This paper describes a novel feature selection algorithm embedded into logistic regression. It specifically addresses high dimensional data with few observations, which are commonly found in the biomedical domain such as microarray data. The overall objective is to optimize the predictive performance of a classifier while favoring also sparse and stable models.Feature relevance is first estimated according to a simple t-test ranking. This initial feature relevance is treated as a feature sampling probability and a multivariate logistic regression is iteratively reestimated on subsets of randomly and non-uniformly sampled features. At each iteration, the feature sampling probability is adapted according to the predictive performance and the weights of the logistic regression. Globally,the proposed selection method can be seen as an ensemble of logistic regression models voting jointly for the final relevance of features.Practical experiments reported on several microarray datasets show that the proposed method offers a comparable or better stability and significantly better predictive performances than logistic regression regularized with Elastic Net. It also outperforms a selection based on Random Forests, another popular embedded feature selection from an ensemble of classifiers.
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