Partial Functional Kriging Regression Models Based on LASSO And Group LASSO

Abstract

For the regression problem containing continuous type response variables and mixed type explanatory variables (vector-valued and functional), this study proposes a partial function linear model incorporating random effects. The model assumes that the two types of explanatory variables are linearly related to the response variable, and their random effects obey a Gaussian process a priori. Methodological level: Functional Principal Component Analysis is used for basis function expansion of functional variables, while Lasso is combined for feature selection of vector-type variables, and Group Lasso is applied to realize group structure screening of functional variables. Parameter estimation is realized by the great likelihood method fusing L1 and Group L1 penalty terms. Numerical simulations show that the method can accurately identify the key features of the two types of variables, and demonstrates higher prediction accuracy than the traditional method in real data applications.