The Experts below are selected from a list of 44664 Experts worldwide ranked by ideXlab platform
Lancelot F. James - One of the best experts on this subject based on the ideXlab platform.
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bayesian Model Selection in finite mixtures by marginal density decompositions
Journal of the American Statistical Association, 2001Co-Authors: Hemant Ishwaran, Lancelot F. JamesAbstract:We consider the problem of estimating the number of components d and the unknown mixing distribution in a finite mixture Model, in which d is bounded by some fixed finite number N. Our approach relies on the use of a prior over the space of mixing distributions with at most N components. By decomposing the resulting marginal density under this prior, we discover a weighted Bayes factor method for consistently estimating d that can be implemented by an iid generalized weighted Chinese restaurant (GWCR) Monte Carlo algorithm. We also discuss a Gibbs sampling method (the blocked Gibbs sampler) for estimating d and also the mixing distribution. We show that our resulting posterior is consistent and achieves the frequentist optimal Op (n−1/4) rate of estimation. We compare the performance of the new GWCR Model Selection Procedure with that of the Akaike information criterion and the Bayes information criterion implemented through an EM algorithm. Applications of our methods to five real datasets and simulation...
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bayesian Model Selection in finite mixtures by marginal density decompositions
Journal of the American Statistical Association, 2001Co-Authors: Hemant Ishwaran, Lancelot F. JamesAbstract:We consider the problem of estimating the number of components d and the unknown mixing distribution in a finite mixture Model, in which d is bounded by some fixed finite number N. Our approach relies on the use of a prior over the space of mixing distributions with at most N components. By decomposing the resulting marginal density under this prior, we discover a weighted Bayes factor method for consistently estimating d that can be implemented by an iid generalized weighted Chinese restaurant (GWCR) Monte Carlo algorithm. We also discuss a Gibbs sampling method (the blocked Gibbs sampler) for estimating d and also the mixing distribution. We show that our resulting posterior is consistent and achieves the frequentist optimal Op (n−1/4) rate of estimation. We compare the performance of the new GWCR Model Selection Procedure with that of the Akaike information criterion and the Bayes information criterion implemented through an EM algorithm. Applications of our methods to five real datasets and simulation...
Hemant Ishwaran - One of the best experts on this subject based on the ideXlab platform.
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bayesian Model Selection in finite mixtures by marginal density decompositions
Journal of the American Statistical Association, 2001Co-Authors: Hemant Ishwaran, Lancelot F. JamesAbstract:We consider the problem of estimating the number of components d and the unknown mixing distribution in a finite mixture Model, in which d is bounded by some fixed finite number N. Our approach relies on the use of a prior over the space of mixing distributions with at most N components. By decomposing the resulting marginal density under this prior, we discover a weighted Bayes factor method for consistently estimating d that can be implemented by an iid generalized weighted Chinese restaurant (GWCR) Monte Carlo algorithm. We also discuss a Gibbs sampling method (the blocked Gibbs sampler) for estimating d and also the mixing distribution. We show that our resulting posterior is consistent and achieves the frequentist optimal Op (n−1/4) rate of estimation. We compare the performance of the new GWCR Model Selection Procedure with that of the Akaike information criterion and the Bayes information criterion implemented through an EM algorithm. Applications of our methods to five real datasets and simulation...
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bayesian Model Selection in finite mixtures by marginal density decompositions
Journal of the American Statistical Association, 2001Co-Authors: Hemant Ishwaran, Lancelot F. JamesAbstract:We consider the problem of estimating the number of components d and the unknown mixing distribution in a finite mixture Model, in which d is bounded by some fixed finite number N. Our approach relies on the use of a prior over the space of mixing distributions with at most N components. By decomposing the resulting marginal density under this prior, we discover a weighted Bayes factor method for consistently estimating d that can be implemented by an iid generalized weighted Chinese restaurant (GWCR) Monte Carlo algorithm. We also discuss a Gibbs sampling method (the blocked Gibbs sampler) for estimating d and also the mixing distribution. We show that our resulting posterior is consistent and achieves the frequentist optimal Op (n−1/4) rate of estimation. We compare the performance of the new GWCR Model Selection Procedure with that of the Akaike information criterion and the Bayes information criterion implemented through an EM algorithm. Applications of our methods to five real datasets and simulation...
Xiaotong Shen - One of the best experts on this subject based on the ideXlab platform.
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generalized degrees of freedom and adaptive Model Selection in linear mixed effects Models
Computational Statistics & Data Analysis, 2012Co-Authors: Bo Zhang, Xiaotong Shen, Sunni L MumfordAbstract:Linear mixed-effects Models involve fixed effects, random effects and covariance structures, which require Model Selection to simplify a Model and to enhance its interpretability and predictability. In this article, we develop, in the context of linear mixed-effects Models, the generalized degrees of freedom and an adaptive Model Selection Procedure defined by a data-driven Model complexity penalty. Numerically, the Procedure performs well against its competitors not only in selecting fixed effects but in selecting random effects and covariance structure as well. Theoretically, asymptotic optimality of the proposed methodology is established over a class of information criteria. The proposed methodology is applied to the BioCycle Study, to determine predictors of hormone levels among premenopausal women and to assess variation in hormone levels both between and within women across the menstrual cycle.
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Model Selection Procedure for high dimensional data
Statistical Analysis and Data Mining, 2010Co-Authors: Yongli Zhang, Xiaotong ShenAbstract:For high-dimensional regression, the number of predictors may greatly exceed the sample size but only a small fraction of them are related to the response. Therefore, variable Selection is inevitable, where consistent Model Selection is the primary concern. However, conventional consistent Model Selection criteria like Bayesian information criterion (BIC) may be inadequate due to their nonadaptivity to the Model space and infeasibility of exhaustive search. To address these two issues, we establish a probability lower bound of selecting the smallest true Model by an information criterion, based on which we propose a Model Selection criterion, what we call RICc, which adapts to the Model space. Furthermore, we develop a computationally feasible method combining the computational power of least angle regression (LAR) with that of RICc. Both theoretical and simulation studies show that this method identifies the smallest true Model with probability converging to one if the smallest true Model is selected by LAR. The proposed method is applied to real data from the power market and outperforms the backward variable Selection in terms of price forecasting accuracy. Copyright © 2010 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 3: 350-358, 2010
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adaptive Model Selection
Journal of the American Statistical Association, 2002Co-Authors: Xiaotong Shen, Jianming YeAbstract:Most Model Selection Procedures use a fixed penalty penalizing an increase in the size of a Model. These nonadaptive Selection Procedures perform well only in one type of situation. For instance, Bayesian information criterion (BIC) with a large penalty performs well for “small” Models and poorly for “large” Models, and Akaike's information criterion (AIC) does just the opposite. This article proposes an adaptive Model Selection Procedure that uses a data-adaptive complexity penalty based on a concept of generalized degrees of freedom. The proposed Procedure, combining the benefit of a class of nonadaptive Procedures, approximates the best performance of this class of Procedures across a variety of different situations. This class includes many well-known Procedures, such as AIC, BIC, Mallows's Cp, and risk inflation criterion (RIC). The proposed Procedure is applied to wavelet thresholding in nonparametric regression and variable Selection in least squares regression. Simulation results and an asymptotic...
Jianming Ye - One of the best experts on this subject based on the ideXlab platform.
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adaptive Model Selection
Journal of the American Statistical Association, 2002Co-Authors: Xiaotong Shen, Jianming YeAbstract:Most Model Selection Procedures use a fixed penalty penalizing an increase in the size of a Model. These nonadaptive Selection Procedures perform well only in one type of situation. For instance, Bayesian information criterion (BIC) with a large penalty performs well for “small” Models and poorly for “large” Models, and Akaike's information criterion (AIC) does just the opposite. This article proposes an adaptive Model Selection Procedure that uses a data-adaptive complexity penalty based on a concept of generalized degrees of freedom. The proposed Procedure, combining the benefit of a class of nonadaptive Procedures, approximates the best performance of this class of Procedures across a variety of different situations. This class includes many well-known Procedures, such as AIC, BIC, Mallows's Cp, and risk inflation criterion (RIC). The proposed Procedure is applied to wavelet thresholding in nonparametric regression and variable Selection in least squares regression. Simulation results and an asymptotic...
Alfred O Hero - One of the best experts on this subject based on the ideXlab platform.
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phase transitions and a Model order Selection criterion for spectral graph clustering
IEEE Transactions on Signal Processing, 2018Co-Authors: Pinyu Chen, Alfred O HeroAbstract:One of the longstanding open problems in spectral graph clustering (SGC) is the so-called Model order Selection problem: automated Selection of the correct number of clusters. This is equivalent to the problem of finding the number of connected components or communities in an undirected graph. We propose an automated Model order Selection (AMOS), a solution to the SGC Model Selection problem under a random interconnection Model using a novel Selection criterion that is based on an asymptotic phase transition analysis. AMOS can more generally be applied to discovering hidden block diagonal structure in symmetric non-negative matrices. Numerical experiments on simulated graphs validate the phase transition analysis, and real-world network data are used to validate the performance of the proposed Model Selection Procedure.
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phase transitions and a Model order Selection criterion for spectral graph clustering
arXiv: Social and Information Networks, 2016Co-Authors: Pinyu Chen, Alfred O HeroAbstract:One of the longstanding open problems in spectral graph clustering (SGC) is the so-called Model order Selection problem: automated Selection of the correct number of clusters. This is equivalent to the problem of finding the number of connected components or communities in an undirected graph. We propose automated Model order Selection (AMOS), a solution to the SGC Model Selection problem under a random interconnection Model (RIM) using a novel Selection criterion that is based on an asymptotic phase transition analysis. AMOS can more generally be applied to discovering hidden block diagonal structure in symmetric non-negative matrices. Numerical experiments on simulated graphs validate the phase transition analysis, and real-world network data is used to validate the performance of the proposed Model Selection Procedure.