  In many high dimensional classification or regression problems set in a
biological context, the complete identification of the set of informative
features is often as important as predictive accuracy, since this can provide
mechanistic insight and conceptual understanding. Lasso and related algorithms
have been widely used since their sparse solutions naturally identify a set of
informative features. However, Lasso performs erratically when features are
correlated. This limits the use of such algorithms in biological problems,
where features such as genes often work together in pathways, leading to sets
of highly correlated features. In this paper, we examine the performance of a
Lasso derivative, the exclusive group Lasso, in this setting. We propose fast
algorithms to solve the exclusive group Lasso, and introduce a solution to the
case when the underlying group structure is unknown. The solution combines
stability selection with random group allocation and introduction of artificial
features. Experiments with both synthetic and real-world data highlight the
advantages of this proposed methodology over Lasso in comprehensive selection
of informative features.
