Both electronic health records and personal health records are typically organized by data type, with medical problems, medications, procedures, and laboratory results chronologically sorted in separate areas of the chart. As a result, it can be difficult to find all of the relevant information for answering a clinical question about a given medical problem. A promising alternative is to instead organize by problems, with related medications, procedures, and other pertinent information all grouped together. A recent effort by Buchanan (2017) manually defined, through expert consensus, 11 medical problems and the relevant labs and medications for each. We show how to use machine learning on electronic health records to instead automatically construct these problem-based groupings of relevant medications, procedures, and laboratory tests. We formulate the learning task as one of knowledge base completion, and annotate a dataset that expands the set of problems from 11 to 32. We develop a model architecture that exploits both pre-trained concept embeddings and usage data relating the concepts contained in a longitudinal dataset from a large health system. We evaluate our algorithms' ability to suggest relevant medications, procedures, and lab tests, and find that the approach provides feasible suggestions even for problems that are hidden during training. The dataset, along with code to reproduce our results, is available at https://github.com/asappresearch/kbc-pomr.