Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.37
URN: urn:nbn:de:0030-drops-75867
URL: https://drops.dagstuhl.de/opus/volltexte/2017/7586/
Chen, Xi ; Freilich, Adam ; Servedio, Rocco A. ; Sun, Timothy
Sample-Based High-Dimensional Convexity Testing
| pdf-format: |
|
Abstract
In the problem of high-dimensional convexity testing, there is an unknown set S in the n-dimensional Euclidean space which is promised to be either convex or c-far from every convex body with respect to the standard multivariate normal distribution. The job of a testing algorithm is then to distinguish between these two cases while making as few inspections of the set S as possible.In this work we consider sample-based testing algorithms, in which the testing algorithm only has access to labeled samples (x,S(x)) where each x is independently drawn from the normal distribution. We give nearly matching sample complexity upper and lower bounds for both one-sided and two-sided convexity testing algorithms in this framework. For constant c, our results show that the sample complexity of one-sided convexity testing is exponential in n, while for two-sided convexity testing it is exponential in the square root of n.
BibTeX - Entry
@InProceedings{chen_et_al:LIPIcs:2017:7586,
author = {Xi Chen and Adam Freilich and Rocco A. Servedio and Timothy Sun},
title = {{Sample-Based High-Dimensional Convexity Testing}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
pages = {37:1--37:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-044-6},
ISSN = {1868-8969},
year = {2017},
volume = {81},
editor = {Klaus Jansen and Jos{\'e} D. P. Rolim and David Williamson and Santosh S. Vempala},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7586},
URN = {urn:nbn:de:0030-drops-75867},
doi = {10.4230/LIPIcs.APPROX-RANDOM.2017.37},
annote = {Keywords: Property testing, convexity, sample-based testing}
}
| Keywords: | Property testing, convexity, sample-based testing | |
| Seminar: | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017) | |
| Issue date: | 2017 | |
| Date of publication: | 11.08.2017 |
