Testing that distributions are close

Batu, Tuğkan; Fortnow, Lance; Rubinfeld, Ronitt; Smith, Warren D.; White, Patrick

doi:10.1109/sfcs.2000.892113

Cited by 169 publications

(240 citation statements)

References 29 publications

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“…In recent years, a number of algorithms for these testing problems have been designed which require a number of samples that is only sublinear in the size of the domain, while making no assumptions on the form of the distribution. For example, on arbitrary domains of size N , testing whether a distribution is close to uniform in statistical distance can be performed with onlyÕ( √ N ) samples [7,2], and distinguishing whether two distributions are the same or far in statistical distance can be performed withÕ(N 2/3 ) samples [4]. Similar results have been obtained for testing whether a joint distribution is independent and estimating the entropy [2,3].…”

Section: Introductionsupporting

confidence: 54%

“…Theorem 4 There is an efficient algorithm TestUniform (see Figure 1) which, given generator access to an unknown monotone distribution p over {−1, 1} n , makes O( n 2 log n ) draws and satisfies the following properties: (i) If p ≡ U then TestUniform outputs "uniform" with probability at least 4 5 ; (ii) If p − U 1 ≥ then TestUniform outputs "nonuniform" with probability at least 4 5 .…”

Section: A Uniformity Testing Algorithmmentioning

confidence: 99%

“…It is well known that A must make at least Ω( 1 2 ) many coin tosses (see e.g. [4]). It is clear that T fair coin tosses can be converted into T /n draws from U, and T biased coin tosses can be converted into T /n draws from P τ , simply by grouping the tosses into strings of length n. Thus any distinguisher as described in the statement of Fact 10 must make Ω( 1 2 n ) many draws from the generator, since otherwise it would yield a distinguisher for the coin problem which requires o( 1 2 ) many coin tosses.…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…But it is well known (see e.g. [4]) that any algorithm for the coin problem requires Ω( 1 2 ) many samples.…”

Section: (Lemma 13)mentioning

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: Introductionsupporting

confidence: 54%

Section: A Uniformity Testing Algorithmmentioning

confidence: 99%

Section: Proof Of Theoremmentioning

confidence: 99%

“…But it is well known (see e.g. [4]) that any algorithm for the coin problem requires Ω( 1 2 ) many samples.…”

Section: (Lemma 13)mentioning

confidence: 99%

See 2 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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“…Some examples include testing uniformity [20,8], independence [7], monotonicity and being unimodal [9], estimating the support sizes [34] and testing a weaker notion than k-wise independence, namely, "almost k-wise independence" [1].…”

Section: Other Related Researchmentioning

confidence: 99%

Testing Non-uniform k-Wise Independent Distributions over Product Spaces

Rubinfeld

Xie

2010

Automata, Languages and Programming

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Abstract. A distribution D over Σ1 × · · · × Σn is called (non-uniform) k-wise independent if for any set of k indices {i1, . . . , i k } and for any z1We study the problem of testing (non-uniform) k-wise independent distributions over product spaces. For the uniform case we show an upper bound on the distance between a distribution D from the set of k-wise independent distributions in terms of the sum of Fourier coefficients of D at vectors of weight at most k. Such a bound was previously known only for the binary field. For the non-uniform case, we give a new characterization of distributions being k-wise independent and further show that such a characterization is robust. These greatly generalize the results of Alon et al.[1] on uniform k-wise independence over the binary field to non-uniform k-wise independence over product spaces. Our results yield natural testing algorithms for k-wise independence with time and sample complexity sublinear in terms of the support size when k is a constant. The main technical tools employed include discrete Fourier transforms and the theory of linear systems of congruences.A full version of this paper is available at

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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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Testing that distributions are close

Cited by 169 publications

References 29 publications

Testing monotone high-dimensional distributions

Testing monotone high-dimensional distributions

Testing Non-uniform k-Wise Independent Distributions over Product Spaces

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

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