We consider the problem of high-dimensional non-linear variable selection for
supervised learning. Our approach is based on performing linear selection among
exponentially many appropriately defined positive definite kernels that
characterize non-linear interactions between the original variables. To select
efficiently from these many kernels, we use the natural hierarchical structure
of the problem to extend the multiple kernel learning framework to kernels that
can be embedded in a directed acyclic graph; we show that it is then possible
to perform kernel selection through a graph-adapted sparsity-inducing norm, in
polynomial time in the number of selected kernels. Moreover, we study the
consistency of variable selection in high-dimensional settings, showing that
under certain assumptions, our regularization framework allows a number of
irrelevant variables which is exponential in the number of observations. Our
simulations on synthetic datasets and datasets from the UCI repository show
state-of-the-art predictive performance for non-linear regression problems.

研究的主要目标是解决高维非线性变量选择的问题，提出了一种基于多核学习框架和有向无环图的核函数选择方法，能够以多项式时间选择核函数，具有高预测性能。