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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 766 (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 37 (12 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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. 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
SMALL BALL PROBABILITIES FOR LINEAR IMAGES OF HIGH DIMENSIONAL DISTRIBUTIONS
"... Abstract. We study concentration properties of random vectors of the form AX, where X = (X1,..., Xn) has independent coordinates and A is a given matrix. We show that the distribution of AX is well spread in space whenever the distributions of Xi are well spread on the line. Specifically, assume tha ..."
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Cited by 2 (1 self)
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Abstract. We study concentration properties of random vectors of the form AX, where X = (X1,..., Xn) has independent coordinates and A is a given matrix. We show that the distribution of AX is well spread in space whenever the distributions of Xi are well spread on the line. Specifically, assume
Results 1  10
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934,849