Lookahead and Piloting Strategies for Variable Selection

Abstract

The traditional variable selection problem has attracted renewed atten- tion from statistical researchers due to the recent advances in data collection, es- pecially in fields such as bioinformatics and marketing. In this paper, we formulate regression variable selection as an optimization problem, propose and study several deterministic and stochastic sequential optimization methods with lookahead. Us- ing several synthetic examples, we show that the stochastic sequential method with lookahead robustly and significantly outperforms a few close competitors, includ- ing the popular stepwise methods. When applied to analyze a yeast amino acid starvation microarray experiment, this method can find many transcription factors that are known to be important for yeast to cope with stress and starvation.