In this work, we leverage machine learning techniques to identify potential biomarkers of oxygen desaturation during sleep exclusively from electroencephalogram (EEG) signals in pediatric patients with sleep apnea. Development of a machine learning technique which can successfully identify EEG signals from patients with sleep apnea as well as identify latent EEG signals which come from subjects who experience oxygen desaturations but do not themselves occur during oxygen desaturation events would provide a strong step towards developing a brain-based biomarker for sleep apnea in order to aid with easier diagnosis of this disease. We leverage a large corpus of data, and show that machine learning enables us to classify EEG signals as occurring during oxygen desaturations or not occurring during oxygen desaturations with an average 66.8% balanced accuracy. We furthermore investigate the ability of machine learning models to identify subjects who experience oxygen desaturations from EEG data that does not occur during oxygen desaturations. We conclude that there is a potential biomarker for oxygen desaturation in EEG data.