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Model-Based Clustering of Mixed Data With Sparse Dependence

IEEE ACCESS 2023年 11卷 75945-75954页

作者： Choi, Young-Geun Ahn, Soohyun Kim, Jayoun Sungkyunkwan Univ Dept Math Educ Seoul 03063 South Korea Ajou Univ Dept Math Suwon 16499 Gyeonggi Do South Korea Seoul Natl Univ Hosp Med Res Collaborating Ctr Seoul 03080 South Korea

Mixed data refers to a mixture of continuous and categorical variables. The clustering problem with mixed data is a long-standing statistical problem. The latent Gaussian mixture model, a model-based approach for such a problem, has received attention owing to its simplicity and interpretability. However, these approaches are prone to dimensionality problems. Specifically, parameters must be estimated for each group, and the number of covariance parameters is quadratic in the number of variables. To address this, we propose "regClustMD," a novel model-based clustering method that can address sparse dependence among variables. We consider a sparse latent Gaussian mixture model, assuming that the precision matrix between variables has sparse nonzero elements. We propose maximizing a penalized complete log-likelihood using the monte carlo expectation-maximization (MCEM) algorithm. Our numerical experiments and real data analyses demonstrated that our method outperformed a counterpart algorithm in both accuracy and failure rate under the correlated data structure.

关键词： INDEX TERMS Latent Gaussian mixture model maximum likelihood model-based clustering monte carlo expectation-maximization algorithm

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An approach to model clustered survival data with dependent censoring

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BIOMETRICAL JOURNAL 2020年第1期62卷 157-174页

作者： Schneider, Silvana Demarqui, Fabio Nogueira Colosimo, Enrico Antonio Mayrink, Vinicius Diniz Univ Fed Rio Grande do Sul Dept Estat Av Bent Goncalves9500 Predio 43-111 Porto Alegre RS Brazil Univ Fed Minas Gerais Dept Estat Belo Horizonte MG Brazil

In this study we introduce a likelihood-based method, via the Weibull and piecewise exponential distributions, capable of accommodating the dependence between failure and censoring times. The methodology is developed for the analysis of clustered survival data and it assumes that failure and censoring times are mutually independent conditional on a latent frailty. The dependent censoring mechanism is accounted through the frailty effect and this is accomplished by means of a key parameter accommodating the correlation between failure and censored observations. The full specification of the likelihood in our work simplifies the inference procedures with respect to Huang and Wolfe since it reduces the computation burden of working with the profile likelihood. In addition, the assumptions made for the baseline distributions lead to models with continuous survival functions. In order to carry out inferences, we devise a monte carlo EM algorithm. The performance of the proposed models is investigated through a simulation study. Finally, we explore a real application involving patients from the Dialysis Outcomes and Practice Patterns Study observed between 1996 and 2015.

关键词： frailty model kidney data monte carlo expectation-maximization algorithm piecewise exponential Weibull

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Dynamic reliability assessment and prediction for repairable systems with interval-censored data

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2017年 159卷 301-309页

作者： Peng, Yizhen Wang, Yu Zi, YanYang Tsui, Kwok-Leung Zhang, Chuhua Xi An Jiao Tong Univ Sch Mech Engn State Key Lab Mfg & Syst Engn Xian 710049 Peoples R China City Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Hong Kong Peoples R China Xi An Jiao Tong Univ Sch Energy & Power Engn Dept Fluid Machinery & Engn Xian 710049 Peoples R China

The 'Test, Analyze and Fix' process is widely applied to improve the reliability of a repairable system. In this process, dynamic reliability assessment for the system has been paid a great deal of attention. Due to instrument malfunctions, staff omissions and imperfect inspection strategies, field reliability data are often subject to interval censoring, making dynamic reliability assessment become a difficult task. Most traditional methods assume this kind of data as multiple normal distributed variables or the missing mechanism as missing at random, which may cause a large bias in parameter estimation. This paper proposes a novel method to evaluate and predict the dynamic reliability of a repairable system subject to interval-censored problem. First, a multiple imputation strategy based on the assumption that the reliability growth trend follows a nonhomogeneous Poisson process is developed to derive the distributions of missing data. Second, a new order statistic model that can transfer the dependent variables into independent variables is developed to simplify the imputation procedure. The unknown parameters of the model are iteratively inferred by the monte carlo expectation maximization (MCEM) algorithm. Finally, to verify the effectiveness of the proposed method, a simulation and a real case study for gas pipeline compressor system are implemented.

关键词： Dynamic reliability Interval censoring monte carlo expectation-maximization algorithm Non-homogeneous Poisson process

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GENERALIZED THEME DICTIONARY MODELS FOR ASSOCIATION PATTERN DISCOVERY

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ANNALS OF APPLIED STATISTICS 2023年第1期17卷 269-293页

作者： Yang, By yang Deng, K. E. Nankai Univ Sch Stat & Data Sci LPMC & KLMDASR Tianjin Peoples R China Tsinghua Univ Ctr Stat Sci Beijing Peoples R China Tsinghua Univ Dept Ind Engn Beijing Peoples R China

Discovering association patterns of items from a collection of baskets composed of different items is an important problem in various fields. Assum-ing that each basket is composed of themes of items randomly sampled from a theme dictionary, the theme dictionary model provides a general framework to achieve efficient association pattern discovery with statistical inference. This paper extends the original theme dictionary model by allowing more than one category of items in a basket and only presence/absence of items is observed for each basket with all quantitative information missing. The ex-tended models can solve a larger range of practical problems that cannot be handled by the original theme dictionary model. Both simulation studies and real data applications confirm the superiority of the proposed methods over the existing ones.

关键词： Association rule mining theme dictionary model cross-category association patterns missing data problem monte carlo expectation-maximization algorithm

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Multivariate claim count regression model with varying dispersion and dependence parameters

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES A-STATISTICS IN SOCIETY 2023年第1期186卷 61-83页

作者： Jeong, Himchan Tzougas, George Fung, Tsz Chai Simon Fraser Univ Dept Stat & Actuarial Sci Burnaby BC Canada Heriot Watt Univ Dept Actuarial Math & Stat Edinburgh Scotland Georgia State Univ Dept Risk Management & Insurance Atlanta GA USA Simon Fraser Univ Dept Stat & Actuarial Sci 8888 Univ Dr Burnaby BC V5A 1S6 Canada

The aim of this paper is to present a regression model for multivariate claim frequency data with dependence structures across the claim count responses, which may be of different sign and range, and overdispersion from the unobserved heterogeneity due to systematic effects in the data. For illustrative purposes, we consider the bivariate Poisson-lognormal regression model with varying dispersion. Maximum likelihood estimation of the model parameters is achieved through a novel monte carlo expectation-maximization algorithm, which is shown to have a satisfactory performance when we exemplify our approach to Local Government Property Insurance Fund data from the state of Wisconsin.

关键词： bivariate Poisson-lognormal regression model with varying dispersion copulas correlations of different signs and magnitude dispersion and dependence parameters monte carlo expectation-maximization algorithm multivariate claim frequency modelling

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Variable selection for joint models of multivariate skew-normal longitudinal and survival data

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STATISTICAL METHODS IN MEDICAL RESEARCH 2023年第9期32卷 1694-1710页

作者： Tang, Jiarui Tang, An-Min Tang, Niansheng Univ N Carolina Dept Biostat Chapel Hill NC USA Yunnan Univ Yunnan Key Lab Stat Modeling & Data Ana Kunming 650091 Peoples R China

Many joint models of multivariate skew-normal longitudinal and survival data have been presented to accommodate for the non-normality of longitudinal outcomes in recent years. But existing work did not consider variable selection. This article investigates simultaneous parameter estimation and variable selection in joint modeling of longitudinal and survival data. The penalized splines technique is used to estimate unknown log baseline hazard function, the rectangle integral method is adopted to approximate conditional survival function. monte carlo expectation-maximization algorithm is developed to estimate model parameters. Based on local linear approximations to conditional expectation of likelihood function and penalty function, a one-step sparse estimation procedure is proposed to circumvent the computationally challenge in optimizing the penalized conditional expectation of likelihood function, which is utilized to select significant covariates and trajectory functions, and identify the departure from normality of longitudinal data. The conditional expectation of likelihood function-based Bayesian information criterion is developed to select the optimal tuning parameter. Simulation studies and a real example from the clinical trial are used to illustrate the proposed methodologies.

关键词： Longitudinal data monte carlo expectation-maximization algorithm skew-normal distribution survival data variable selection

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Factor analysis for ranked data with application to a job selection attitude survey

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES A-STATISTICS IN SOCIETY 2005年第3期168卷 583-597页

作者： Yu, PLH Lam, KF Lo, SM Univ Hong Kong Dept Stat & Actuarial Sci Hong Kong Hong Kong Peoples R China

Factor analysis is a powerful tool to identify the common characteristics among a set of variables that are measured on a continuous scale. In the context of factor analysis for non-continuous-type data, most applications are restricted to item response data only. We extend the factor model to accommodate ranked data. The monte carlo expectation-maximization algorithm is used for parameter estimation at which the E-step is implemented via the Gibbs sampler. An analysis based on both complete and incomplete ranked data (e.g. rank the top q out of k items) is considered. Estimation of the factor scores is also discussed. The method proposed is applied to analyse a set of incomplete ranked data that were obtained from a survey that was carried out in GuangZhou, a major city in mainland China, to investigate the factors affecting people's attitude towards choosing jobs.

关键词： factor analysis factor score Gibbs sampler monte carlo expectation-maximization algorithm ranked data

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A MARKOV RANDOM FIELD-BASED APPROACH TO CHARACTERIZING HUMAN BRAIN DEVELOPMENT USING SPATIAL-TEMPORAL TRANSCRIPTOME DATA

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ANNALS OF APPLIED STATISTICS 2015年第1期9卷 429-451页

作者： Lin, Zhixiang Sanders, Stephan J. Li, Mingfeng Sestan, Nenad State, Matthew W. Zhao, Hongyu Yale Univ Interdept Program Computat Biol & Bioinformat New Haven CT 06511 USA Univ Calif San Francisco Dept Psychiat San Francisco CA 94143 USA Yale Univ Kavli Inst Neurosci Dept Neurobiol New Haven CT 06520 USA Yale Univ Yale Sch Publ Hlth Dept Biostat New Haven CT 06520 USA

Human neurodevelopment is a highly regulated biological process. In this article, we study the dynamic changes of neurodevelopment through the analysis of human brain microarray data, sampled from 16 brain regions in 15 time periods of neurodevelopment. We develop a two-step inferential procedure to identify expressed and unexpressed genes and to detect differentially expressed genes between adjacent time periods. Markov Random Field (MRF) models are used to efficiently utilize the information embedded in brain region similarity and temporal dependency in our approach. We develop and implement a monte carlo expectation-maximization (MCEM) algorithm to estimate the model parameters. Simulation studies suggest that our approach achieves lower misclassification error and potential gain in power compared with models not incorporating spatial similarity and temporal dependency.

关键词： Markov Random Field model spatial and temporal data neurodevelopment microarray monte carlo expectation-maximization algorithm gene expression differential expression

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Modeling the random effects covariance matrix for longitudinal data with covariates measurement error

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STATISTICS IN MEDICINE 2018年第28期37卷 4167-4184页

作者： Hoque, Md Erfanul Torabi, Mahmoud Univ Manitoba Dept Stat Winnipeg MB Canada Univ Manitoba Dept Community Hlth Sci Winnipeg MB R3E 0W3 Canada

Longitudinal data occur frequently in practice such as medical studies and life sciences. Generalized linear mixed models (GLMMs) are commonly used to analyze such data. It is typically assumed that the random effects covariance matrix is constant among subjects in these models. In many situations, however, the correlation structure may differ among subjects and ignoring this heterogeneity can lead to biases in model parameters estimate. Recently, Lee et al developed a heterogeneous random effects covariance matrix for GLMMs for error-free covariates. Covariates measured with error also happen frequently in the longitudinal data set-up (eg, blood pressure and cholesterol level). Ignoring this issue in the data may produce bias in model parameters estimate and lead to wrong conclusions. In this paper, we propose an approach to properly model the random effects covariance matrix based on covariates in the class of GLMMs, where we also have covariates measured with error. The resulting parameters from the decomposition of random effects covariance matrix have a sensible interpretation and can be easily modeled without the concern of positive definiteness of the resulting estimator. The performance of the proposed approach is evaluated through simulation studies, which show that the proposed method performs very well in terms of bias, mean squared error, and coverage rate. An application of the proposed method is also provided using a longitudinal data from Manitoba follow-up study.

关键词： cholesky decomposition longitudinal data measurement error monte carlo expectation-maximization algorithm random effects

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An efficient forward-reverse expectation-maximization algorithm for statistical inference in stochastic reaction networks

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STOCHASTIC ANALYSIS AND APPLICATIONS 2016年第2期34卷 193-231页

作者： Bayer, Christian Moraes, Alvaro Tempone, Raul Vilanova, Pedro Weierstrass Inst Appl Anal & Stochast Berlin Germany King Abdullah Univ Sci & Technol Comp Elect & Math Sci & Engn Thuwal Saudi Arabia

In this work, we present an extension of the forward-reverse representation introduced by Bayer and Schoenmakers (Annals of Applied Probability, 24(5):1994-2032, 2014) to the context of stochastic reaction networks (SRNs). We apply this stochastic representation to the computation of efficient approximations of expected values of functionals of SRN bridges, that is, SRNs conditional on their values in the extremes of given time intervals. We then employ this SRN bridge-generation technique to the statistical inference problem of approximating reaction propensities based on discretely observed data. To this end, we introduce a two-phase iterative inference method in which, during phase I, we solve a set of deterministic optimization problems where the SRNs are replaced by their reaction-rate ordinary differential equations approximation;then, during phase II, we apply the monte carlo version of the expectation-maximization algorithm to the phase I output. By selecting a set of overdispersed seeds as initial points in phase I, the output of parallel runs from our two-phase method is a cluster of approximate maximum likelihood estimates. Our results are supported by numerical examples.

关键词： inference for stochastic reaction networks bridges for continuous-time Markov chains Forward-reverse algorithm monte carlo expectation-maximization algorithm 60J75 92C60 92C42 60J22 60J27 65C05 62M05 65C60

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