Gaussian Process Prior And LASSO-Based Semiparametric Regression Model

The curse of dimensionality and autocorrelation effects are two common challenges encountered in regression models. In response to these issues, this paper proposes a semiparametric model based on L1 regularization and Gaussian process priors. On the one hand, the proposed method addresses the linear part using LASSO, which alleviates the curse of dimensionality and facilitates variable selection. On the other hand, it assigns a Gaussian process prior to the random effects, and by using different kernel functions, the model can handle autocorrelation effects in the response data while enhancing model flexibility. Moreover, the proposed method quantifies the uncertainty of the predictions. Simulation experiments demonstrate the high predictive performance of the method. Finally, the method shows promising results in two real-world data tasks: the HP Financial Inclusion Index and Economic Development Levels.