Combinatorial Group Testing and Sparse Recovery Schemes with Near-Optimal Decoding Time

Cheraghchi, Mahdi; Nakos, Vasileios

doi:10.1109/focs46700.2020.00115

Cited by 15 publications

(22 citation statements)

References 62 publications

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“…Let Dec(y, M ) be the naive decoding procedure that takes y and M as the two inputs and produces a set of indices in [49]. Therefore, if M is a superimposed (d, n, r)-code then Criterion 1 holds.…”

Section: B Morphology Of the Brainmentioning

confidence: 99%

A simple self-decoding model for neural coding

Bui

2022

Preprint

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Neural coding is an important tool to discover the inner workings of mind. In this work, we propose and consider a simple but novel self-decoding model for neural coding based on the principle that the neuron body represents ongoing stimulus while dendrites are used to store that stimulus as a memory. In particular, suppose t spiking presynaptic neurons transmit any stimulus directly to a population of suppose n postsynaptic neurons, a postsynaptic neuron spikes if it does not connect to an inhibitory presynaptic neuron, and every stimulus is represented by up to suppose d spiking postsynaptic neurons. Our hypothesis is that the brain is organized to functionally satisfy the following six criteria: (i) decoding objective, i.e., there are up to suppose r − 1 ≥ 0 additional spiking postsynaptic neurons in response to a stimulus along with the spiking postsynaptic neurons representing the stimulus, (ii) smoothness, i.e., similar stimuli are encoded similarly by the presynaptic neurons, (iii) optimal information transmission, i.e., suppose t is minimized, (iv) optimal energetic cost, i.e., only the suppose t presynaptic neurons and the postsynaptic neurons representing a stimulus spike, (v) low-dimensional representation, i.e., suppose d = o(n), and (vi) sparse coding, i.e., suppose t = o(n). Our finding is that some criteria cause or correlate with others. Let the characteristic set of a postsynaptic neuron be the set of the presynaptic neurons it connects with. We prove that (i) holds if and only if the union of the r characteristic sets of any r postsynaptic neurons is not included in the union of the d characteristic sets of d other postsynaptic neurons. Consequently, (ii) is attained. More importantly, we suggest that the decoding objective (i) and optimal information transmission (iii) play a fundamental role in neural computation, while (v) and (vi) correlate to each other and correlate with (iii) and (iv). We examine our hypothesis by statistically testing functional connectivity network and the presynaptic-postsynaptic connectivity in layer 2 of the medial entorhinal cortex of a rat.

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Section: B Morphology Of the Brainmentioning

confidence: 99%

A simple self-decoding model for neural coding

Bui

2022

Preprint

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“…While extensive works have studied the number of tests for various group testing strategies (see [2] for a survey), relatively fewer have sought efficient poly(k log n) decoding time. For the standard noiseless group testing problem, the most relevant existing results come from two recent concurrent works [11,32], which showed that there exists a non-adaptive group testing algorithm that succeeds with O(k log n) tests and has O(k log n) decoding time. We build on these splitting techniques in this paper (see Figures 1, 3, and 4 below).…”

Section: Related Workmentioning

confidence: 99%

“…In a distinct but related line of works, the for-all recovery guarantee (i.e., zero error probability) was considered [10,25,31,22,11], with typical results for the unconstrained setting requiring O(k Explicit COMP [16] O(γkn…”

Section: Related Workmentioning

confidence: 99%

“…While algorithms for such settings typically do not transfer directly to the group testing problem, we detail one relatively direct approach for the noisy setting in Appendix D, and contrast it with our own. In addition, we note that our work builds primarily on [11,32], which in turn built on tree-based algorithms such as [13,26].…”

Section: Related Workmentioning

confidence: 99%

“…In this paper, we present algorithms for sparsity-constrained (bounded tests-per-item or items-per-test) and noisy variants of group testing with a near-optimal sublinear decoding time, building on techniques recently proposed for the unconstrained noiseless group testing problem [11,32]. These extensions come with new challenges presented by the infeasibility of the designs in [11,32] in the sparsity-constrained setting, and the need to handle both false positive and false negative tests in the noisy setting.…”

Section: Introductionmentioning

confidence: 99%

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Fast Splitting Algorithms for Sparsity-Constrained and Noisy Group Testing

Price

Scarlett

Tan

2021

Preprint

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In group testing, the goal is to identify a subset of defective items within a larger set of items based on tests whose outcomes indicate whether at least one defective item is present. This problem is relevant in areas such as medical testing, DNA sequencing, communication protocols, and many more. In this paper, we study (i) a sparsity-constrained version of the problem, in which the testing procedure is subjected to one of the following two constraints: items are finitely divisible and thus may participate in at most γ tests; or tests are size-constrained to pool no more than ρ items per test; and (ii) a noisy version of the problem, where each test outcome is independently flipped with some constant probability. Under each of these settings, considering the for-each recovery guarantee with asymptotically vanishing error probability, we introduce a fast splitting algorithm and establish its near-optimality not only in terms of the number of tests, but also in terms of the decoding time. While the most basic formulations of our algorithms require Ω(n) storage for each algorithm, we also provide low-storage variants based on hashing, with similar recovery guarantees.

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High prevalence group testing in epidemiology with geometrically inspired algorithms

Schenk,

Caf,

Knabl

et al. 2023

Sci Rep

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Demand for mass surveillance during peak times of the SARS-CoV-2 pandemic caused high workload for clinical laboratories. Efficient and cost conserving testing designs by means of group testing can substantially reduce resources during possible future emergency situations. The novel hypercube algorithm proposed by Mutesa et al. 2021 published in Nature provides methodological proof of concept and points out the applicability to epidemiological testing. In this work, the algorithm is explored and expanded for settings with high group prevalence. Numerical studies investigate the limits of the adapted hypercube methodology, allowing to optimize pooling designs for specific requirements (i.e. number of samples and group prevalence). Hyperparameter optimization is performed to maximize test-reduction. Standard deviation is examined to investigate resilience and precision. Moreover, empirical validation was performed by elaborately pooling SARS-CoV-2 virus samples according to numerically optimized pooling designs. Laboratory experiments with SARS-CoV-2 sample groups, ranging from 50 to 200 items, characterized by group prevalence up to 10%, are successfully processed and analysed. Test-reductions from 50 to 72.5% were achieved in the experimental setups when compared to individual testing. Higher theoretical test-reduction is possible, depending on the number of samples and the group prevalence, indicated by simulation results.

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Combinatorial Group Testing and Sparse Recovery Schemes with Near-Optimal Decoding Time

Cited by 15 publications

References 62 publications

A simple self-decoding model for neural coding

A simple self-decoding model for neural coding

Fast Splitting Algorithms for Sparsity-Constrained and Noisy Group Testing

High prevalence group testing in epidemiology with geometrically inspired algorithms

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