Aleatoric Uncertainty Estimation of Overnight Sleep Statistics through Posterior Sampling using Conditional Normalizing Flows

In sleep staging, a polysomnography is visually scored by a human expert, who creates a hypnogram that classifies the measurement into a sequence of sleep stages, from which overnight sleep statistics, such as total sleep time, are derived. Because inter-scorer agreement between humans is limited, deep learning methods trained to automate sleep staging have aleatoric uncertainty about both hypnogram and overnight statistics. We would like to estimate this aleatoric uncertainty, which can be achieved by means of posterior sampling. Current approaches model the hypnogram through a time-based factorization of categorical distributions over sleep stages. This discards time-dependent information, invalidating posterior sampling of the overnight statistics. Instead of factorizing, we propose to jointly model the sequence of sleep stages, by introducing U-Flow, a conditional normalizing flow network. We compare U-Flow to factorized baselines, leveraging 921 recordings, and show that it achieves similar performance in terms of accuracy and Cohen's kappa on the majority voted hypnograms, while outperforming in terms of uncertainty estimation of the overnight sleep statistics.