On finding a subset of non-defective items from a large population using group tests: Recovery algorithms and bounds

Nyquist sampling at very high carriers can be prohibitively costly for low power wireless devices. In spectrum sensing, this limit calls for an analog front-end that can sweep different bands quickly, in order to use the available spectrum opportunistically. In this paper we propose a new sub-Nyquist analog front-end and a sensing strategy formulated as a sequential utility optimization problem. The sensing action maximizes a utility function decreasing linearly with the number of measurements, and increasing as a function of the active spectrum components that are correctly detected. The optimization selects the best linear combinations of sub-bands to mix, in order to accrue maximum utility. The structure of the utility represents the trade-off between exploration, exploitation and risk of making an error, that is characteristic of the spectrum sensing problem. We first present the analog front-end architecture, and then map the measurement model into the abstract optimization problem proposed, and analyzed, in the remainder of the paper. We characterize the optimal policy, under constraints on the sensing matrix, and derive the approximation factor of the greedy approach we introduce to solve the problem. Numerical simulations showcase the benefits of combining active spectrum sensing with sub-Nyquist sampling.

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“…our results are not asymptotic. The same considerations apply to similar information-theoretic approaches in [30]- [32].…”

Section: B a Group Testing Approachmentioning

confidence: 85%

An Active Sequential Xampling Detector for Spectrum Sensing

Ferrari

Scaglione

2018

IEEE Trans. Cogn. Commun. Netw.

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“…Most prior works in group testing have focused on identifying properties of all items in their universe (Atia and Saligrama 2012) and very little work has also gone into identifying subsets of items. (Sharma and Murthy 2015) have looked into identification of subset from majority class using fewer tests and bound the number of required groups. Our work looks into selecting subsets from both majority and minority classes.…”

Section: Related Workmentioning

confidence: 99%

“…Similar to noiseless scenario, identifying all workers and idlers in noisy setting takes considerably more tasks than identifying subsets of participants. Note, we assume that workers in N are in majority i.e., number of workers exceed the number of idlers N − K > K. In group testing, subset identification in noisier settings has been previously explored in (Sharma and Murthy 2015), where subset is restricted to the majority class (workers in our case). Analysis in (Sharma 2014) shows reduction in the number of group Algorithm 2 Red-CoBa: Reduced Column based algorithm for identifying subset of workers and subset of idlers Require: M: number of tasks, N: total number of participants, p: parameter, L: worker subset size, D: idler subset size, ψ: parameter 1: for all i ∈ [1, 2, 3 .…”

Section: Subsets In Noisy Group Testsmentioning

confidence: 99%

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Quality Estimation of Workers in Collaborative Crowdsourcing Using Group Testing

Ojha

Talukdar

2016

HCOMP

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Crowdsourcing is increasingly being used to solve complex tasks that require contributions from groups of individuals. In this paper, we consider the problem of distinguishing workers from idlers (who do not contribute positively) in group-based tasks. We consider a group as our smallest observable unit that can be evaluated and assume no knowledge of individual participant’s contribution. We propose the use of group testing based methods for estimating quality of an individual, based on the performance of teams they have been part of. We further extend these algorithms to identify subsets of workers and give theoretical analysis on size of these subsets. We account for several real-world constraints in our model and present empirical support to our theoretical guarantees by an array of simulation experiments.

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Computationally Tractable Algorithms for Finding a Subset of Non-Defective Items From a Large Population

Sharma

Murthy

2017

IEEE Trans. Inform. Theory

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In the classical non-adaptive group testing setup, pools of items are tested together, and the main goal of a recovery algorithm is to identify the complete defective set given the outcomes of different group tests. In contrast, the main goal of a non-defective subset recovery algorithm is to identify a subset of non-defective items given the test outcomes. In this paper, we present a suite of computationally efficient and analytically tractable non-defective subset recovery algorithms. By analyzing the probability of error of the algorithms, we obtain bounds on the number of tests required for non-defective subset recovery with arbitrarily small probability of error. Our analysis accounts for the impact of both the additive noise (false positives) and dilution noise (false negatives). By comparing with the information theoretic lower bounds, we show that the upper bounds on the number of tests are order-wise tight up to a log 2 K factor, where K is the number of defective items. We also provide simulation results that compare the relative performance of the different algorithms and provide further insights into their practical utility.The proposed algorithms significantly outperform the straightforward approaches of testing items oneby-one, and of first identifying the defective set and then choosing the non-defective items from the complement set, in terms of the number of measurements required to ensure a given success rate. Index TermsNon-adaptive group testing, boolean compressed sensing, non-defective subset recovery, inactive subset identification, linear program analysis, combinatorial matching pursuit, sparse signal models.

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On finding a subset of non-defective items from a large population using group tests: Recovery algorithms and bounds

Cited by 3 publications

References 17 publications

An Active Sequential Xampling Detector for Spectrum Sensing

An Active Sequential Xampling Detector for Spectrum Sensing

Quality Estimation of Workers in Collaborative Crowdsourcing Using Group Testing

Computationally Tractable Algorithms for Finding a Subset of Non-Defective Items From a Large Population

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