Advances in both technology and medicine have enabled monumental progress toward the realization of precision medicine. In particular, machine learning algorithms -- powered by electronic health records, genomic information, wearable sensors, and medical images -- are positioned to become an integral part of the clinical workflow. While a tremendous amount of biomedical data is being generated and collected on a daily basis, plenty of data are still not routinely captured due to invasiveness, inconvenience, or cost. In this dissertation, we first describe the development and validation of a machine learning model that uses pre-operative data readily available in the electronic health record to predict post-operative in-hospital mortality. We then present multiple novel computational methods for accurately imputing unobserved health data using several different types of observed data, including physiological waveforms, genomics, and videos.