NDLI: $L_{p}-testing$

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$L_{p}-testing$

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$L_{p}-testing$

Content Provider	ACM Digital Library
Author	Berman, Piotr Raskhodnikova, Sofya Yaroslavtsev, Grigory
Abstract	We initiate a systematic study of sublinear algorithms for approximately testing properties of real-valued data with respect to $L_{p}$ distances for p = 1, 2. Such algorithms distinguish datasets which either have (or are close to having) a certain property from datasets which are far from having it with respect to $L_{p}$ distance. For applications involving noisy real-valued data, using $L_{p}$ distances allows algorithms to withstand noise of bounded $L_{p}$ norm. While the classical property testing framework developed with respect to Hamming distance has been studied extensively, testing with respect to $L_{p}$ distances has received little attention. We use our framework to design simple and fast algorithms for classic problems, such as testing monotonicity, convexity and the Lipschitz property, and also distance approximation to monotonicity. In particular, for functions over the hypergrid domains $[n]^{d},$ the complexity of our algorithms for all these properties does not depend on the linear dimension n. This is impossible in the standard model. Most of our algorithms require minimal assumptions on the choice of sampled data: either uniform or easily samplable random queries suffice. We also show connections between the $L_{p}-testing$ model and the standard framework of property testing with respect to Hamming distance. Some of our results improve existing bounds for Hamming distance.
Starting Page	164
Ending Page	173
Page Count	10
File Format	PDF MP4
ISBN	9781450327107
DOI	10.1145/2591796.2591887
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-05-31
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Monotone Lipschitz and submodular functions Property testing Approximating distance to a property
Content Type	Audio Text
Resource Type	Article

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