Generalized Sparse Additive Model with Unknown Link Function

--Generalized additive models (GAM) have been successfully applied to high dimensional data analysis. T o alleviate this problem, we propose a new sparse additive model, named generalized sparse additive model with unknown link function (GSAMUL), in which the component functions are estimated by B-spline basis and the unknown link function is estimated by a multi-layer perceptron (MLP) network. The proposed GSAMUL can realize both variable selection and hidden interaction. We integrate this estimation into a bilevel optimization problem, where the data is split into training set and validation set. In theory, we provide the guarantees about the convergence of the approximate procedure. In applications, experimental evaluations on both synthetic and real world data sets consistently validate the e ff ectiveness of the proposed approach. I ntroduction Additive models and generalized additive models (GAMs) have been widely used in data analysis when exploring the nonlinear e ff ects of the variables on the response [1]-[6]. Especially for high-dimensional data, they are useful to address "the curse of dimensionality" [7], [8].