Spline based sparseness and smoothness for partially nonlinear model via C-fused Lasso

One of the most beneficial and widely used models for data analysis are partially nonlinear models (PNLRM), which consists of parametric and nonparametric components. Since the model includes the coefficients of both the parametric and nonparametric parts, the complexity of the model will be high and its interpretation will be very difficult. In this study, we propose a procedure that not only achieves sparseness, but also smoothness for PNLRM to obtain a simpler model that better explains the relationship between the response and covariates. Thus, the fused Lasso problem is taken into account where nonparametric components are expressed as a spline basis function, and then the Fused Lasso estimation problem is built and expressed in terms of conic quadratic programming. Applications are conducted to evaluate the performance of the proposed method by considering commonly utilized measures. Promising results are obtained, especially in the data with nonlinearly correlated variables.