Article

Sublinear algorithms for testing monotone and unimodal distributions

Authors:

Tugkan Batu,

Ravi Kumar,

Ronitt RubinfeldAuthors Info & Claims

STOC '04: Proceedings of the thirty-sixth annual ACM symposium on Theory of computing

Pages 381 - 390

https://doi.org/10.1145/1007352.1007414

Published: 13 June 2004 Publication History

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Abstract

The complexity of testing properties of monotone and unimodal distributions, when given access only to samples of the distribution, is investigated. Two kinds of sublinear-time algorithms---those for testing monotonicity and those that take advantage of monotonicity---are provided. The first algorithm tests if a given distribution on [n] is monotone or far away from any monotone distribution in L₁-norm; this algorithm uses O(√n) samples and is shown to be nearly optimal. The next algorithm, given a joint distribution on [n] x [n], tests if it is monotone or is far away from any monotone distribution in L₁-norm; this algorithm uses O(n^3/2) samples. The problems of testing if two monotone distributions are close in L₁-norm and if two random variables with a monotone joint distribution are close to being independent in L₁-norm are also considered. Algorithms for these problems that use only poly(log n) samples are presented. The closeness and independence testing algorithms for monotone distributions are significantly more efficient than the corresponding algorithms as well as the lower bounds for arbitrary distributions. Some of the above results are also extended to unimodal distributions.

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Index Terms

Sublinear algorithms for testing monotone and unimodal distributions
1. Mathematics of computing
  1. Probability and statistics
2. Theory of computation
  1. Design and analysis of algorithms

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STOC '04: Proceedings of the thirty-sixth annual ACM symposium on Theory of computing

June 2004

660 pages

ISBN:1581138520

DOI:10.1145/1007352

Program Chair:
László Babai
University of Chicago, Chicago, IL

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 13 June 2004

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June 13 - 16, 2004

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Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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