Statistica Sinica 17(2007), 985-1003

LOOKAHEAD AND PILOTING STRATEGIES FOR

VARIABLE SELECTION

Junni L. Zhang$^1$, Ming T. Lin$^2$, Jun S. Liu$^3$ and Rong Chen$^{1,2}$

$^1$Peking University, $^2$University of Illinois at Chicago, and $^3$Harvard University

Abstract: The traditional variable selection problem has attracted renewed attention from statistical researchers due to the recent advances in data collection, especially 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. Using several synthetic examples, we show that the stochastic sequential method with lookahead robustly and significantly outperforms a few close competitors, including 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.

Key words and phrases: AIC, Akaike information criterion, BIC, Bayesian information criterion, gene regulation, Gibbs sampler, microarray data, sequential Monte Carlo, TFBM, transcription factor binding-site motif.