Abstract: We apply classical and Bayesian lasso regularizations [4, 5] to a family of regression models with the presence of mixture and noise variables [2]. We analyse the performance of these estimates with respect to ordinary least squares estimators by a simulation study and a real data application. Our results demonstrate the superior performance of Bayesian lasso, particularly via coordinate ascent variational inference [1], in terms of variable selection accuracy and response optimization.
Joint work with: Fabián Manríquez, Instituto de Estadística, Universidad de Valparaíso, Valparaíso, Chile and Manuel Pereira-Barahona, Departamento de Estadística, Universidad del Bío-Bío, Concepción, Chile
References
[1] Blei, D.M., Kucukelbir, A. & McAuliffe, J.D. Variational Inference:A Review for Statisticians. J. Am. Stat. Assoc. 112(518), 859-877 (2017).
[2] Goldfarb, H.B., Borror, C.M. and Montgomery, D.C. Mixtureprocess variable experiments with noise variables, J. Qual. Technol. 35, 393-405 (2003).
[3] González-Navarrete, M., Manríquez-Méndez, F. & Pereira-Barahona, M.: Lasso regularization for mixture experiments with noise variables, Preprint arXiv:2406.12237.
[4] Park, T. and Casella, G. The Bayesian lasso. J. Am. Stat. Assoc. 103(482): 681-686 (2008).
[5] Tibshirani, R. Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B Methodol. 58(1), 267-288 (1996).
Semblance: Manuel González-Navarrete has a degree in education and is a state teacher in mathematics from University of La Frontera (UFRO) in Chile. He has a master's degree and a doctorate in statistics from University of Sao Paulo (USP), in Brazil. He held a postdoc position at the Institute of Mathematics and Statistics at USP and Gran Sasso Science Institute in Italy.
He was an assistant professor in the Department of Statistics at the University of Bío-Bío, in Concepción, Chile between 2018 and 2023. He is currently an associate professor at the Department of Mathematics and Statistics at UFRO, in Temuco, Chile.
His lines of research are probability, stochastic processes and statistical mechanics. Moreover, in recent years he has developed work in statistics, studying regression models with classical and Bayesian tools.
He has taught and a supervised thesis at the undergraduate and graduate level, published several articles and has been principal investigator and/or collaborator in national and international projects.