TY - GEN

T1 - Almost optimal distribution-free sample-based testing of k-modality

AU - Ron, Dana

AU - Rosin, Asaf

N1 - Publisher Copyright:
© 2020 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

PY - 2020/8/1

Y1 - 2020/8/1

N2 - For an integer k ≥ 0, a sequence σ = σ1,..., σn over a fully ordered set is k-modal, if there exist indices 1 = a0 < a1 < · · · < ak+1 = n such that for each i, the subsequence σai,..., σai+1 is either monotonically non-decreasing or monotonically non-increasing. The property of k-modality is a natural extension of monotonicity, which has been studied extensively in the area of property testing. We study one-sided error property testing of k-modality in the distribution-free sample-based model. We prove an upper bound of1 O (√kn log k/ε) on the sample complexity, and an almost matching lower bound of Ω (√kn/ε). When the underlying distribution is uniform, we obtain a completely tight bound of Θ (√kn/ε), which generalizes what is known for sample-based testing of monotonicity under the uniform distribution.

AB - For an integer k ≥ 0, a sequence σ = σ1,..., σn over a fully ordered set is k-modal, if there exist indices 1 = a0 < a1 < · · · < ak+1 = n such that for each i, the subsequence σai,..., σai+1 is either monotonically non-decreasing or monotonically non-increasing. The property of k-modality is a natural extension of monotonicity, which has been studied extensively in the area of property testing. We study one-sided error property testing of k-modality in the distribution-free sample-based model. We prove an upper bound of1 O (√kn log k/ε) on the sample complexity, and an almost matching lower bound of Ω (√kn/ε). When the underlying distribution is uniform, we obtain a completely tight bound of Θ (√kn/ε), which generalizes what is known for sample-based testing of monotonicity under the uniform distribution.

KW - Distribution-free property testing

KW - K-modality

KW - Sample-based property testing

UR - http://www.scopus.com/inward/record.url?scp=85091270930&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.APPROX/RANDOM.2020.27

DO - 10.4230/LIPIcs.APPROX/RANDOM.2020.27

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AN - SCOPUS:85091270930

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2020

A2 - Byrka, Jaroslaw

A2 - Meka, Raghu

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

Y2 - 17 August 2020 through 19 August 2020

ER -