Non-adaptive Learning of a Hidden Hypergraph

Abasi, Hasan; Bshouty, Nader H.; Mazzawi, Hanna

doi:10.1007/978-3-319-24486-0_6

Cited by 8 publications

(24 citation statements)

References 27 publications

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“…We then use the reduction of Abasi et. al in [15] to give a non-adaptive algorithm that runs in poly(d d , n) time and asks O(d 3 2 d log n) queries. This is result (9) in the table.…”

Section: Results For Non-adaptive Learningmentioning

confidence: 99%

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Exact learning of juntas from membership queries

Bshouty

Costa

2018

Theoretical Computer Science

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In this paper we study adaptive and non-adaptive exact learning of Juntas from membership queries. We use new techniques to find new bounds, narrow some of the gaps between the lower bounds and upper bounds and find new deterministic and randomized algorithms with small query and time complexities.Some of the bounds are tight in the sense that finding better ones either gives a breakthrough result in some long-standing combinatorial open problem or needs a new technique that is beyond the existing ones.

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“…We then use the reduction of Abasi et. al in [15] to give a non-adaptive algorithm that runs in poly(d d , n) time and asks O(d 3 2 d log n) queries. This is result (9) in the table.…”

Section: Results For Non-adaptive Learningmentioning

confidence: 99%

“…For the second algorithm we apply the reduction described in [15] to the above algorithm. We first give the reduction.…”

Section: Theorem 2 There Is a Deterministic Non-adaptive Algorithm Tmentioning

confidence: 99%

Exact learning of juntas from membership queries

Bshouty

Costa

2018

Theoretical Computer Science

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“…We significantly reduce the upper bound on the number of tests for constructing disjunct matrices compared with the work of Chen et al [3]. This improvement paves the way to improve results not only in group testing, but also in other fields such as graph learning [23] and cover-free families [24].…”

Section: A Contributionmentioning

confidence: 88%

Improved non-adaptive algorithms for threshold group testing with a gap

Bui

Cheraghchi

Echizen

2020

Preprint

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The basic goal of threshold group testing is to identify up to d defective items among a population of n items, where d is usually much smaller than n. The outcome of a test on a subset of items is positive if the subset has at least u defective items, negative if it has up to defective items, where 0 ≤ < u, and arbitrary otherwise. This is called threshold group testing with a gap. There are a few reported studies on test designs and decoding algorithms for identifying defective items. Most of the previous studies have not been feasible because there are numerous constraints on their problem settings or the decoding complexities of their proposed schemes are relatively large. Therefore, it is compulsory to reduce the number of tests as well as the decoding complexity, i.e., the time for identifying the defective items, for achieving practical schemes.The work presented here makes five contributions. The first is a corrected theorem for a non-adaptive algorithm for threshold group testing proposed by Chen and Fu. The second is an improvement in the construction of disjunct matrices, which are the main tools for tackling (threshold) group testing. Specifically, we present a better upper bound on the number of tests for disjunct matrices compared to related work. The third and fourth contributions are a reduction in the number of tests and a reduction in the decoding time for identifying defective items in a noisy setting on test outcomes. The fifth contribution is a demonstration of the resulting improvements by simulation for previous work and the proposed schemes.

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“…Without considering the decoding procedure, Chen et al [4] showed that the number of non-adaptive tests is O z p r r p s s p ln n p , where p = s + r and ⌊ z−1 2 ⌋ is the maximum number of erroneous outcomes. Abasi [25] considered a fraction of the errors in test outcomes under the conditions r < s and r ≤ O ln 2 p ln ln p . Abasi showed that all positive complexes can be identified in time poly(t)×O(n ln n), where t = O(r 11 (4s) r+7 ln n).…”

Section: Comparisonmentioning

confidence: 99%

“…Chen et al [4] and Chin et al [5] gave two upper bounds on the number of tests. Without considering erroneous outcomes, Abasi et al [24] reported the first algorithm requiring O(t 1+o (1) ln n) tests to identify positive complexes in time poly(t) • O(n ln n), where t is the number of rows in an (s+r, r; 1]-disjunct matrix. By considering erroneous outcomes, Abasi [25] needed t = poly(s r , ln n) tests to identify all positive complexes in time poly(t)•O(n ln n).…”

Section: Introductionmentioning

confidence: 99%

Efficient and error-tolerant schemes for non-adaptive complex group testing and its application in complex disease genetics

Bui,

Kuribayashi,

Cheraghchi

et al. 2019

Preprint

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The goal of combinatorial group testing is to efficiently identify up to d defective items in a large population of n items, where d ≪ n. Defective items satisfy certain properties while the remaining items in the population do not. To efficiently identify defective items, a subset of items is pooled and then tested. In this work, we consider complex group testing (CmplxGT) in which a set of defective items consists of subsets of positive items (called positive complexes). CmplxGT is classified into two categories: classical CmplxGT (CCmplxGT) and generalized Cm-plxGT (GCmplxGT). In CCmplxGT, the outcome of a test on a subset of items is positive if the subset contains at least one positive complex, and negative otherwise. In GCmplxGT, the outcome of a test on a subset of items is positive if the subset has a certain number of items of some positive complex, and negative otherwise. For CCmplxGT, we present a scheme that efficiently identifies all positive complexes in time t × poly(d, ln n) in the presence of erroneous outcomes, where t is a predefined parameter. As d ≪ n, this is significantly better than the currently best time of poly(t) × O(n ln n). Moreover, in specific cases, the number of tests in our proposed scheme is smaller than previous work. For GCmplxGT, we present a scheme that efficiently identifies all positive complexes. These schemes are directly applicable in various areas such as complex disease genetics, molecular biology, and learning a hidden graph.

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Non-adaptive Learning of a Hidden Hypergraph

Cited by 8 publications

References 27 publications

Exact learning of juntas from membership queries

Exact learning of juntas from membership queries

Improved non-adaptive algorithms for threshold group testing with a gap

Efficient and error-tolerant schemes for non-adaptive complex group testing and its application in complex disease genetics

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