Minimum complexity density estimation

By Andrew R. Barron, Thomas M. Cover. 1991

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Causal Inference Using the Algorithmic Markov Condition (2008, methodology): “We rephra se the minimum complexity estimator described by Barron and Cover [40]: Given a string-valued random variable X and a samplex1, .”
Discovering objects and their location in images (2005, methodology): “Discussion: In the experiments it was necessary to specify the number of topics K, however Bayesian [20] or minimum complexity methods [3] can be used to infer the number of topics implied by a corpus.”
From ɛ-entropy to KL-entropy: Analysis of minimum information complexity density estimation (2006, methodology): “Although the bound based on the index of resolvability in Theorem 4.1 is quite useful for non-parametric problems (see (Barron & Cover, 1991) for examples), it does not handle the parametric case satisfactorily.”
Gaussian model selection (2001, methodology): “…PASCAL.MASSART@MATH.U–PSUD.FR Mathematics Subject Classification (1991): 62G07, 62C20, 41A46 Our approach to model selection via penalization has been inspired by the pioneering paper of Barron and Cover (1991) and first introduced in the context of density estimation in Birgé and Massart (1997).”
Nonparametric Regression with Correlated Errors (2001, methodology): “General schemes have also been proposed for the construction of adaptive estimators by model selection in Barron and Cover [7], Birg e and Massart [11], Barron, Birg e and Massart [6], Yang and Barron [75] and Yang [74], Lugosi and Nobel [47] and others.”
Schwarz, Wallace, and Rissanen: Intertwining Themes in Theories of Model Selection (2001, background): “One is Barron’s work on minimum complexity density estimation (Barron & Cover, 1991; Yang & Barron, 1998), in which he shows not only that such estimators converge to the correct model, but that the rate of convergence can be bound by an index of resolvability.”
Theory of classification : a survey of some recent advances (2005, background): “We refer to Cover [63], Dudley [80] [83], Steele [204], Wenocur and Dudley [238], Assouad [15], Khovanskii [118], Macintyre and Sontag [149], Goldberg and Jerrum [101], Karpinski and A. Macintyre [114], Koiran and Sontag [121], Anthony and Bartlett [9], and Bartlett and Maass [28].”
Discovering object categories in image collections (2005, methodology): “Discussion: In the experiments it was necessary to specify the number of topicsK, however Bayesian [21] or minimum complexity methods [2] can be used to infer the number of topics implied by a corpus.”
Structural Risk Minimization Over Data-Dependent Hierarchies (1998, methodology): “Furthermore, with the exception of the methods discussed in [8] , all such methods take the form of minimizing a cost function comprising an empirical risk plus an additive complexity term which does not depend on the data.”
Rate Distribution Between Model and Signal (2007, methodology): “Our general approach towards rate distribution is based on that used in the context of the minimum description length (MDL) principle [1, 2].”
Toward a method of selecting among computational models of cognition. (2002, background): “Barron and Cover (1991) showed that BMS and MDL are asymptotically equivalent given large sample sizes; that is, both will converge to the true model if the true model is correctly specified.”
Predictability, Complexity, and Learning (2000, background): “Similar conceptual problems plague even true nonparametric examples, as considered, for example, by Barron and Cover (1991).”