Heteroscedastic Laplace mixture of experts regression models and applications

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.

A skew–normal mixture of joint location, scale and skewness models

Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied problems. In this paper, we propose and study a novel class of models： a skew-normal mixture of joint location, scale and skewness models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population. The issues of maximum likelihood estimation are addressed. In particular, an Expectation-Maximization （EM） algorithm for estimating the model parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments. Results from the analysis of a real data set from the Body Mass Index （BMI） data are presented.

Dynamic soft sensor development based on Gaussian mixture regression for fermentation processes

The dynamic soft sensor based on a single Gaussian process regression(GPR) model has been developed in fermentation processes.However,limitations of single regression models,for multiphase/multimode fermentation processes,may result in large prediction errors and complexity of the soft sensor.Therefore,a dynamic soft sensor based on Gaussian mixture regression(GMR) was proposed to overcome the problems.Two structure parameters,the number of Gaussian components and the order of the model,are crucial to the soft sensor model.To achieve a simple and effective soft sensor,an iterative strategy was proposed to optimize the two structure parameters synchronously.For the aim of comparisons,the proposed dynamic GMR soft sensor and the existing dynamic GPR soft sensor were both investigated to estimate biomass concentration in a Penicillin simulation process and an industrial Erythromycin fermentation process.Results show that the proposed dynamic GMR soft sensor has higher prediction accuracy and is more suitable for dynamic multiphase/multimode fermentation processes.

Variable Selection for Robust Mixture Regression Model with Skew Scale Mixtures of Normal Distributions

In this paper, we propose a robust mixture regression model based on the skew scale mixtures of normal distributions (RMR-SSMN) which can accommodate asymmetric, heavy-tailed and contaminated data better. For the variable selection problem, the penalized likelihood approach with a new combined penalty function which balances the SCAD and l2 penalty is proposed. The adjusted EM algorithm is presented to get parameter estimates of RMR-SSMN models at a faster convergence rate. As simulations show, our mixture models are more robust than general FMR models and the new combined penalty function outperforms SCAD for variable selection. Finally, the proposed methodology and algorithm are applied to a real data set and achieve reasonable results.

Effect of Submerged Arc Welding Flux Component on Softening Temperature

Based on simplex algorithm of optimal design, the multicomponent mixture regression model was used to investigate physical properties of submerged arc welding flux. The effect of complex interaction of seven components in agglomerated flux on softening temperature was analyzed. The results indicate that the interaction of MgO-TiO2-CaCOa-AI20a increases the softening temperature of flux, but the additions of CaF2 and ZrO2 can decrease the softening temperature.