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Applied Mathematics-A Journal of Chinese Universities  2021, Vol. 36 Issue (1): 60-69    
    
Heteroscedastic Laplace mixture of experts regression models and applications
WU Liu-cang1,ZHANG Shu-yu2 LI Shuang-shuang3
1,2Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China.
3College of Mathematics and Informatics, Fujian Normal University, Fuzhou 350117, China.
Heteroscedastic Laplace mixture of experts regression models and applications
WU Liu-cang1,ZHANG Shu-yu2 LI Shuang-shuang3
1,2Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China.
3College of Mathematics and Informatics, Fujian Normal University, Fuzhou 350117, China.
 全文: PDF 
摘要： Mixture of Experts (MoE) regression models are widely studied in statistics and
machine learning for modeling heterogeneity in data for regression, clustering and classification.
Laplace distribution is one of the most important statistical tools to analyze thick and tail
data. Laplace Mixture of Linear Experts (LMoLE) regression models are based on the Laplace
distribution which is more robust. Similar to modelling variance parameter in a homogeneous
population, we propose and study a new novel class of models: heteroscedastic Laplace mixture
of experts regression models to analyze the heteroscedastic data coming from a heterogeneous
population in this paper. The issues of maximum likelihood estimation are addressed. In
particular, Minorization-Maximization (MM) algorithm for estimating the regression parameters
is developed. Properties of the estimators of the regression coefficients are evaluated through
Monte Carlo simulations. Results from the analysis of two real data sets are presented.
关键词：  mixture of experts regression models;  heteroscedastic mixture of experts regression models;  Laplace distribution;  MM algorithm
    
Abstract: Mixture of Experts (MoE) regression models are widely studied in statistics and
machine learning for modeling heterogeneity in data for regression, clustering and classification.
Laplace distribution is one of the most important statistical tools to analyze thick and tail
data. Laplace Mixture of Linear Experts (LMoLE) regression models are based on the Laplace
distribution which is more robust. Similar to modelling variance parameter in a homogeneous
population, we propose and study a new novel class of models: heteroscedastic Laplace mixture
of experts regression models to analyze the heteroscedastic data coming from a heterogeneous
population in this paper. The issues of maximum likelihood estimation are addressed. In
particular, Minorization-Maximization (MM) algorithm for estimating the regression parameters
is developed. Properties of the estimators of the regression coefficients are evaluated through
Monte Carlo simulations. Results from the analysis of two real data sets are presented.
Key words:  mixture of experts regression models    heteroscedastic mixture of experts regression models    Laplace distribution    MM algorithm
出版日期: 2021-03-01
CLC:  62F10  
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引用本文:

WU Liu-cang, ZHANG Shu-yu LI Shuang-shuang. Heteroscedastic Laplace mixture of experts regression models and applications[J]. Applied Mathematics-A Journal of Chinese Universities, 2021, 36(1): 60-69.

WU Liu-cang, ZHANG Shu-yu LI Shuang-shuang. Heteroscedastic Laplace mixture of experts regression models and applications. Applied Mathematics-A Journal of Chinese Universities, 2021, 36(1): 60-69.

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http://www.zjujournals.com/amjcub/CN/    或    http://www.zjujournals.com/amjcub/CN/Y2021/V36/I1/60

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[2] Hector J. Gomez, Neveka M. Olmos, Hector Varela, Heleno Bolfarine. Inference for a truncated positive normal distribution[J]. Applied Mathematics-A Journal of Chinese Universities, 2018, 33(2): 163-.