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AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS 2024年第1期66卷 77-102页

作者： Wang, Zhu Univ Tennessee Hlth Sci Ctr Dept Prevent Med 66 N Pauline St Memphis TN 38163 USA

Robust estimation is primarily concerned with providing reliable parameter estimates in the presence of outliers. Numerous robust loss functions have been proposed in regression and classification, along with various computing algorithms. In modern penalised generalised linear models (GLMs), however, there is limited research on robust estimation that can provide weights to determine the outlier status of the observations. This article proposes a unified framework based on a large family of loss functions, a composite of concave and convex functions (CC-family). Properties of the CC-family are investigated, and CC-estimation is innovatively conducted via the iteratively reweighted convex optimisation (IRCO), which is a generalisation of the iteratively reweighted least squares in robust linear regression. For robust GLM, the IRCO becomes the iteratively reweighted GLM. The unified framework contains penalised estimation and robust support vector machine (SVM) and is demonstrated with a variety of data applications.

关键词： CC-estimator mm algorithm IRCO robust SVM variable selection

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A General Inferential Framework for Singly-Truncated Bivariate Normal Models with Applications in Economics

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COMPUTATIONAL ECONOMICS 2024年第5期64卷 2747-2781页

作者： Liu, Yin Tian, Guo-Liang Zhang, Chi Qin, Hong Zhongnan Univ Econ & Law Sch Math & Stat Wuhan Hubei Peoples R China Southern Univ Sci & Technol Dept Stat & Data Sci Shenzhen Guangdong Peoples R China Shenzhen Univ Coll Econ Shenzhen Guangdong Peoples R China

To analyze the singly-truncated bivariate economic data, we establish a class of singly-truncated bivariate normal distributions via stochastically representing the original bivariate normal random vector as a mixture of the singly-truncated part and its complementary components. Aided with the stochastic representaion, we creatively construct two novel unified and simple algorithms-the expectation-maximization algorithm as well as the minorization-maximization algorithm-to calculate the maximum likelihood estimates of the means and covariance matrix for the model of interest. In addition, we also develop a DA algorithm for posterior sampling in Bayesian analysis. Both simulation results and two real data applications in economics, collaborated by comparisons with existing methods, demonstrate the effectiveness and stability of proposed methodologies.

关键词： Economic index EM algorithm mm algorithm Singly-truncated bivariate normal distribution Stochastic representation Truncated data

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mm for penalized estimation

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TEST 2022年第1期31卷 54-75页

作者： Wang, Zhu UT Hlth San Antonio Dept Populat Hlth Sci San Antonio TX 78229 USA

Penalized estimation can conduct variable selection and parameter estimation simultaneously. The general framework is to minimize a loss function subject to a penalty designed to generate sparse variable selection. The majorization-minimization (mm) algorithm is a computational scheme for stability and simplicity, and the mm algorithm has been widely applied in penalized estimation. Much of the previous work has focused on convex loss functions such as generalized linear models. When data are contaminated with outliers, robust loss functions can generate more reliable estimates. Recent literature has witnessed a growing impact of nonconvex loss-based methods, which can generate robust estimation for data contaminated with outliers. This article investigates mm algorithm for penalized estimation, provides innovative optimality conditions and establishes convergence theory with both convex and nonconvex loss functions. With respect to applications, we focus on several nonconvex loss functions, which were formerly studied in machine learning for regression and classification problems. Performance of the proposed algorithms is evaluated on simulated and real data including cancer clinical status. Efficient implementations of the algorithms are available in the R package mpath in CRAN.

关键词： Classification mm algorithm Nonconvex Quadratic majorization Regression Robust estimation Variable selection

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CMPLE: Correlation Modeling to Decode Photosynthesis Using the Minorize-Maximize algorithm

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JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS 2024年 1-24页

作者： Chattopadhyay, Abhijnan Hoh, Donghee Kramer, David M. Maiti, Tapabrata Sinha, Samiran Natl Inst Environm Hlth Sci NIH Epidemiol Branch Res Triangle Pk Durham NC USA MSU DOE Plant Res Lab E Lansing MI USA Michigan State Univ Dept Biochem & Mol Biol E Lansing MI USA Michigan State Univ Dept Stat & Probabil E Lansing MI USA Texas A&M Univ Dept Stat College Stn TX 77843 USA

In plant genomic experiments, correlations among various biological traits (phenotypes) give new insights into how genetic diversity may have tuned biological processes to enhance fitness under diverse conditions. Consequently, knowing how the correlations are affected by genetic (G) and environmental (E) factors helps develop climate-resilient plants. However, the current literature lacks any method for assessing the effect of predictors on pairwise correlations among multiple phenotypes together with easily interpretable model parameters. To address this need, we propose to model pairwise correlations directly in terms of G and E and develop a computationally efficient inference procedure. Two major novelties in our methodology are (1) the use of a composite pairwise likelihood method to avoid the positive definiteness restriction on the correlation matrix and (2) the use of a novel Minorize-Maximize (mm) algorithm for the efficient estimation of a large number of parameters. The proposed method shows excellent numerical performance on synthetic datasets. The analysis of the motivating data on cowpea reveals that the rates of solar energy storage by photosynthesis (the aggregate trait) are differentially affected by different genetic loci through two distinct processes: "photoinhibition" which results from photodamage caused by excess light, and "photoprotection" which protects plants from photodamage but also results in energy loss. Supplementary material to this paper is provided online.

关键词： Correlation modeling Gene-environment interaction mm algorithm Pairwise composite likelihood Phenome-wide association study Standard deviation modeling

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De-Noising of Sparse Signals Using Mixture Model Shrinkage Function

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IEEE ACCESS 2023年 11卷 7551-7563页

作者： Ullah, Hayat Amir, Muhammad Iqbal, Muhammad Malik, Suheel Abdullah Jadoon, Muhammad Mohsin Khan NYU Tandon Sch Engn Dept Elect & Comp Engn New York NY 11201 USA Int Islamic Univ Islamabad Dept Elect Engn Islamabad 44000 Pakistan Tampere Univ Dept Automat & Mech Engn Tampere 33720 Finland Pak Austria Fachhsch Inst Fac Elect Com IT & Design Haripur 22653 Pakistan

In this work a new thresholding function referred to as 'mixture model shrinkage' (mmS) based on the minimization of a convex cost function is proposed. Normally, thresholding functions underestimate larger signal amplitudes during the de-noising process. The proposed model is a more flexible shrinkage function as it solves the underestimation problem to a greater extent and thus efficiently de-noises the signal without affecting signal amplitudes. The Expectation minimization (EM) algorithm is used to find the model parameters along with the majorization-minimization (mm) algorithm that minimize the monotonic cost function. The proposed model is then applied for de-noising group sparse signals and Shepp Logan phantom images. Our experimental study shows that mmS outclasses current thresholding functions and overlapping group shrinkage algorithm without results suffering from underestimation. Furthermore, the proposed model has the smallest Root Mean Square Error (RMSE) for de-noising group sparse signals.

关键词： Noise reduction Transforms Thresholding (Imaging) Mixture models Signal processing algorithms Noise measurement Wavelet coefficients Convex optimization EM algorithm maximum a posteriori estimator (MAP) mm algorithm PSNR RMSE sparse signal processing

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A multinomial canonical decomposition model, with emphasis on the analysis of multivariate binary data

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METRIKA 2025年 1-30页

作者： de Rooij, Mark Leiden Univ Methodol & Stat Dept Leiden Netherlands

In this paper, we propose to decompose the canonical parameter of a multinomial model into a set of participant scores and category scores. External information about the participants or the categories can be used to restrict these scores. Therefore, we impose the constraint that the scores are linear combinations of the external variables. For the estimation of the parameters of the decomposition, we derive a majorization-minimization algorithm. We place special emphasis on the case where the categories represent profiles of binary response variables. In that case, the multinomial model becomes a regression model for multiple binary response variables and researchers might be interested in the effect of an external variable for the participant (i.e., a predictor) on a binary response variable or in the effect of this predictor on the association among binary response variables. We derive interpretational rules for these relationships in terms of changes in log odds or log odds ratios. Connections between our multinomial canonical decomposition and loglinear models, multinomial logistic regression, multinomial reduced rank logistic regression, and double constrained correspondence analysis are discussed. We use two empirical data sets, the first to show the relationships between a loglinear analysis approach and our modelling approach. The second data set is used as an illustration of our modelling approach and describes the model selection and interpretation in detail.

关键词： Multinomial distribution Bilinear model mm algorithm Reduced rank model Generalized SVD

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Sparse logistic functional principal component analysis for binary data

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STATISTICS AND COMPUTING 2023年第1期33卷 1-12页

作者： Zhong, Rou Liu, Shishi Li, Haocheng Zhang, Jingxiao Renmin Univ China Ctr Appl Stat Sch Stat Beijing Peoples R China Hangzhou Dianzi Univ Sch Econ Hangzhou Peoples R China Univ Calgary Dept Math & Stat Calgary AB Canada

Functional binary datasets occur frequently in real practice, whereas discrete characteristics of the data can bring challenges to model estimation. In this paper, we propose a sparse logistic functional principal component analysis (SLFPCA) method to handle functional binary data. The SLFPCA looks for local sparsity of the eigenfunctions to obtain convenience in interpretation. We formulate the problem through a penalized Bernoulli likelihood with both roughness penalty and sparseness penalty terms. An innovative algorithm is developed for the optimization of the penalized likelihood using majorization-minimization algorithm. The proposed method is accompanied by R package SLFPCA for implementation. The theoretical results indicate both consistency and sparsistency of the proposed method. We conduct a thorough numerical experiment to demonstrate the advantages of the SLFPCA approach. Our method is further applied to a physical activity dataset.

关键词： Functional principal component analysis Penalized Bernoulli likelihood Binary data Local sparsity mm algorithm

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Distributed Precoding for Network Massive MIMO Systems Without Data Sharing

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IEEE SYSTEMS JOURNAL 2023年第4期17卷 6057-6068页

作者： Zhu, Wen-Jie Sun, Chen Gao, Xiqi Southeast Univ Natl Mobile Commun Res Lab Nanjing 210096 Peoples R China Purple Mt Labs Nanjing 211100 Peoples R China

This article delves into the distributed precoding for network massive multiinput-multioutput (NM-MIMO) systems where no user data stream is shared among the base stations (BSs). Aiming to navigate the challenge of minimizing information exchange for weighted sum-rate(WSR) maximization, which inherently places substantial demands on signaling overheads, we begin by reformulating the original problem as a BS-specific format. Inspired by such a rewritten form, we propose a virtualWSR as the objective function to derive an approximation of this reformulated problem. For a specific BS, the calculation of this virtual WSR is solely contingent upon the precoders within its own cell and low-dimensional virtual covariance matrices as initial values. Through an iterative approach facilitated by the minorization-maximization (mm) algorithm, we attain a stationary point for the maximization of nonconcave virtualWSR. With the locally generated virtual covariance matrices exchanged as initial values, the precoding matrix within each cell can be optimized independently and concurrently. This method eliminates the need for additional external exchanges throughout the iterative process. The simulation indicates the efficacy of our proposed approach in achieving a favorable WSR.

关键词： Distributed processing mm algorithm network massive MIMO WSR maximization

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A new algorithm and a discussion about visualization for logistic reduced rank regression

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Behaviormetrika 2024年第1期51卷 389-410页

作者： de Rooij, Mark Institute of Psychology Department Methodology and Statistics Leiden University Leiden Netherlands

Logistic reduced rank regression is a useful data analysis tool when we have multiple binary response variables and a set of predictors. In this paper, we describe logistic reduced rank regression and present a new majorization minimization algorithm for the estimation of model parameters. Furthermore, we discuss Type I and Type D triplots for visualizing the results of a logistic reduced rank regression model, compare them, and then develop a hybrid triplot using elements of both types. Two empirical data sets are analyzed. This analysis is used to (1) compare the new algorithm to an existing one in terms of speed;and (2) to show the hybrid triplot and its interpretation. © 2023, The Author(s).

关键词： Constrained PCA Generalized SVD mm algorithm Visualization

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Distributed Learning of Finite Gaussian Mixtures

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JOURNAL OF MACHINE LEARNING RESEARCH 2022年第1期23卷 1-40页

作者： Zhang, Qiong Chen, Jiahua Univ British Columbia Dept Stat Vancouver BC V6T 1Z4 Canada

Advances in information technology have led to extremely large datasets that are often kept in different storage centers. Existing statistical methods must be adapted to overcome the resulting computational obstacles while retaining statistical validity and efficiency. In this situation, the split-and-conquer strategy is among the most effective solutions to many sta-tistical problems, including quantile processes, regression analysis, principal eigenspaces, and exponential families. This paper applies this strategy to develop a distributed learning procedure of finite Gaussian mixtures. We recommend a reduction strategy and invent an effective majorization-minimization algorithm. The new estimator is consistent and retains root-n consistency under some general conditions. Experiments based on simulated and real-world datasets show that the proposed estimator has comparable statistical perfor-mance with the global estimator based on the full dataset, if the latter is feasible. It can even outperform the global estimator for the purpose of clustering if the model assumption does not fully match the real-world data. It also has better statistical and computational performance than some existing split-and-conquer approaches.

关键词： Barycenter Gaussian mixture Global convergence Mixture reduction mm algorithm Model-based clustering Split-and-conquer

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