A local approach to parameter space reduction for regression and classification tasks (Q6536826)

The so-called curse of dimensionality generates prohibitive difficulties for numerical algorithms when the parameter spaces are very large, i.e., have a very large number of unknowns. Therefore dimension-reduction is of the essence in all methods that solve typical high-dimensional problems. (Optimization algorithms immediately come to mind, but also approximation problems of various sorts.) Active set methods are know to be extremely useful in methods for solving nonlinear optimisation problems with constraints, and an important, similar method (the method of ``local active subspaces'') is proposed and studied in this paper.