Sublinear algorithms for testing monotone and unimodal distributions

Batu, Tuğkan; Kumar, Ravi; Rubinfeld, Ronitt

doi:10.1145/1007352.1007414

Cited by 75 publications

(116 citation statements)

References 16 publications

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“…a product distribution) or far from any independent distribution. All of these lower bounds are in contrast with the known results for monotone distributions over totally ordered domains [3,5], where there exist algorithms that require only a polylogarithmic in the total domain size number of samples.…”

Section: Introductionmentioning

confidence: 74%

“…This leads us naturally to the question of whether there are interesting classes of distributions for which these testing problems are exponentially easier in terms of sample complexity. Recently a number of algorithms that use exponentially fewer samples on monotone and unimodal distributions over totally ordered domains have been devised [3,5]. A distribution over a totally ordered discrete domain (w.l.o.g.…”

Section: Introductionmentioning

confidence: 99%

“…, N }) is monotone if for all x, y in the domain such that x ≤ y, we have that the probability assigned to x is at most the probability assigned to y. For monotone distributions on totally ordered domains, estimating the entropy, testing whether two distributions are close and testing whether a joint distribution over pairs (x, y) is close to independent can all be done in polylogarithmic time in the size of the domain [3,5].…”

Section: Introductionmentioning

confidence: 99%

“…In [3,5], an efficient test is given for determining whether a monotone distribution over a totally ordered domain is uniform. The test estimates whether the weight of the largest half of the elements (according to the total order on the domain) is approximately 1/2.…”

Section: Introductionmentioning

confidence: 99%

“…We note that the techniques used to achieve upper bound results for the problem of testing various properties of distributions over totally ordered domains [3,5] essentially relied on showing that every monotone distribution p over a totally ordered domain could be approximated by a distribution q with a very concise description of the following form: the domain is partitioned into a polylogarithmic (in the size of the domain) number of contiguous segments, such that the distribution q is uniform over each segment. The testing algorithms efficiently find an approximation to this segmentation.…”

Section: Introductionmentioning

confidence: 99%

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Testing monotone high-dimensional distributions

Rubinfeld

Servedio

2005

Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing

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A monotone distribution P over a (partially) ordered domain assigns higher probability to y than to x if y ≥ x in the order. We study several natural problems concerning testing properties of monotone distributions over the n-dimensional Boolean cube, given access to random draws from the distribution being tested. We give a poly(n)-time algorithm for testing whether a monotone distribution is equivalent to or -far (in the L 1 norm) from the uniform distribution. A key ingredient of the algorithm is a generalization of a known isoperimetric inequality for the Boolean cube. We also introduce a method for proving lower bounds on various problems of testing monotone distributions over the n-dimensional Boolean cube, based on a new decomposition technique for monotone distributions. We use this method to show that our uniformity testing algorithm is optimal up to polylog(n) factors, and also to give exponential lower bounds on the complexity of several other problems, including testing whether a monotone distribution is identical to or -far from a fixed known monotone product distribution and approximating the entropy of an unknown monotone distribution.

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Section: Introductionmentioning

confidence: 74%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Testing monotone high-dimensional distributions

Rubinfeld

Servedio

2005

Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing

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Comparative analysis of the natriuretic peptide precursor gene cluster in vertebrates reveals loss of ANF and retention of CNP‐3 in chicken

Houweling

Somi

Massink

et al. 2005

Developmental Dynamics

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We identified and characterized the chicken natriuretic peptide precursor gene cluster and found its organization to be highly conserved compared with the mammalian Nppb-Nppa cluster. However, phylogenetic analysis indicated that the putative chicken natriuretic peptide precursor genes are the homologues of CNP-3 and Nppb, respectively. Comparative expression analysis revealed that, in human, mouse, and rat hearts, Nppb is a novel marker for the differentiating working myocardium. Its expression pattern is strikingly similar to that of Nppa before birth, and diverges only after birth. In contrast, whereas the chicken Nppb gene expression profile resembled that of mammalian Nppb, the CNP-3 gene showed very limited expression in the heart, not resembling the pattern of either Nppa or Nppb. These results show that, in chicken, the Nppa gene has been lost from the natriuretic peptide precursor gene cluster, whereas the CNP-3 gene has been retained.

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Asymptotic Nonparametric Statistical Analysis of Stationary Time Series

Ryabko¹

2019

SpringerBriefs in Computer Science

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Sublinear algorithms for testing monotone and unimodal distributions

Cited by 75 publications

References 16 publications

Testing monotone high-dimensional distributions

Testing monotone high-dimensional distributions

Comparative analysis of the natriuretic peptide precursor gene cluster in vertebrates reveals loss of ANF and retention of CNP‐3 in chicken

Asymptotic Nonparametric Statistical Analysis of Stationary Time Series

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