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19,279
The empirical eigenvalue distribution of a Gram matrix: from independence to stationarity
 Markov Proc. Rel. Fields 11 (2005
"... Abstract. Consider a N × n matrix Zn = (Zn) where the individual entries are a j1j2 realization of a properly rescaled stationary gaussian random field: Z n 1 ∑ j1j2 = √ h(k1, k2)U(j1 − k1, j2 − k2), n (k1,k2)∈Z 2 where h ∈ ℓ1 (Z2) is a deterministic complex summable sequence and (U(j1, j2);(j1, j2 ..."
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Cited by 20 (8 self)
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2) ∈ Z2) is a sequence of independent complex gaussian random variables with mean zero and unit variance. The purpose of this article is to study the limiting empirical distribution of the eigenvalues of Gram random matrices such as ZnZ ∗ n and (Zn + An)(Zn + An) ∗ where An is a deterministic
The Empirical Eigenvalue Distribution of a Gram Matrix: from Independence to Stationarity∗
, 2005
"... Abstract. Consider a N × n matrix Zn = (Znj1j2) where the individual entries are a realization of a properly rescaled stationary Gaussian random field: ..."
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Abstract. Consider a N × n matrix Zn = (Znj1j2) where the individual entries are a realization of a properly rescaled stationary Gaussian random field:
Powerlaw distributions in empirical data
 ISSN 00361445. doi: 10.1137/ 070710111. URL http://dx.doi.org/10.1137/070710111
, 2009
"... Powerlaw distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and manmade phenomena. Unfortunately, the empirical detection and characterization of power laws is made difficult by the large fluctuations that occur in the t ..."
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Cited by 607 (7 self)
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Powerlaw distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and manmade phenomena. Unfortunately, the empirical detection and characterization of power laws is made difficult by the large fluctuations that occur
The Skill Content of Recent Technological Change: An Empirical Exploration
, 2000
"... Recent empirical and case study evidence documents a strong association between the adoption of computers and increased use of college educated or nonproduction workers. With few exceptions, the conceptual link explaining how computer technology complements skilled labor or substitutes for unskille ..."
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Cited by 643 (28 self)
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Recent empirical and case study evidence documents a strong association between the adoption of computers and increased use of college educated or nonproduction workers. With few exceptions, the conceptual link explaining how computer technology complements skilled labor or substitutes
Linear models and empirical bayes methods for assessing differential expression in microarray experiments.
 Stat. Appl. Genet. Mol. Biol.
, 2004
"... Abstract The problem of identifying differentially expressed genes in designed microarray experiments is considered. Lonnstedt and Speed (2002) derived an expression for the posterior odds of differential expression in a replicated twocolor experiment using a simple hierarchical parametric model. ..."
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Cited by 1321 (24 self)
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from spot filtering or spot quality weights. The posterior odds statistic is reformulated in terms of a moderated tstatistic in which posterior residual standard deviations are used in place of ordinary standard deviations. The empirical Bayes approach is equivalent to shrinkage of the estimated
Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 676 (15 self)
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to work well. In this paper we investigate loopy prop agation empirically under a wider range of conditions. Is there something special about the errorcorrecting code setting, or does loopy propagation work as an approximation scheme for a wider range of networks? ..\ x(:x).) (1) where: and: The message
Approximating discrete probability distributions with dependence trees
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1968
"... A method is presented to approximate optimally an ndimensional discrete probability distribution by a product of secondorder distributions, or the distribution of the firstorder tree dependence. The problem is to find an optimum set of n1 first order dependence relationship among the n variables ..."
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Cited by 881 (0 self)
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variables. It is shown that the procedure derived in this paper yields an approximation of a minimum difference in information. It is further shown that when this procedure is applied to empirical observations from an unknown distribution of tree dependence, the procedure is the maximumlikelihood estimate
On the distribution of the largest eigenvalue in principal components analysis
 ANN. STATIST
, 2001
"... Let x �1 � denote the square of the largest singular value of an n × p matrix X, all of whose entries are independent standard Gaussian variates. Equivalently, x �1 � is the largest principal component variance of the covariance matrix X ′ X, or the largest eigenvalue of a pvariate Wishart distribu ..."
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Cited by 422 (4 self)
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Let x �1 � denote the square of the largest singular value of an n × p matrix X, all of whose entries are independent standard Gaussian variates. Equivalently, x �1 � is the largest principal component variance of the covariance matrix X ′ X, or the largest eigenvalue of a pvariate Wishart
On the control of automatic processes: A parallel distributed processing account of the Stroop effect
 Psychological Review
, 1990
"... Traditional views of automaticity are in need of revision. For example, automaticity otten has been treated as an allornone phenomenon, and traditional ~es have held that automatic processes are independent of attention. Yet recent empirical data suggest that automatic processes are continuous, a ..."
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Cited by 511 (45 self)
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Traditional views of automaticity are in need of revision. For example, automaticity otten has been treated as an allornone phenomenon, and traditional ~es have held that automatic processes are independent of attention. Yet recent empirical data suggest that automatic processes are continuous
Randomized Gossip Algorithms
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2006
"... Motivated by applications to sensor, peertopeer, and ad hoc networks, we study distributed algorithms, also known as gossip algorithms, for exchanging information and for computing in an arbitrarily connected network of nodes. The topology of such networks changes continuously as new nodes join a ..."
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Cited by 532 (5 self)
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distribute the computational burden and in which a node communicates with a randomly chosen neighbor. We analyze the averaging problem under the gossip constraint for an arbitrary network graph, and find that the averaging time of a gossip algorithm depends on the second largest eigenvalue of a doubly
Results 1  10
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