A1234
Title: Algorithms for exact variable selection in regression
Authors: Cristian Gatu - Alexandru Ioan Cuza University of Iasi (Romania) [presenting]
M Hofmann - University of Oviedo (Spain)
Marios Demosthenous - Cyprus University of Technology (Cyprus)
Erricos Kontoghiorghes - Cyprus University of Technology and Birkbeck University of London (Cyprus)
Abstract: Computational strategies for computing the best subset models in regression are proposed. The algorithms are based on regression tree structures that generate all possible subset models. Efficient branch-and-bound algorithms that find the best submodels without generating the entire tree are described. Approximate algorithms that improve the computational performance are investigated. An R package called lmSubsets for regression subset selection is described, aiming to provide a versatile tool for subset regression. The case of high-dimensional data where the number of variables exceeds the number of observations is considered. Within this context, a novel combinatorial solution is proposed that generates a high-dimensional regression tree to select the optimal model of size up to k variables, where k is smaller than the available observations in the data. The approach avoids evaluating the same model more than once and utilizes previous computations for evaluating subsequent combinations of variables, thus reducing the computational cost. Experimental results are presented and analyzed.
