The objectives of this "perspective" paper are to review some recent advances in sparse feature selection for regression and classification, as well as compressed sensing, and to discuss how these might be used to develop tools to advance personalized cancer therapy. As an illustration of the possibilities, a new algorithm for sparse regression is presented, and is applied to predict the time to tumor recurrence in ovarian cancer. A new algorithm for sparse feature selection in classification problems is presented, and its validation in endometrial cancer is briefly discussed. Some open problems are also presented.
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