparse Recovery

Cited by 35 publications

References 32 publications

Searching for Anomalies Over Composite Hypotheses

Searching for Anomalies Over Composite Hypotheses

Are there needles in a moving haystack? Adaptive sensing for detection of dynamically evolving signals

Adaptive Sensing for Estimation of Structured Sparse Signals

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