On finding a set of healthy individuals from a large population

Sharma, Abhay; Murthy, Chandra R.

doi:10.1109/ita.2013.6502960

Cited by 3 publications

(18 citation statements)

References 12 publications

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“…Similar observations on partial recovery were made in [14] in the absence of list decoding, i.e., with L = k. Moreover, setting α * = 0 corresponds to the problem studied in [22,23], namely, finding a subset of non-defective items of a given size. The scaling regimes considered in [22,23] correspond to a large list size L = Θ(p), and in this case, the potential gains are much more significant.…”

Section: Negative Resultsmentioning

confidence: 60%

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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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Section: Negative Resultsmentioning

confidence: 60%

“…The scaling regimes considered in [22,23] correspond to a large list size L = Θ(p), and in this case, the potential gains are much more significant. Our results reveal the limitations of using smaller list sizes L = o(p).…”

Section: Negative Resultsmentioning

confidence: 99%

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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“…-The presented bounds on the number of tests for different algorithms are within O(log 2 K) factor, where K is the number of defective items, of the information theoretic lower bounds which were derived in our past work [21].…”

Section: Furthermentioning

confidence: 73%

“…We also note that, as argued in Section III-C, RoLpAl++ performs similar to RoLpAl for small values of L and for large values of L the performance of the former is the same as that of CoLpAl. Also, as mentioned in Section IV, we note the linear increase in M with L, especially for small values of L. We also compare the algorithms proposed in this work with an algorithm that identifies the non-defective items by first identifying the defective items, i.e., we compare the "direct" and "indirect" approach [21] of March 17, 2018 DRAFT identifying a non-defective subset. We first employ a defective set recovery algorithm for identifying the defective set and then choose L items uniformly at random from the complement set.…”

Section: Simulationsmentioning

confidence: 93%

“…Note that the non-uniform scenario is equivalent to the uniform recovery scenario when the defective set is chosen uniformly at random from the set of N K possible choices. For the latter scenario, information theoretic lower bounds on the number of tests for the non-defective subset recovery problem were derived in [21] using Fano's inequality. We use these bounds in assessing the performance of the proposed algorithms (see Section IV).…”

Section: Signal Modelmentioning

confidence: 99%

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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

Sharma

Murthy

2018

IEEE Trans. Signal Process.

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In this paper, we derive mutual information based upper and lower bounds on the number of nonadaptive group tests required to identify a given number of "non-defective" items from a large population containing a small number of "defective" items. We show that a reduction in the number of tests is achievable compared to the approach of first identifying all the defective items and then picking the required number of non-defective items from the complement set. In the asymptotic regime with the population size N → ∞, to identify L non-defective items out of a population containing K defective items, when the tests are reliable, our results show that CsK 1−o(1) (Φ(α 0 , β 0 ) + o(1)) measurements are sufficient, where C s is a constant independent of N, K and L, and Φ(α 0 , β 0 ) is a bounded function of α 0 lim N →∞ L N −K and β 0 lim N →∞ K N −K . Further, in the nonadaptive group testing setup, we obtain rigorous upper and lower bounds on the number of tests under both dilution and additive noise models. Our results are derived using a general sparse signal model, by virtue of which, they are also applicable to other important sparse signal based applications such as compressive sensing. Index TermsSparse signal models, nonadaptive group testing, inactive subset recovery. DRAFT to guaranteed detection of a small number of defective items. Two such properties were considered: disjunctness and separability [4]. 1 A probabilistic approach was adopted in [14]-[17], where random test matrix designs were considered, and upper and lower bounds on the number of tests required to satisfy the properties of disjunctness or separability with high probability were derived. In particular, [17] analyzed the performance of group testing under the so-called dilution noise. Another study [22] uses random test designs, and develops computationally efficient algorithms for identifying defective items from the noisy test outcomes by exploiting the connection with compressive sensing. A very recent work [25] uses novel information theoretic techniques, based on information density, to study the phase transitions for Bernoulli test matrix designs and measurement-optimal recovery algorithms. A general sparse signal model for studying group testing problems, that turns out to be very useful in dealing with noisy settings, was proposed and used in [18]- [21]. In this framework, the group testing problem was formulated as a detection problem and a one-to-one correspondence was established with a communication channel model. Using information theoretic arguments, mutual information based expressions (that are easily computable for a wide variety of noisy channels) for upper and lower bounds on the number of tests were obtained [21]. In the related field of compressive sensing, an active line of research has focused on the conditions under which reliable signal recovery from observations drawn from a linear sparse signal model is possible, for example, conditions on the number of measurements required and on isometry properties of the measur...

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On finding a set of healthy individuals from a large population

Cited by 3 publications

References 12 publications

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

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

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

On Finding a Subset of Non-Defective Items from a Large Population

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