Abstract: Recent advances in machine learning, computer vision, natural language processing, and robotics, offer a tremendous opportunity to transform medicine, from reactive and hospital centered to proactive and patient-centered. To fulfill this promise, new methods need to be developed which are more interpretable, can handle data at multiple spatial and temporal scales, and are robust to data heterogeneity and limited amounts of annotations. The first part of this talk will overview our recent work on the theory of deep learning, including sufficient conditions to guarantee that local minima are globally optimal, as well as an analysis of the optimization and regularization properties of dropout. The second part of this talk will overview our recent work on the development of methods for interpreting biomedical datasets arising in blood cell analysis, regenerative medicine, digital pathology, brain imaging, surgery and rehabilitation therapy.