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Motivation: Gene selection has become a common task in most gene expressionstudies. The objective of such research is often to identify the smallestpossible set of genes that can still achieve good predictive performance. Theproblem of assigning tumours to a known class is a particularly importantexample that has received considerable attention in the last ten years. Many ofthe classification methods proposed recently require some form ofdimension-reduction of the problem. These methods provide a single model as anoutput and, in most cases, rely on the likelihood function in order to achievevariable selection.  Results: We propose a prediction-based objective function that can betailored to the requirements of practitioners and can be used to assess andinterpret a given problem. The direct optimization of such a function can bevery difficult because the problem is potentially discontinuous and nonconvex.We therefore propose a general procedure for variable selection that resemblesimportance sampling to explore the feature space. Our proposal comparesfavorably with competing alternatives when applied to two cancer data sets inthat smaller models are obtained for better or at least comparableclassification errors. Furthermore by providing a set of selected modelsinstead of a single one, we construct a network of possible models for a targetprediction accuracy level.

A Paradigmatic Regression Algorithm for Gene Selection Problems