检索结果-内蒙古大学图书馆

Efficient Bayesian Inference for Generalized Bradley-Terry Models

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2012年第1期21卷 174-196页

作者： Caron, Francois Doucet, Arnaud Univ Bordeaux 1 INRIA Bordeaux Sud Ouest F-33405 Talence France Univ Bordeaux 1 Inst Math Bordeaux F-33405 Talence France Univ Oxford Dept Stat Oxford OX1 3TG England

The Bradley-Terry model is a popular approach to describe probabilities of the possible outcomes when elements of a set are repeatedly compared with one another in pairs. It has found many applications including animal behavior, chess ranking, and multiclass classification. Numerous extensions of the basic model have also been proposed in the literature including models with ties, multiple comparisons, group comparisons, and random graphs. From a computational point of view, Hunter has proposed efficient iterative minorization-maximization (mm) algorithms to perform maximum likelihood estimation for these generalized Bradley-Terry models whereas Bayesian inference is typically performed using Markov chain Monte Carlo algorithms based on tailored Metropolis Hastings proposals. We show here that these mm algorithms can be reinterpreted as special instances of expectation-maximization algorithms associated with suitable sets of latent variables and propose some original extensions. These latent variables allow us to derive simple Gibbs samplers for Bayesian inference. We demonstrate experimentally the efficiency of these algorithms on a variety of applications.

关键词： Data augmentation EM algorithm Gibbs sampler Maximum likelihood estimation MCMC algorithms mm algorithm Plackett-Luce model Rank data

来源：评论

学校读者我要写书评

暂无评论

Total variation, adaptive total variation and nonconvex smoothly clipped absolute deviation penalty for denoising blocky images

引用

PATTERN RECOGNITION 2010年第8期43卷 2609-2619页

作者： Chopra, Aditya Lian, Heng VIT Univ Sch Comp Sci Vellore Tamil Nadu India Nanyang Technol Univ Div Math Sci Sch Phys & Math Sci Singapore 637371 Singapore

The total variation-based image denoising model has been generalized and extended in numerous ways, improving its performance in different contexts. We propose a new penalty function motivated by the recent progress in the statistical literature on high-dimensional variable selection. Using a particular instantiation of the majorization-minimization algorithm, the optimization problem can be efficiently solved and the computational procedure realized is similar to the spatially adaptive total variation model. Our two-pixel image model shows theoretically that the new penalty function solves the bias problem inherent in the total variation model. The superior performance of the new penalty function is demonstrated through several experiments. Our investigation is limited to "blocky" images which have small total variation. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： mm algorithm SCAD penalty Total variation denoising

来源：评论

学校读者我要写书评

暂无评论

SPARSE LOGISTIC PRINCIPAL COMPONENTS ANALYSIS FOR BINARY DATA

引用

ANNALS OF APPLIED STATISTICS 2010年第3期4卷 1579-1601页

作者： Lee, Seokho Huang, Jianhua Z. Hu, Jianhua Hankuk Univ Foreign Studies Dept Stat Yongin 449771 Gyeonggi Do South Korea Texas A&M Univ Dept Stat College Stn TX 77843 USA Univ Texas Houston MD Anderson Canc Ctr Dept Biostat Div Quantitat Sci Houston TX 77030 USA

We develop a new principal components analysis (PCA) type dimension reduction method for binary data. Different from the standard PCA which is defined on the observed data, the proposed PCA is defined on the logit transform of the success probabilities of the binary observations. Sparsity is introduced to the principal component (PC) loading vectors for enhanced interpretability and more stable extraction of the principal components. Our sparse PCA is formulated as solving an optimization problem with a criterion function motivated from a penalized Bernoulli likelihood. A Majorization-Minimization algorithm is developed to efficiently solve the optimization problem. The effectiveness of the proposed sparse logistic PCA method is illustrated by application to a single nucleotide polymorphism data set and a simulation study.

关键词： Binary data dimension reduction mm algorithm LASSO PCA regularization sparsity

来源：评论

学校读者我要写书评

暂无评论

RECONSTRUCTING DNA COPY NUMBER BY PENALIZED ESTIMATION AND IMPUTATION

引用

ANNALS OF APPLIED STATISTICS 2010年第4期4卷 1749-1773页

作者： Zhang, Zhongyang Lange, Kenneth Ophoff, Roel Sabatti, Chiara Univ Calif Los Angeles Dept Stat Los Angeles CA 90095 USA Univ Calif Los Angeles Dept Biomath Human Genet & Stat Los Angeles CA 90095 USA Univ Calif Los Angeles Ctr Neurobehav Genet Los Angeles CA 90095 USA Univ Calif Los Angeles Dept Human Genet Los Angeles CA 90095 USA

Recent advances in genomics have underscored the surprising ubiquity of DNA copy number variation (CNV). Fortunately, modern genotyping platforms also detect CNVs with fairly high reliability. Hidden Markov models and algorithms have played a dominant role in the interpretation of CNV data. Here we explore CNV reconstruction via estimation with a fused-lasso penalty as suggested by Tibshirani and Wang [Biostatistics 9 (2008) 18-29]. We mount a fresh attack on this difficult optimization problem by the following: (a) changing the penalty terms slightly by substituting a smooth approximation to the absolute value function, (b) designing and implementing a new mm (majorization-minimization) algorithm, and (c) applying a fast version of Newton's method to jointly update all model parameters. Together these changes enable us to minimize the fused-lasso criterion in a highly effective way. We also reframe the reconstruction problem in terms of imputation via discrete optimization. This approach is easier and more accurate than parameter estimation because it relies on the fact that only a handful of possible copy number states exist at each SNP. The dynamic programming framework has the added bonus of exploiting information that the current fused-lasso approach ignores. The accuracy of our imputations is comparable to that of hidden Markov models at a substantially lower computational cost.

关键词： l(1) penalty fused lasso dynamic programming mm algorithm

来源：评论

学校读者我要写书评

暂无评论

Principal Components Analysis for Binary Data

Principal Components Analysis for Binary Data

引用

作者： Lee, Seokho Texas A&M University

Principal components analysis (PCA) has been widely used as a statistical tool for the dimension reduction of multivariate data in various application areas and extensively studied in the long history of statistics. One of the limitations of PCA machinery is that PCA can be applied only to the continuous type variables. Recent advances of information technology in various applied areas have created numerous large diverse data sets with a high dimensional feature space, including high dimensional binary data. In spite of such great demands, only a few methodologies tailored to such binary dataset have been suggested. The methodologies we developed are the model-based approach for generalization to binary data. We developed a statistical model for binary PCA and proposed two stable estimation procedures using mm algorithm and variational method. By considering the regularization technique, the selection of important variables is automatically achieved. We also proposed an efficient algorithm for model selection including the choice of the number of principal components and regularization parameter in this study.

关键词： BINARY DATA DIMENSION REDUCTION mm algorithm LASSO PCA REGULARIZATION SPARSITY VARIATIONAL METHOD Book Thesis

来源：评论

学校读者我要写书评

暂无评论

A MIXTURE OF EXPERTS MODEL FOR RANK DATA WITH APPLICATIONS IN ELECTION STUDIES

引用

ANNALS OF APPLIED STATISTICS 2008年第4期2卷 1452-1477页

作者： Gormley, Isobel Claire Murphy, Thomas Brendan Univ Coll Dublin Sch Math Sci Dublin Ireland

A voting bloc is defined to be a group of voters who have similar voting preferences. The cleavage of the Irish electorate into voting blocs is of interest. Irish elections employ a "single transferable vote" electoral systems under this system voters rank some or all of the electoral candidates in order of preference. These rank votes provide a rich source of preference information from which inferences about the composition of the electorate may be drawn. Additionally, the influence of social factors or covariates on the electorate composition is of interest. A mixture of experts model is a mixture model in which the model parameters are functions of covariates. A mixture of experts model for rank data is developed to provide a model-based method to cluster Irish voters into voting blocs, to examine the influence of social factors on this clustering and to examine the characteristic preferences of the voting blocs. The Benter model for rank data is employed as the family of component densities within the mixture of experts model;generalized linear model theory is employed to model the influence of covariates oil the mixing proportions. Model fitting is achieved via a hybrid of the EM and mm algorithms. An example of the methodology is illustrated by examining all Irish presidential election. The existence of voting blocs in the electorate is established and it is determined that age and government satisfaction levels are important factors influencing voting in this election.

关键词： Rank data mixture models generalized linear models EM algorithm mm algorithm

来源：评论

学校读者我要写书评

暂无评论

On Use of the mm algorithm for Channel Estimation in MIMO OFDM

On Use of the MM Algorithm for Channel Estimation in MIMO OF...

引用

2005年无线通信、网络和移动计算国际会议

作者： Rong Chen Haibin Zhang Youyun Xu Hanwen Luo Department of Electronic Engineering Shanghai Jiaotong University Shanghai 200030 P.R.China

ISBN: (纸本)078039335X

In this paper, the general channel estimator for MIMO OFDM is derived and mm algorithms are used to reduce computational complexity. The first M of mm stands for majorization(minorization) and the second M stands for minimization(maximization). It's well known that EM algorithms are powerful tools for channel estimation using iterative calculation. Indeed, every EM-type algorithm is a special case of the more general class of mm algorithms. To construct an EM-type algorithm is skillful and complicated. In contrast, the mm algorithms are easier to be understood and applied. In addition to constructing channel estimation algorithms based on the mm principle we also analyze the convergence property of the mm-type algorithms. Finally, the simulation results demonstrate the performance of mm-type channel estimation algorithms.

关键词： MIMO systems OFDM modulation channel estimation convergence of numerical methods MIMO OFDM mm algorithm channel estimation algorithms convergence property iterative methods

来源：评论

学校读者我要写书评

暂无评论

Majorize-minimize algorithm for multiresponse sparse regression

Majorize-minimize algorithm for multiresponse sparse regress...

引用

32nd IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Simila, Timo Helsinki Univ Technol Lab Comp & Informat Sci FI-02015 Espoo Finland

ISBN: (纸本)1424407281

Multiresponse sparse regression is the problem of estimating many response variables using a common subset of input variables. Our model is linear, so row sparsity of the coefficient matrix implies subset selection. This is formulated as the problem of minimizing the residual sum of squares, where the row norms of the coefficient matrix are penalized. The proposed approach differs from existing ones in that any penalty function that is increasing, differentiable, and concave can be used. A convergent majorize-minimize algorithm is adopted for minimization. We also propose an active set strategy for tracking the nonzero rows of the coefficient matrix when the minimization is performed for a sequence of descending values of the penalty parameter. Numerical experiments are given to illustrate the active set strategy and analyze penalization with different degrees of concavity.

关键词： mm algorithm variable selection row sparse matrices simultaneous sparse approximation

来源：评论

学校读者我要写书评

暂无评论

Variable selection using mm algorithms

引用

ANNALS OF STATISTICS 2005年第4期33卷 1617-1642页

作者： Hunter, DR Li, RZ Penn State Univ Dept Stat University Pk PA 16802 USA

Variable selection is fundamental to high-dimensional statistical modeling. Many variable selection techniques may be implemented by maximum penalized likelihood using various penalty functions. Optimizing the penalized likelihood function is often challenging because it may be nondifferentiable and/or nonconcave. This article proposes a new class of algorithms for finding a maximizer of the penalized likelihood for a broad class of penalty functions. These algorithms operate by perturbing the penalty function slightly to render it differentiable, then optimizing this differentiable function using a minorize-maximize (mm) algorithm. mm algorithms are useful extensions of the well-known class of EM algorithms, a fact that allows us to analyze the local and global convergence of the proposed algorithm using some of the techniques employed for EM algorithms. In particular, we prove that when our mm algorithms converge, they must converge to a desirable point;we also discuss conditions under which this convergence may be guaranteed. We exploit the Newton-Raphson-like aspect of these algorithms to propose a sandwich estimator for the standard errors of the estimators. Our method performs well in numerical tests.

关键词： AIC BIC EM algorithm LASSO mm algorithm penalized likelihood oracle estimator SCAD

来源：评论

学校读者我要写书评

暂无评论

mm algorithms for generalized Bradley-Terry models

引用

ANNALS OF STATISTICS 2004年第1期32卷 384-406页

作者： Hunter, DR Penn State Univ Dept Stat University Pk PA 16802 USA

The Bradley-Terry model for paired comparisons is a simple and much-studied means to describe the probabilities of the possible outcomes when individuals are judged against one another in pairs. Among the many studies of the model in the past 75 years, numerous authors have generalized it in several directions, sometimes providing iterative algorithms for obtaining maximum likelihood estimates for the generalizations. Building on a theory of algorithms known by the initials mm, for minorization-maximization, this paper presents a powerful technique for producing iterative maximum likelihood estimation algorithms for a wide class of generalizations of the Bradley-Terry model. While algorithms for problems of this type have tended to be custom-built in the literature, the techniques in this paper enable their mass production. Simple conditions are stated that guarantee that each algorithm described will produce a sequence that converges to the unique maximum likelihood estimator. Several of the algorithms and convergence results herein are new.

关键词： Bradley-Terry model Luce's choice axiom maximum likelihood estimation mm algorithm Newton-Raphson Plackett-Luce model

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：