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EM algorithm for bounded generalized t mixture model with an application to image segmentation

COMPUTATIONAL & APPLIED MATHEMATICS 2025年第1期44卷 1-21页

作者： Mahdavi, Abbas Balakrishnan, Narayanaswamy Jamalizadeh, Ahad Vali E Asr Univ Rafsanjan Dept Stat Rafsanjan Iran McMaster Univ Dept Math & Stat Hamilton ON Canada Shahid Bahonar Univ Kerman Fac Math & Comp Dept Stat Kerman Iran

This paper develops an EM-type algorithm for fitting the bounded generalized t mixture (BGTM) model. Due to heavy tails, high kurtosis and bounded nature, the BGTM model provides a flexible and suitable model for many computer vision and pattern recognition problems. We develop a feasible expectation conditional maximization (ecme) algorithm for computing the maximum likelihood estimates of model parameters via selection mechanism. To validate the effectiveness of the proposed methodology, we conduct experiments on both simulated data and real natural images. The obtained results demonstrate that the model and the estimation algorithm outperforms its sub-models in terms of both accuracy and computational efficiency.

关键词： ecme algorithm Mixture model Generalized t distribution Bounded distribution

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An EM algorithm for estimating the parameters of the skew generalized t-normal distribution with application to robust finite mixture modeling

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2025年第3期54卷 615-632页

作者： Mahdavi, Abbas Desmond, Anthony F. Jamalizadeh, Ahad Vali E Asr Univ Rafsanjan Dept Stat Rafsanjan Iran Univ Guelph Dept Math & Stat Guelph ON Canada Shahid Bahonar Univ Kerman Fac Math & Comp Dept Stat Kerman Iran

The present article describes an EM-type algorithm for estimation of the skew generalized t-normal (SGTN) distribution. The family of SGTN distributions can provide certain types of flexibility such as heavy tails and high kurtosis. The complexity of the SGTN distribution is traced to the ratio of the t density and distribution function of a normal distribution in the likelihood equations. To cope with this problem, we develop a feasible ecme algorithm for computing maximum likelihood estimates of model parameters via a selection mechanism. The proposed approach provides a robust parameter estimation method for the finite mixture model. Standard errors for the parameter estimates can be obtained via a general information-based method. Experimental results on simulated data and one real data example demonstrate the efficacy and usefulness of the proposed methodology.

关键词： ecme algorithm Finite mixture model Generalized t-normal distribution Truncated normal distribution

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A robust class of nonlinear autoregressive models with regression function and dependent innovations using semiparametric kernel estimation

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2024年第1期94卷 50-68页

作者： Alaei, Bita Zare, Karim Shokri, Soheil Maleki, Mohsen Hajrajabi, Arezo Islamic Azad Univ Dept Stat Marvdasht Branch Marvdasht Iran Islamic Azad Univ Rasht Branch Dept Stat Rasht Iran Univ Isfahan Fac Math & Stat Dept Stat Esfahan Iran Imam Khomeini Int Univ Fac Basic Sci Dept Stat Qazvin Iran Islamic Azad Univ Dept Stat Marvdasht Branch Marvdasht *** Fars Iran

In this study, researchers examine a nonlinear autoregressive (NLAR) time-series model with regression function and dependent innovations in which the errors of the model follow the two-piece scale mixtures of normal (TP-SMN) distributions. Robustness and atypical forms of the proposed class of two-piece distributions along with the flexibility of the nonlinear autoregressive model develop desirable properties which can be applied to several types of datasets. The nonlinear regression function part of the autoregressive time-series model is estimated via the semiparametric and nonparametric curve estimation based on the conditional least square method and nonparametric kernel approach. The maximum likelihood (ML) estimates of the model parameters, using a suitable hierarchical representation of the TP-SMN family on the model are obtained via an expectation maximization (EM)-type algorithm. Performances and usefulness of the proposed model and estimates are shown via simulation studies and a real dataset.

关键词： ecme algorithm autoregressive model maximum likelihood estimates scale mixtures of the normal family two-piece distributions

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Flexible Factor Model for Handling Missing Data in Supervised Learning

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Communications in Mathematics and Statistics 2023年第2期11卷 477-501页

作者： Andriette Bekker Farzane Hashemi Mohammad Arashi Department of Statistics Faculty of Natural and Agricultural SciencesUniversity of PretoriaPretoriaSouth Africa Department of Statistics Faculty of Mathematical SciencesUniversity of KashanKashanIran Department of Statistics Faculty of Mathematical SciencesFerdowsi University of MashhadMashhadIran

This paper presents an extension of the factor analysis model based on the normal mean-variance mixture of the Birnbaum-Saunders in the presence of nonresponses and missing *** model can be used as a powerful tool to model non-normal features observed from data such as strongly skewed and heavy-tailed *** data may occur due to operator error or incomplete data capturing therefore cannot be ignored in factor analysis *** implement an EM-type algorithm for maximum likelihood estimation and propose single imputation of possible missing values under a missing at random *** potential and applicability of our proposed method are illustrated through analyzing both simulated and real datasets.

关键词： Automobile dataset Asymmetry ecme algorithm Factor analysis model Heavy tails Incomplete data Liver disorders dataset

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Robust mixture regression modeling based on two-piece scale mixtures of normal distributions

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2023年第1期17卷 181-210页

作者： Zarei, Atefeh Khodadadi, Zahra Maleki, Mohsen Zare, Karim Islamic Azad Univ Marvdasht Branch Dept Stat Marvdasht Iran Univ Isfahan Fac Math & Stat Dept Stat Esfahan *** Iran

The inference of mixture regression models (MRM) is traditionally based on the normal (symmetry) assumption of component errors and thus is sensitive to outliers or symmetric/asymmetric lightly/heavy-tailed errors. To deal with these problems, some new mixture regression models have been proposed recently. In this paper, a general class of robust mixture regression models is presented based on the two-piece scale mixtures of normal (TP-SMN) distributions. The proposed model is so flexible that can simultaneously accommodate asymmetry and heavy tails. The stochastic representation of the proposed model enables us to easily implement an EM-type algorithm to estimate the unknown parameters of the model based on a penalized likelihood. In addition, the performance of the considered estimators is illustrated using a simulation study and a real data example.

关键词： ecme algorithm Mixture regression models Penalized likelihood Two-piece scale mixtures of normal distributions

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Robust clustering based on finite mixture of multivariate fragmental distributions

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STATISTICAL MODELLING 2023年第3期23卷 247-272页

作者： Maleki, Mohsen McLachlan, Geoffrey J. Lee, Sharon X. Univ Isfahan Fac Math & Stat Dept Stat Esfahan *** Iran Univ Queensland Dept Math St Lucia Qld Australia Univ Adelaide Sch Math Sci Adelaide SA Australia

A flexible class of multivariate distributions called scale mixtures of fragmental normal (SMFN) distributions, is introduced. Its extension to the case of a finite mixture of SMFN (FM-SMFN) distributions is also proposed. The SMFN family of distributions is convenient and effective for modelling data with skewness, discrepant observations and population heterogeneity. It also possesses some other desirable properties, including an analytically tractable density and ease of computation for simulation and estimation of parameters. A stochastic representation of the SMFN distribution is given and then a hierarchical representation is described, the latter aids in parameter estimation, derivation of statistical properties and simulations. Maximum likelihood estimation of the FM-SMFN distribution via the expectation-maximization (EM) algorithm is outlined before the clustering performance of the proposed mixture model is illustrated using simulated and real datasets. In particular, the ability of FM-SMFN distributions to model data generated from various well-known families is demonstrated.

关键词： ecme algorithm Kurtosis maximum likelihood estimates multi-variate scale mixtures of normal family multivariate fragmental distributions

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Bounded Flexible Scale Mixture of Normal Distributions with Application to Image Segmentation

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JOURNAL OF THE INDIAN SOCIETY FOR PROBABILITY AND STATISTICS 2024年第2期25卷 825-848页

作者： Mahdavi, Abbas Ong, Seng Huat Jamalizadeh, Ahad Vali E Asr Univ Rafsanjan Dept Stat Rafsanjan Iran UCSI Univ Inst Actuarial Sci & Data Analyt Kuala Lumpur Malaysia Univ Malaya Inst Math Sci Kuala Lumpur Malaysia Shahid Bahonar Univ Kerman Fac Math & Comp Dept Stat Kerman Iran

A bounded flexible scale mixture of normal (BFSMN) distributions is proposed as a novel device for modeling asymmetric and bounded data. Some characterizations and probabilistic properties of the BFSMN distributions and an extension to finite mixtures thereof are discussed. Based on a sort of selection mechanism, we design a feasible expectation-conditional maximization either algorithm to compute the maximum likelihood estimates of model parameters. To validate the effectiveness of the proposed methodology, we conduct experiments on both simulated data and real natural images and magnetic resonance images. The obtained results demonstrate the efficacy and usefulness of the proposed methodology.

关键词： Bounded distribution ecme algorithm Mixture model Scale mixtures Medical and healthcare

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Partially linear models based on heavy-tailed and asymmetrical distributions

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STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT 2022年第5期36卷 1243-1253页

作者： Bazrafkan, Masoumeh Zare, Karim Maleki, Mohsen Khodadi, Zaha Islamic Azad Univ Dept Stat Marvdasht Branch Marvdasht Iran Univ Isfahan Fac Math & Stat Dept Stat Esfahan *** Iran

In this paper, we provide an extension for partially linear models (PLMs) to allow the errors to follow a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family. The TP-SMN is a rich class of distributions that covers symmetric/asymmetric as well as lightly/heavily tailed distributions which can be used to model datasets with outlying and also atypical data. Using a suitable hierarchical representation of the TP-SMN family developed specifically for PLM, we derived an EM-type algorithm for iteratively computing maximum penalized likelihood estimates of the proposed model parameters. We examined the performance of the proposed PLM model and methodology using simulation studies and a real dataset to show the robust aspects of this model.

关键词： ecme algorithm Partially linear model Two-piece scale mixtures of normal distributions

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Biphasic growth modelling in elasmobranchs based on asymmetric and heavy-tailed errors

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ENVIRONMENTAL BIOLOGY OF FISHES 2021年第5期104卷 615-628页

作者： Contreras-Reyes, Javier E. Wiff, Rodrigo Soto, Javier Donovan, Carl R. Araya, Miguel Univ Valparaiso Fac Ciencias Inst Estadist Valparaiso Chile Pontificia Univ Catolica Chile Ctr Appl Ecol & Sustainabil CAPES UC Ave Libertador Bernardo OHiggins 340 Santiago Chile Pontificia Univ Catolica Chile Inst Milenio Socio Ecol Costera SECOS Ave Libertador Bernardo OHiggins 340 Santiago Chile Univ Bio Bio Fac Ciencias Dept Estadist Concepcion Chile Univ St Andrews Sch Math & Stat Ctr Res Ecol & Environm Modelling St Andrews Fife Scotland Univ Arturo Prat Fac Recursos Nat Renovables Area Biol Marina & Acuicultura Iquique Chile

Growth in fishes is usually modelled by a function encapsulating a common growth mechanism across ages. However, several theoretical works suggest growth may comprise two distinct mechanistic phases arising from changes in reproductive investment, diet, or habitat. These models are termed two-state or biphasic, where acceleration in growth typically changes around some transition age. Such biphasic models have already been successfully applied in elasmobranch species, where such transitions are detectable from length-at-age data alone, but where estimation has assumed normally distributed errors, which is inappropriate for such slow-growing and long-lived fishes. Using recent advances in growth parameter estimation, we implement a biphasic growth model with asymmetric and heavy-tailed errors. We use data from six datasets, encompassing four species of elasmobranchs, to compare the performance of the von Bertalanffy and biphasic models under normal, skew-normal, and Student-t error distributions. Conditional expectation maximization estimation proves both effective and efficient in this context. Most datasets analysed here supported asymmetric and heavy-tailed errors and biphasic growth, producing parameter estimates different from previous studies.

关键词： Elasmobranchs Two-stage growth von Bertalanffy model Sharks Skates Skew-t distribution ecme algorithm

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Heteroscedastic nonlinear regression models using asymmetric and heavy tailed two-piece distributions

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ASTA-ADVANCES IN STATISTICAL ANALYSIS 2021年第3期105卷 451-467页

作者： Hoseinzadeh, Akram Maleki, Mohsen Khodadadi, Zahra Islamic Azad Univ Dept Stat Marvdasht Branch Marvdasht Iran Univ Isfahan Fac Math & Stat Dept Stat Esfahan *** Iran

In this paper, heteroscedastic nonlinear regression (HNLR) models under the flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family were examined. This novel class of nonlinear regression (NLR) models is a generalization of the well-known heteroscedastic symmetrical nonlinear regression models. The TP-SMN is a rich class of distributions that covers symmetric and asymmetric as well as heavy-tailed distributions. Using the suitable hierarchical representation of the family, the researchers first derived an EM-type algorithm for iteratively computing maximum likelihood (ML) estimates of the parameters. Then, in order to examine the performance of the proposed models and methods, some simulation studies were presented to show the robust aspect of this flexible class against outlying and also atypical data. As the last step, a natural real dataset was fitted under the proposed HNLR models.

关键词： ecme algorithm Heteroscedastic nonlinear regression model Two– piece scale mixtures of normal distributions

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