Faithful Variable Screening for High-Dimensional Convex Regression

Understand

We study the problem of variable selection in convex nonparametric regression.

• Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the relevant variables.
• Our approach is a two-stage quadratic programming method that estimates a sum of one-dimensional convex functions, followed by one-dimensional concave regression fits on the residuals.
• In contrast to previous methods for sparse additive models, the optimization is finite dimensional and requires no tuning parameters for smoothness.