Acute respiratory distress syndrome (ARDS) is a fulminant inflammatory lung injury that develops in patients with critical illnesses, affecting 200,000 patients in the United States annually. However, a recent study suggests that most patients with ARDS are diagnosed late or missed completely and fail to receive life-saving treatments. This is primarily due to the dependency of current diagnosis criteria on chest x-ray, which is not necessarily available at the time of diagnosis. In machine learning, such an information is known as Privileged Information - information that is available at training but not at testing. However, in diagnosing ARDS, privileged information (chest x-rays) are sometimes only available for a portion of the training data. To address this issue, the Learning Using Partially Available Privileged Information (LUPAPI) paradigm is proposed. As there are multiple ways to incorporate partially available privileged information, three models built on classical SVM are described. Another complexity of diagnosing ARDS is the uncertainty in clinical interpretation of chest x-rays. To address this, the LUPAPI framework is then extended to incorporate label uncertainty, resulting in a novel and comprehensive machine learning paradigm - Learning Using Label Uncertainty and Partially Available Privileged Information (LULUPAPI). The proposed frameworks use Electronic Health Record (EHR) data as regular information, chest x-rays as partially available privileged information, and clinicians' confidence levels in ARDS diagnosis as a measure of label uncertainty. Experiments on an ARDS dataset demonstrate that both the LUPAPI and LULUPAPI models outperform SVM, with LULUPAPI performing better than LUPAPI.