Acute Respiratory Distress Syndrome (ARDS) is a fulminant lung injury occurring in Intensive Care Unit patients that have undergone Acute Respiratory Failure. Many afflicted patients are missed because doctors do not order the chest radiographs necessary for diagnosis, leading to a mortality rate of 40%. A Clinical Decision Support System for ARDS that prompts doctors to order radiographs for at-risk patients could reduce this mortality rate. We designed such a Support System that only relies on bedside measurements for classification but uses retrospective information from chest radiographs to train more intelligently. This is a machine learning problem called Learning Using Privileged Information. Radiographs, however, are not taken for all patients in ARDS training sets, so we established and solved three Learning Using Partially Available Privileged Information models. Each of these three models treats privileged information uniquely and was tested against the others for efficacy. Even with chest radiographs, diagnosis of ARDS can be ambiguous and patients can be misdiagnosed. Our model trains such that high-confidence cases are given more influence than uncertain ones. This is known as Learning Using Label Uncertainty. Taken together these problems yield the Learning Using Label Uncertainty and Partially Available Privileged Information (LULUPAPI) model. The LULUPAPI model will not only improve ARDS diagnosis, it applies to any medical problem in which extra, partially-available information is available at training and there is ambiguity in diagnosis.