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7,673
Which Problems Have Strongly Exponential Complexity?
 Journal of Computer and System Sciences
, 1998
"... For several NPcomplete problems, there have been a progression of better but still exponential algorithms. In this paper, we address the relative likelihood of subexponential algorithms for these problems. We introduce a generalized reduction which we call SubExponential Reduction Family (SERF) t ..."
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Cited by 242 (11 self)
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For several NPcomplete problems, there have been a progression of better but still exponential algorithms. In this paper, we address the relative likelihood of subexponential algorithms for these problems. We introduce a generalized reduction which we call SubExponential Reduction Family (SERF
Exponential family harmoniums with an application to . . .
"... Directed graphical models with one layer of observed random variablesand one or more layers of hidden random variables have been the dominant modelling paradigm in many research fields. Although this approach has met with considerable success, the causal semantics of these models can make it diffi ..."
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Cited by 150 (22 self)
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it difficult to infer the posterior distribution over thehidden variables. In this paper we propose an alternative twolayer model based on exponential family distributions and the semantics of undirected models. Inference in these "exponential family harmoniums " is fast while learning is performed
Sure independence screening for ultrahigh dimensional feature space
, 2006
"... Variable selection plays an important role in high dimensional statistical modeling which nowadays appears in many areas and is key to various scientific discoveries. For problems of large scale or dimensionality p, estimation accuracy and computational cost are two top concerns. In a recent paper, ..."
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Cited by 283 (26 self)
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, Candes and Tao (2007) propose the Dantzig selector using L1 regularization and show that it achieves the ideal risk up to a logarithmic factor log p. Their innovative procedure and remarkable result are challenged when the dimensionality is ultra high as the factor log p can be large and their uniform
Finiteness of Redundancy, Regret, Shtarkov Sums, and Jeffreys Integrals in Exponential Families
, 2009
"... The normalized maximum likelihood (NML) distribution plays a fundamental role in the MDL approach to statistical inference. It is only defined for statistical families with a finite Shtarkov sum. Here we characterize, for 1dimensional exponential families, when the Shtarkov sum is finite. This tur ..."
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The normalized maximum likelihood (NML) distribution plays a fundamental role in the MDL approach to statistical inference. It is only defined for statistical families with a finite Shtarkov sum. Here we characterize, for 1dimensional exponential families, when the Shtarkov sum is finite
Algebraic Algorithms for Sampling from Conditional Distributions
 Annals of Statistics
, 1995
"... We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so a ..."
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Cited by 268 (20 self)
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We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so
Operations for Learning with Graphical Models
 Journal of Artificial Intelligence Research
, 1994
"... This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Wellknown examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models ..."
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Cited by 276 (13 self)
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are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, and the manipulation of probability models from the exponential family. Two standard algorithm schemas
STATISTICAL PROPERTIES OF DYNAMICAL SYSTEMS WITH SOME HYPERBOLICITY
, 1997
"... This paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts (though not necessarily all) of their phase spaces. The main results are for discrete time systems. To put this work into context, recall that for Axiom A attractors the ..."
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Cited by 260 (14 self)
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]), and there are detailed analyses of specific kinds of dynamical systems including, for example, billiards, 1dimensional and Hénontype maps ([S2], [BSC]; [HK], [J]; [BC2], [BY1]). Statistical properties such as exponential decay of correlations are not enjoyed by all diffeomorphisms with nonzero Lyapunov exponents
Bayesian Exponential Family PCA
"... Principal Components Analysis (PCA) has become established as one of the key tools for dimensionality reduction when dealing with real valued data. Approaches such as exponential family PCA and nonnegative matrix factorisation have successfully extended PCA to nonGaussian data types, but these tec ..."
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Cited by 21 (7 self)
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Principal Components Analysis (PCA) has become established as one of the key tools for dimensionality reduction when dealing with real valued data. Approaches such as exponential family PCA and nonnegative matrix factorisation have successfully extended PCA to nonGaussian data types
Exponential Families and Conjugate Priors 1 Exponential Families
, 2007
"... Inference with continuous distributions present an additional challenge compared to inference with discrete distributions: how to represent these continuous objects within finitememory computers? A common solution to this problem is to use a (much smaller) subset (or family) of distributions instea ..."
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of distribution that has special properties with respect to statistical inference is the exponential family, introduced by Pitman (father), Darmois and Koopman. As a preview, here are some important properties of the exponential family that explain their central role in statistics: • Suppose X1, X2,... are iid
Results 11  20
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7,673