|Gaston H. Gonnet - Swiss Federal Institute of Technology in Zurich (Switzerland)|
Title: The Best-Basis algorithm for linear regressions, a quantitative improvement over stepwise regression and its applications.
The Best-Basis algorithm selects a small number of regression variables which reduce the approximation error the most. This is similar in spirit to stepwise regression, but substantially more effective. This algorithm has a natural use, to find good approximations which are not overfitted. In our experience, it has an even more interesting application when we use it to select a subset of variables which are the best candidates to be used in models where high dimensionality is harmful or unwanted (e.g. nearest-neighbor techniques). We will explain the main ideas of the algorithm, and two relevant examples of uses in modeling.