Abstract
We consider the problems of variable selection and parameter estimation in nonparametric additive models for high-dimensional data. In recent years, several methods are proposed to model nonlinear relationships in high-dimensional data by using spline basis functions and group penalties. We focus on the special case of nonlinearity as nonlinear {\it monotone} effects on the response, as is often a natural assumption in medicine and biology. We construct a method to estimate and select variables using monotone spline basis functions (I-splines). The additive components in the model are represented by the I-spline basis function expansions and the component selection becomes that of selecting the groups of coefficients in the I-spline basis function expansion. We use a recent procedure called cooperative lasso to select sign-coherent groups, that is selecting the groups with either non-negative or non-positive coefficients. This leads to the selection of the important covariates that have nonlinear monotone increasing or monotone decreasing effect on the response in high-dimensional regression problems. Simulated data and real data examples from genomics illustrate the effectiveness of the proposed method.
This is joint work with Linn Cecilie Bergersen and Ingrid K. Glad