A mathematical programming formulation is proposed to eliminate irrelevant and redundant features for collaborative computer aided diagnosis which requires to detect multiple clinically-related malignant structures from medical images. A probabilistic interpretation is described to justify our formulations. The proposed formulation is optimized through an effective alternating optimization algorithm that is easy to implement and relatively fast to solve. This collaborative prediction approach has been implemented and validated on the automatic detection of solid lung nodules by jointly detecting ground glass opacities.