Electronic medical records (EMRs) are capturing increasing amounts of data per patient. For clinicians to efficiently and accurately understand a patient's clinical state, better ways are needed to determine when and how to display EMR data. We built a prototype system that records how physicians view EMR data, which we used to train models that predict which EMR data will be relevant in a given patient. We call this approach a Learning EMR (LEMR). A physician used the prototype to review 59 intensive care unit (ICU) patient cases. We used the data-access patterns from these cases to train logistic regression models that, when evaluated, had AUROC values as high as 0.92 and that averaged 0.73, supporting that the approach is promising. A preliminary usability study identified advantages of the system and a few concerns about implementation. Overall, 3 of 4 ICU physicians were enthusiastic about features of the prototype.