Variational Bayesian Lasso for spline regression

Abstract

This work presents a new scalable automatic Bayesian Lasso methodology with variational inference for non-parametric splines regression that can capture the non-linear relationship between a response variable and predictor variables. Note that under non-parametric point of view the regression curve is assumed to lie in a infinite dimension space. Regression splines use a finite approximation of this infinite space, representing the regression function by a linear combination of basis functions. The crucial point of the approach is determining the appropriate number of bases or equivalently number of knots, avoiding over-fitting/under-fitting. A decision-theoretic approach was devised for knot selection. Comprehensive simulation studies were conducted in challenging scenarios to compare alternative criteria for knot selection, thereby ensuring the efficacy of the proposed algorithms. Additionally, the performance of the proposed method was assessed using real-world datasets. The novel procedure demonstrated good performance in capturing the underlying data structure by selecting the appropriate number of knots/basis.