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A globally convergent algorithm for lasso-penalized mixture of linear regression models

COMPUTATIONAL STATISTICS & DATA ANALYSIS 2018年 119卷 19-38页

作者： Lloyd-Jones, Luke R. Nguyen, Hien D. McLachlan, Geoffrey J. Univ Queensland Inst Mol Biosci St Lucia Qld 4072 Australia Univ Queensland Sch Math & Phys St Lucia Qld 4072 Australia La Trobe Univ Dept Math & Stat Bundoora Vic 3086 Australia

Variable selection is an old and pervasive problem in regression analysis. One solution is to impose a lasso penalty to shrink parameter estimates toward zero and perform continuous model selection. The lasso-penalized mixture of linear regressions model (L-MLR) is a class of regularization methods for the model selection problem in the fixed number of variables setting. A new algorithm is proposed for the maximum penalized-likelihood estimation of the L-MLR model. This algorithm is constructed via the minorization maximization algorithm paradigm. Such a construction allows for coordinate-wise updates of the parameter components, and produces globally convergent sequences of estimates that generate monotonic sequences of penalized log-likelihood values. These three features are missing in the previously presented approximate expectation maximization algorithms. The previous difficulty in producing a globally convergent algorithm for the maximum penalized-likelihood estimation of the L-MLR model is due to the intractability of finding exact updates for the mixture model mixing proportions in the maximization-step. This issue is resolved by showing that it can be converted into a simple numerical root finding problem that is proven to have a unique solution. The method is tested in simulation and with an application to Major League Baseball salary data from the 1990s and the present day, where the concept of whether player salaries are associated with batting performance is investigated. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Lasso Mixture of linear regressions model mm algorithm Major League Baseball

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Robust boosting with truncated loss functions

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ELECTRONIC JOURNAL OF STATISTICS 2018年第1期12卷 599-650页

作者： Wang, Zhu Connecticut Childrens Med Ctr Dept Res Hartford CT 06106 USA

Boosting is a powerful machine learning tool with attractive theoretical properties. In recent years, boosting algorithms have been extended to many statistical estimation problems. For data contaminated with outliers, however, development of boosting algorithms is very limited. In this paper, innovative robust boosting algorithms utilizing the majorization-minimization (mm) principle are developed for binary and multi-category classification problems. Based on truncated loss functions, the robust boosting algorithms share a unified framework for linear and nonlinear effects models. The proposed methods can reduce the heavy influence from a small number of outliers which could otherwise distort the results. In addition, adaptive boosting for the truncated loss functions are developed to construct more sparse predictive models. We present convergence guarantees for smooth surrogate loss functions with both iteration-varying and constant step-sizes. We conducted empirical studies using data from simulations, a pediatric database developed for the US Healthcare Cost and Utilization Project, and breast cancer gene expression data. Compared with non-robust boosting, robust boosting improves classification accuracy and variable selection.

关键词： Robust method machine learning boosting difference of convex mm algorithm

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Hybrid sparse blind deconvolution: an implementation of SOOT algorithm to real data

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JOURNAL OF GEOPHYSICS AND ENGINEERING 2018年第3期15卷 621-626页

作者： Pakmanesh, Parvaneh Goudarzi, Alireza Kourki, Meisam Grad Univ Adv Technol Kerman Iran

Getting information of seismic data depends on deconvolution as an important processing step;it provides the reflectivity series by signal compression. This compression can be obtained by removing the wavelet effects on the traces. The recently blind deconvolution has provided reliable performance for sparse signal recovery. In this study, two deconvolution methods have been implemented to the seismic data;the convolution of these methods provides a robust spiking deconvolution approach. This hybrid deconvolution is applied using the sparse deconvolution (mm algorithm) and the Smoothed-One-Over-Two algorithm (SOOT) in a chain. The mm algorithm is based on the minimization of the cost function defined by standards l1 and l2. After applying the two algorithms to the seismic data, the SOOT algorithm provided well-compressed data with a higher resolution than the mm algorithm. The SOOT algorithm requires initial values to be applied for real data, such as the wavelet coefficients and reflectivity series that can be achieved through the mm algorithm. The computational cost of the hybrid method is high, and it is necessary to be implemented on post-stack or pre-stack seismic data of complex structure regions.

关键词： deconvolution mm algorithm SOOT algorithm inversion sparsity

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Ties in one block comparison experiments: a generalization of the Mallows-Bradley-Terry ranking model

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JOURNAL OF APPLIED STATISTICS 2017年第14期44卷 2621-2644页

作者： Sawadogo, Amadou Dossou-Gbete, Simplice Lafon, Dominique Univ Felix Houphouet Boigny Dept Math & Comp 22 BP 582 Abidjan 22 Cote Ivoire Univ Pau & Pays Adour Lab Math & Their Applicat Pau CNRS Federat IPRA Pau France Ecole Mines Ales Pau France

This study is concerned with the extension of the Mallows-Bradley-Terry ranking model for one block comparison consisting of all the items of interest to situations which allow an expression of no preference. We consider a modification of the Mallows-Bradley-Terry ranking model by introducing an additional parameter, called an index of discrimination, in the model. This permits ties in the model. The maximum likelihood estimates of the parameters are found using a Maximization-Minimization algorithm: the evaluation of the mathematical expectations involved in the log-likelihood equation is obtained by generating samples of Monte Carlo Markov chain from the stationary distribution. In addition, a simulation study for asymptotic properties assessment has been made. The proposed method is applied to analyze data election.

关键词： Babington Smith model Mallows-Bradley-Terry model rank data maximum likelihood estimation mm algorithm MCMC

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BLIND IMAGE DECONVOLUTION USING STUDENT'S-T PRIOR WITH OVERLAPPING GROUP SPARSITY

BLIND IMAGE DECONVOLUTION USING STUDENT'S-T PRIOR WITH OVERL...

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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Jeon, In S. Kang, Deokyoung Yoo, Suk I. Seoul Natl Univ Dept Comp Sci & Engn Seoul South Korea

ISBN: (纸本)9781509041176

In this paper, we solve blind image deconvolution problem that is to remove blurs form a signal degraded image without any knowledge of the blur kernel. Since the problem is ill-posed, an image prior plays a significant role in accurate blind deconvolution. Traditional image prior assumes coefficients in filtered domains are sparse. However, it is assumed here that there exist additional structures over the sparse coefficients. Accordingly, we propose new problem formulation for the blind image deconvolution, which utilize the structural information by coupling Student's-t image prior with overlapping group sparsity. The proposed method resulted in an effective blind deconvolution algorithm that outperforms other state-of-the-art algorithms.

关键词： image restoration blind deconvolution Bayesian Student's-t prior group sparsity mm algorithm

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Variable Selection for Binary Spatial Regression: Penalized Quasi-Likelihood Approach

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BIOMETRICS 2016年第4期72卷 1164-1172页

作者： Feng, Wenning Sarkar, Abdhi Lim, Chae Young Maiti, Tapabrata Amer Express New York NY 10285 USA Michigan State Univ E Lansing MI 48824 USA Seoul Natl Univ Seoul South Korea

We consider the problem of selecting covariates in a spatial regression model when the response is binary. Penalized likelihood-based approach is proved to be effective for both variable selection and estimation simultaneously. In the context of a spatially dependent binary variable, an uniquely interpretable likelihood is not available, rather a quasi-likelihood might be more suitable. We develop a penalized quasi-likelihood with spatial dependence for simultaneous variable selection and parameter estimation along with an efficient computational algorithm. The theoretical properties including asymptotic normality and consistency are studied under increasing domain asymptotics framework. An extensive simulation study is conducted to validate the methodology. Real data examples are provided for illustration and applicability. Although theoretical justification has not been made, we also investigate empirical performance of the proposed penalized quasi-likelihood approach for spatial count data to explore suitability of this method to a general exponential family of distributions.

关键词： Binary response Increasing domain asymptotics LASSO mm algorithm Penalized quasi-likelihood SCAD Spatial regression Variable selection

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GenSVM: A Generalized Multiclass Support Vector Machine

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JOURNAL OF MACHINE LEARNING RESEARCH 2016年第1期17卷 1-42页

作者： van den Burg, Gerrit J. J. Groenen, Patrick J. F. Erasmus Univ Econometr Inst POB 1738 NL-3000 DR Rotterdam Netherlands

Traditional extensions of the binary support vector machine (SVM) to multiclass problems are either heuristics or require solving a large dual optimization problem. Here, a generalized multiclass SVM is proposed called GenSVM. In this method classification boundaries for a K-class problem are constructed in a (K-1)-dimensional space using a simplex encoding. Additionally, several different weightings of the misclassification errors are incorporated in the loss function, such that it generalizes three existing multiclass SVMs through a single optimization problem. An iterative majorization algorithm is derived that solves the optimization problem without the need of a dual formulation. This algorithm has the advantage that it can use warm starts during cross validation and during a grid search, which significantly speeds up the training phase. Rigorous numerical experiments compare linear GenSVM with seven existing multiclass SVMs on both small and large data sets. These comparisons show that the proposed method is competitive with existing methods in both predictive accuracy and training time, and that it significantly outperforms several existing methods on these criteria.

关键词： support vector machines SVM multiclass classification iterative majorization mm algorithm classifier comparison

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Label-Noise Resistant Logistic Regression for Functional Data Classification with an Application to Alzheimer's Disease Study

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BIOMETRICS 2016年第4期72卷 1325-1335页

作者： Lee, Seokho Shin, Hyejin Lee, Sang Han Hankuk Univ Foreign Studies Dept Stat Yongin Gyeonggi South Korea Samsung Elect Software R&D Ctr Frontier CS Lab Seoul South Korea Nathan S Kline Inst Psychiat Res New York NY USA

Alzheimer's disease (AD) is usually diagnosed by clinicians through cognitive and functional performance test with a potential risk of misdiagnosis. Since the progression of AD is known to cause structural changes in the corpus callosum (CC), the CC thickness can be used as a functional covariate in AD classification problem for a diagnosis. However, misclassified class labels negatively impact the classification performance. Motivated by AD-CC association studies, we propose a logistic regression for functional data classification that is robust to misdiagnosis or label noise. Specifically, our logistic regression model is constructed by adopting individual intercepts to functional logistic regression model. This approach enables to indicate which observations are possibly mislabeled and also lead to a robust and efficient classifier. An effective algorithm using mm algorithm provides simple closed-form update formulas. We test our method using synthetic datasets to demonstrate its superiority over an existing method, and apply it to differentiating patients with AD from healthy normals based on CC from MRI.

关键词： Alzheimer's disease Fisher consistency Functional data classification Label noise mm algorithm Outlier detection Robust classification

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Theoretical grounding for estimation in conditional independence multivariate finite mixture models

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JOURNAL OF NONPARAMETRIC STATISTICS 2016年第4期28卷 683-701页

作者： Zhu, Xiaotian Hunter, David R. Abbvie Inc 1 North Waukegan Rd N Chicago IL USA Penn State Univ Dept Stat University Pk PA 16802 USA

For the nonparametric estimation of multivariate finite mixture models with the conditional independence assumption, we propose a new formulation of the objective function in terms of penalised smoothed Kullback-Leibler distance. The nonlinearly smoothed majorisation-minimisation (NSmm) algorithm is derived from this perspective. An elegant representation of the NSmm algorithm is obtained using a novel projection-multiplication operator, a more precise monotonicity property of the algorithm is discovered, and the existence of a solution to the main optimisation problem is proved for the first time.

关键词： Mixture model penalised smoothed likelihood mm algorithm

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Blind image deconvolution using Student's-t prior with overlapping group sparsity

Blind image deconvolution using Student's-t prior with overl...

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： In S. Jeon Deokyoung Kang Suk I. Yoo Dept. of Computer Science and Engineering Seoul National University South Korea

ISBN: (纸本)9781509041183

关键词： image restoration blind deconvolution Bayesian Student's-t prior group sparsity mm algorithm blind deconvolution image restoration technique Imagery (Psychotherapy) images Image Bayesian inference deconvolution Blind Problem Formulation

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