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Estimating the Support of a HighDimensional Distribution
, 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
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Cited by 781 (29 self)
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Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We
Testing monotone highdimensional distributions
 In STOC
, 2005
"... 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 ndimensional Boolean cube, given access to random draws from the distributi ..."
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Cited by 28 (9 self)
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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 ndimensional Boolean cube, given access to random draws from
METRIC ENTROPY OF HIGH DIMENSIONAL DISTRIBUTIONS
, 2007
"... Let Fd be the collection of all ddimensional probability distribution functions on [0, 1] d, d ≥ 2. The metric entropy of Fd under the L2([0, 1] d) norm is studied. The exact rate is obtained for d =1, 2 and bounds are given for d>3. Connections with small deviation probability for Brownian she ..."
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Cited by 11 (8 self)
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Let Fd be the collection of all ddimensional probability distribution functions on [0, 1] d, d ≥ 2. The metric entropy of Fd under the L2([0, 1] d) norm is studied. The exact rate is obtained for d =1, 2 and bounds are given for d>3. Connections with small deviation probability for Brownian
Remarks on LowDimensional Projections of HighDimensional Distributions
, 1996
"... . Let P = P (q) be a probability distribution on qdimensional space. Necessary and sufficient conditions are derived under which a random ddimensional projection of P converges weakly to a fixed distribution Q on R d as q tends to infinity, while d is an arbitrary fixed number. This complemen ..."
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Cited by 1 (0 self)
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Program ERB CHRXCT 940693. 1 Introduction A standard method of exploring highdimensional dataset...
In search of nonGaussian components of a highdimensional distribution
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2006
"... Finding nonGaussian components of highdimensional data is an important preprocessing step for efficient information processing. This article proposes a new linear method to identify the “nonGaussian subspace ” within a very general semiparametric framework. Our proposed method, called NGCA (non ..."
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Cited by 12 (6 self)
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Finding nonGaussian components of highdimensional data is an important preprocessing step for efficient information processing. This article proposes a new linear method to identify the “nonGaussian subspace ” within a very general semiparametric framework. Our proposed method, called NGCA (non
A New Approach For Testing Symmetry Of A HighDimensional Distribution*
"... . Testing symmetry of a univariate distribution has been received much attention. Aki (1993) proposed a test for symmetry in highdimensional space and investigated its asymptotic behavior. We in this paper develop a new approach for testing symmetry of a multivaraite distribution. The test is const ..."
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Cited by 1 (0 self)
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. Testing symmetry of a univariate distribution has been received much attention. Aki (1993) proposed a test for symmetry in highdimensional space and investigated its asymptotic behavior. We in this paper develop a new approach for testing symmetry of a multivaraite distribution. The test
Approximating the moments of marginals of high dimensional distributions, Annals of Probability, to appear
 Department of Mathematics, University of Michigan
"... For probability distributions on R n, we study the optimal sample size N = N(n, p) that suffices to uniformly approximate the pth moments of all onedimensional marginals. Under the assumption that the marginals have bounded 4p moments, we obtain the optimal bound N = O(n p/2) for p>2. This bound ..."
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Cited by 5 (1 self)
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For probability distributions on R n, we study the optimal sample size N = N(n, p) that suffices to uniformly approximate the pth moments of all onedimensional marginals. Under the assumption that the marginals have bounded 4p moments, we obtain the optimal bound N = O(n p/2) for p>2
That was fast! Speeding up NN search of high dimensional distributions.
"... We present a data structure for fast nearest neighbor retrieval of generative models of documents based on KullbackLeibler (KL) divergence. Our data structure, which shares some similarity with Bregman Ball Trees, consists of a hierarchical partition of a database, and uses a novel branch and bound ..."
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Cited by 1 (1 self)
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Trees on high dimensional data. In addition, our strategy is applicable also to probability distributions with hidden state variables, and is not limited to regular exponential family distributions. Experiments demonstrate substantial speedups over both Bregman Ball Trees and over brute force search
Results 1  10
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839,650