Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms

Chan, Chun Lam; Hou, Pak; Jaggi, Sidharth; Saligrama, Venkatesh

doi:10.1109/allerton.2011.6120391

Cited by 131 publications

(214 citation statements)

References 20 publications

(57 reference statements)

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“…• One may seek practical decoding techniques having low computational complexity and storage [10,11,13], whereas a complementary line of research considers measurement-optimal fundamental limits that hold regardless of such considerations. Such studies help to assess practical methods and determine the level of further improvement possible.…”

Section: )mentioning

confidence: 99%

“…In the noiseless setting with adaptive measurements, an algorithm by Hwang [7] is known to achieve the optimal phase transition. In the non-adaptive setting, several techniques have been shown to be optimal in terms of scaling laws [10,11,13], requiring O(k log p) measurements and polynomial space and time. However, the implied constants in the number of measurements are generally suboptimal.…”

Section: )mentioning

confidence: 99%

“…• The measurement vectors may be designed deterministically [6][7][8], or one may seek to characterize the behavior when they are generated randomly [9][10][11][12]. Among the latter class, the prevalent distribution is that in which the entries of X are independent and identically distributed (i.i.d.)…”

Section: )mentioning

confidence: 99%

See 2 more Smart Citations

Phase Transitions in Group Testing

Scarlett¹,

Cevher²

2015

Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms

159

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The group testing problem consists of determining a sparse subset of a set of items that are "defective" based on a set of possibly noisy tests, and arises in areas such as medical testing, fault detection, communication protocols, pattern matching, and database systems. We study the fundamental limits of any group testing procedure regardless of its computational complexity. In the noiseless case with the number of defective items k scaling with the total number of items p as O(p θ ) (θ ∈ (0, 1)), we show that the probability of reconstruction error tends to one when n ≤ k log 2 (1)), for some explicit constant c(θ). For θ ≤ 1 3 , we show that c(θ) = 1, thus providing an exact threshold on the required number measurements, i.e. a phase transition, which was previously known only in the limit as θ → 0. Analogous necessary and sufficient conditions are derived for the noisy setting, and also for a relaxed partial recovery criterion.

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Section: )mentioning

confidence: 99%

Section: )mentioning

confidence: 99%

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Phase Transitions in Group Testing

Scarlett¹,

Cevher²

2015

Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms

159

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“…List decoding has been used previously in group testing for various purposes [4,[17][18][19], including as an intermediate step for standard group testing [18], and for combating adversarial noise [17]. The work most relevant to ours is [20], which shows that when k and L behave as O(1), the required number of tests remains of the form (3); see also [19] for a more stringent performance criterion related to the COMP algorithm [21].…”

Section: Previous Workmentioning

confidence: 97%

How little does non-exact recovery help in group testing?

Scarlett

Cevher

2017

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We consider the group testing problem, in which one seeks to identify a subset of defective items within a larger set of items based on a number of tests. We characterize the informationtheoretic performance limits in the presence of list decoding, in which the decoder may output a list containing more elements than the number of defectives, and the only requirement is that the true defective set is a subset of the list, or more generally, that their overlap exceeds a given threshold. We show that even under this highly relaxed criterion, in several scaling regimes the asymptotic number of tests is no smaller than the exact recovery setting. However, we also provide examples where a reduction is provably attained. We support our theoretical findings with numerical experiments.

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“…[5]), or a "worst-case" noise model [6] wherein the total number of false positive and negative test outcomes are assumed to be bounded from above. 1 Since the measurements are noisy, the problem of estimating the set of defective items is more challenging. 2 In this work we focus primarily on noise models wherein a positive test outcome is a false positive with the same probability as a negative test outcome being a noisy positive.…”

Section: Introductionmentioning

confidence: 99%

Non-Adaptive Group Testing: Explicit Bounds and Novel Algorithms

Chan

Jaggi

Saligrama

et al. 2014

IEEE Trans. Inform. Theory

Self Cite

108

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Abstract-We consider some computationally efficient and provably correct algorithms with near-optimal sample-complexity for the problem of noisy non-adaptive group testing. Group testing involves grouping arbitrary subsets of items into pools. Each pool is then tested to identify the defective items, which are usually assumed to be "sparse". We consider non-adaptive randomly pooling measurements, where pools are selected randomly and independently of the test outcomes. We also consider a model where noisy measurements allow for both some false negative and some false positive test outcomes (and also allow for asymmetric noise, and activation noise). We consider three classes of algorithms for the group testing problem (we call them specifically the "Coupon Collector Algorithm", the "Column Matching Algorithms", and the "LP Decoding Algorithms" -the last two classes of algorithms (versions of some of which had been considered before in the literature) were inspired by corresponding algorithms in the Compressive Sensing literature. The second and third of these algorithms have several flavours, dealing separately with the noiseless and noisy measurement scenarios. Our contribution is novel analysis to derive explicit sample-complexity bounds -with all constants expressly computed -for these algorithms as a function of the desired error probability; the noise parameters; the number of items; and the size of the defective set (or an upper bound on it). We also compare the bounds to information-theoretic lower bounds for sample complexity based on Fano's inequality and show that the upper and lower bounds are equal up to an explicitly computable universal constant factor (independent of problem parameters).

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Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms

Cited by 131 publications

References 20 publications

Phase Transitions in Group Testing

Phase Transitions in Group Testing

How little does non-exact recovery help in group testing?

Non-Adaptive Group Testing: Explicit Bounds and Novel Algorithms

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