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Variable selection using the EM and cem algorithms in mixtures of linear mixed models

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2023年第13期93卷 2196-2231页

作者： Novais, Luisa Faria, Susana Univ Minho Dept Math P-4710057 Braga Portugal Univ Minho Ctr Mol & Environm Biol P-4710057 Braga Portugal

In order to deal with data of great complexity, the need to develop new methods for variable selection has emerged. Among the new methods, methods based on penalty functions have received great attention. These methods can be used in complex data problems since they shrink a subset of coefficient estimates to zero, thus removing the associated variables from the model, which allows the identification of the subset of the most relevant explanatory variables and, consequently, drastically reduces the computational burden. In this work we analyse the problem of variable selection in mixtures of linear mixed models. In order to do it, we compare the performance of a penalized likelihood approach for variable selection via the Expectation-Maximization and the Classification Expectation-Maximization algorithms through a simulation study and a real-world application.

关键词： EM algorithm cem algorithm mixture models penalized likelihood variable selection

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Co-clustering contaminated data: a robust model-based approach

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2024年第1期18卷 121-161页

作者： Fibbi, Edoardo Perrotta, Domenico Torti, Francesca Van Aelst, Stefan Verdonck, Tim Katholieke Univ Leuven Dept Math Celestijnenlaan 200B B-3001 Leuven Belgium European Commiss Joint Res Ctr Via Enrico Fermi 2749 I-21027 Ispra Italy

The exploration and analysis of large high-dimensional data sets calls for well-thought techniques to extract the salient information from the data, such as co-clustering. Latent block models cast co-clustering in a probabilistic framework that extends finite mixture models to the two-way setting. Real-world data sets often contain anomalies which could be of interest per se and may make the results provided by standard, non-robust procedures unreliable. Also estimation of latent block models can be heavily affected by contaminated data. We propose an algorithm to compute robust estimates for latent block models. Experiments on both simulated and real data show that our method is able to resist high levels of contamination and can provide additional insight into the data by highlighting possible anomalies.

关键词： Co-clustering Robustness Trimming LBM cem algorithm

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Stochastic blockmodeling of linked networks

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SOCIAL NETWORKS 2022年第0期70卷 240-252页

作者： Skulj, Damjan Ziberna, Ales Univ Ljubljana Fac Social Sci Kardeljeva Pl 5 SI-1000 Ljubljana Slovenia

Blockmodeling linked networks aims to simultaneously cluster two or more sets of units into clusters based on a network where ties are possible both between units from the same set as well as between units of different sets. While this has already been developed for generalized and k-means blockmodeling, our approach is based on the well-known stochastic blockmodeling technique, utilizing a mixture model. Estimation is performed using the cem algorithm, which iteratively estimates the parameters by maximizing a suitable likelihood function and reclusters the units according to the parameters. The steps are repeated until the likelihood function ceases to improve. A key drawback of the basic algorithm is that it treats all units equally, consequently yielding higher influence to larger parts of the data. The greater size, however, does not necessarily imply higher importance. To mitigate this asymmetry, we propose a solution where underrepresented parts of the data are given more influence through an appropriate weighting. This idea leads to the so-called weighted likelihood approach, where the ordinary likelihood function is replaced by a weighted likelihood. The efficiency of the different approaches is tested via simulations. It is shown through simulations that the weighted likelihood approach performs better for larger networks and a clearer blockmodel structure, especially when the one-mode blockmodels within the smaller sets are clearer.

关键词： Stochastic blockmodeling Linked network Weighted likelihood cem algorithm Mixture model

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Estimation of parameters in multivariate wrapped models for data on ap-torus

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COMPUTATIONAL STATISTICS 2021年第1期36卷 193-215页

作者： Nodehi, Anahita Golalizadeh, Mousa Maadooliat, Mehdi Agostinelli, Claudio Tarbiat Modares Univ Dept Stat Tehran Iran Inst Res Fundamental Sci IPM Sch Biol Sci POB 19395-5746 Tehran Iran Marquette Univ Dept Math & Stat Sci Milwaukee WI 53233 USA Univ Trento Dept Math Trento Italy

Multivariate circular observations, i.e. points on a torus arise frequently in fields where instruments such as compass, protractor, weather vane, sextant or theodolite are used. Multivariate wrapped models are often appropriate to describe data points scattered onp-dimensional torus. However, the statistical inference based on such models is quite complicated since each contribution in the log-likelihood function involves an infinite sum of indices in Z(p), wherepis the dimension of the data. To overcome this problem, for moderate dimensionp, we propose two estimation procedures based on Expectation-Maximisation and Classification Expectation-Maximisation algorithms. We study the performance of the proposed techniques on a Monte Carlo simulation and further illustrate the advantages of the new procedures on three real-world data sets.

关键词： cem algorithm EM algorithm Estimation procedures Multivariate wrapped distributions Torus

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Robust estimation for multivariate wrapped models

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METRON-INTERNATIONAL JOURNAL OF STATISTICS 2021年第2期79卷 225-240页

作者： Saraceno, Giovanni Agostinelli, Claudio Greco, Luca Univ Trento Dept Math Trento Italy Univ Sannio Dept DEMM Benevento Italy

A weighted likelihood technique for robust estimation of multivariate Wrapped distributions of data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise inference for standard techniques such as maximum likelihood method. Therefore, there is the need to handle such model inadequacies in the fitting process by a robust technique and an effective downweighting of observations not following the assumed model. Furthermore, the employ of a robust method could help in situations of hidden and unexpected substructures in the data. Here, it is suggested to build a set of data-dependent weights based on the Pearson residuals and solve the corresponding weighted likelihood estimating equations. In particular, robust estimation is carried out by using a Classification EM algorithm whose M-step is enhanced by the computation of weights based on current parameters' values. The finite sample behavior of the proposed method has been investigated by a Monte Carlo numerical study and real data examples.

关键词： cem algorithm Multivariate wrapped distributions Pearson residuals Robust estimators Torus Weighted likelihood

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An extension of the K-means algorithm to clustering skewed data

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COMPUTATIONAL STATISTICS 2019年第1期34卷 373-394页

作者： Melnykov, Volodymyr Zhu, Xuwen Univ Alabama Tuscaloosa AL 35487 USA Univ Louisville Louisville KY 40292 USA

Grouping similar objects into common groups, also known as clustering, is an important problem of unsupervised machine learning. Various clustering algorithms have been proposed in literature. In recent years, the need to analyze large amounts of data has led to reconsidering some fundamental clustering procedures. One of them is the celebrated K-means algorithm popular among practitioners due to its speedy performance and appealingly intuitive construction. Unfortunately, the algorithm often shows poor performance unless data groups have spherical shapes and approximately same sizes. In many applications, this restriction is so severe that the use of the K-means algorithm becomes questionable, misleading, or simply incorrect. We propose an extension of K-means that preserves the speed and intuitive interpretation of the original algorithm while providing greater flexibility in modeling clusters. The idea of the proposed generalization relies on the exponential transformation of Manly originally designed to obtain near-normally distributed data. The suggested modification is derived and illustrated on several datasets with good results.

关键词： Exponential transformation cem algorithm Cluster analysis Skewness

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Finding the Number of Normal Groups in Model-Based Clustering via Constrained Likelihoods

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2018年第2期27卷 404-416页

作者： Cerioli, Andrea Angel Garcia-Escudero, Luis Mayo-Iscar, Agustin Riani, Marco Univ Parma Dipart Sci Econ & Aziendali Parma Italy Univ Valladolid Dept Estadist & IO Valladolid Spain Univ Valladolid IMUVA Valladolid Spain

Deciding the number of clusters k is one of the most difficult problems in cluster analysis. For this purpose, complexity-penalized likelihood approaches have been introduced in model-based clustering, such as the well-known Bayesian information criterion and integrated complete likelihood criteria. However, the classification/mixture likelihoods considered in these approaches are unbounded without any constraint on the cluster scatter matrices. Constraints also prevent traditional EM and cem algorithms from being trapped in (spurious) local maxima. Controlling the maximal ratio between the eigenvalues of the scatter matrices to be smaller than a fixed constant c >= 1 is a sensible idea for setting such constraints. A new penalized likelihood criterion which takes into account the higher model complexity that a higher value of c entails is proposed. Based on this criterion, a novel and fully automated procedure, leading to a small ranked list of optimal (k, c) couples is provided. A new plot called "car-bike," which provides a concise summary of the solutions, is introduced. The performance of the procedure is assessed both in empirical examples and through a simulation study as a function of cluster overlap. Supplementary materials for the article are available online.

关键词： BIC cem algorithm Clustering EM algorithm ICL Mixtures

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Early diagnosis of gestational trophoblastic neoplasia based on trajectory classification with compartment modeling

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BMC MEDICAL RESEARCH METHODOLOGY 2016年第1期16卷 1-10页

作者： Burny, Claire Rabilloud, Muriel Golfier, Francois Massardier, Jerome Hajri, Touria Schott, Anne-Marie Subtil, Fabien Hosp Civils Lyon Serv Biostat F-69003 Lyon France Univ Lyon F-69000 Lyon France Univ Lyon 1 F-69100 Villeurbanne France CNRS Equipe Biostat Sante Lab Biometrie & Biol Evolut UMR 5558 F-69100 Villeurbanne France Lyon Sud Univ Hosp Dept Gynaecol & Oncol Surg Obstet Lyon France Lyon Sud Univ Hosp French Trophoblast Dis Reference Ctr Lyon France Univ Hosp Femme Mere Enfant Dept Obstet Lyon France Hosp Civils Lyon Equipe Accueil 4129 Pole Informat Med Evaluat Rech F-69003 Lyon France

Background: In randomized clinical trials or observational studies, it is common to collect biomarker values longitudinally on a cohort of individuals. The investigators may be interested in grouping individuals that share similar changes of biomarker values and use these groups for diagnosis or therapeutic purposes. However, most classical model-based classification methods rely mainly on empirical models such as splines or polynomials and do not reflect the physiological processes. Methods: A model-based classification method was developed for longitudinal biomarker measurements through a pharmacokinetic model that describes biomarker changes over time. The method is illustrated using data on human Chorionic Gonadotrophic Hormone measurements after curettage of hydatidiform moles. Results: The resulting classification was linked to the evolution toward gestational trophoblastic neoplasia and may be used as a tool for early diagnosis. The diagnostic accuracy of the pharmacokinetic model was more reproducible than the one of a purely mathematical model that did not take into account the biological processes. Conclusion: The use of pharmacokinetic models in model-based classification approaches can lead to clinically useful classifications.

关键词： Early diagnosis Model-based classification cem algorithm Compartment model Longitudinal study

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Piecewise Regression Mixture for Simultaneous Functional Data Clustering and Optimal Segmentation

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JOURNAL OF CLASSIFICATION 2016年第3期33卷 374-411页

作者： Chamroukhi, Faicel Univ Toulon & Var F-83957 La Garde France Aix Marseille Univ F-13397 Marseille France Lab Paul Painleve Villeneuve Dascq France

This paper introduces a novel mixture model-based approach to the simultaneous clustering and optimal segmentation of functional data, which are curves presenting regime changes. The proposed model consists of a finite mixture of piecewise polynomial regression models. Each piecewise polynomial regression model is associated with a cluster, and within each cluster, each piecewise polynomial component is associated with a regime (i.e., a segment). We derive two approaches to learning the model parameters: the first is an estimation approach which maximizes the observed-data likelihood via a dedicated expectation-maximization (EM) algorithm, then yielding a fuzzy partition of the curves into K clusters obtained at convergence by maximizing the posterior cluster probabilities. The second is a classification approach and optimizes a specific classification likelihood criterion through a dedicated classification expectation-maximization (cem) algorithm. The optimal curve segmentation is performed by using dynamic programming. In the classification approach, both the curve clustering and the optimal segmentation are performed simultaneously as the cem learning proceeds. We show that the classification approach is a probabilistic version generalizing the deterministic K-means-like algorithm proposed in Hbrail, Hugueney, Lechevallier, and Rossi (2010). The proposed approach is evaluated using simulated curves and real-world curves. Comparisons with alternatives including regression mixture models and the K-means-like algorithm for piecewise regression demonstrate the effectiveness of the proposed approach.

关键词： Model-based clustering Functional data analysis Optimal curve segmentation Mixture models Piecewise regression EM algortihm cem algorithm

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On the Spectral Decomposition in Normal Discriminant Analysis

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2014年第6期43卷 1471-1489页

作者： Bagnato, Luca Greselin, Francesca Punzo, Antonio Univ Cattolica Sacro Cuore Dipartimento Discipline Matemat Finanza Matemat & I-20123 Milan Italy Milano Bicocca Univ Dept Stat & Quantitat Methods Milan Italy Univ Catania Dipartimento Econ & Impresa Catania Italy

This article enlarges the covariance configurations, on which the classical linear discriminant analysis is based, by considering the four models arising from the spectral decomposition when eigenvalues and/or eigenvectors matrices are allowed to vary or not between groups. As in the classical approach, the assessment of these configurations is accomplished via a test on the training set. The discrimination rule is then built upon the configuration provided by the test, considering or not the unlabeled data. Numerical experiments, on simulated and real data, have been performed to evaluate the gain of our proposal with respect to the linear discriminant analysis.

关键词： cem algorithm EM algorithm Mixture models Multiple testing procedures Normal discriminant analysis Spectral decomposition

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