Quantifying Aleatoric and Epistemic Uncertainty Using Density Estimation in Latent Space

The distribution of a neural network's latent representations has been successfully used to detect Out-of-Distribution (OOD) data. Since OOD detection denotes a popular benchmark for epistemic uncertainty estimates, this raises the question of a deeper correlation. This work investigates whether the distribution of latent representations indeed contains information about the uncertainty associated with the predictions of a neural network. Prior work identifies epistemic uncertainty with the surprise, thus the negative log-likelihood, of observing a particular latent representation, which we verify empirically. Moreover, we demonstrate that the output-conditional distribution of hidden representations allows quantifying aleatoric uncertainty via the entropy of the predictive distribution. We analyze epistemic and aleatoric uncertainty inferred from the representations of different layers and conclude with the exciting finding that the hidden repesentations of a deterministic neural network indeed contain information about its uncertainty. We verify our findings on both classification and regression models.