Looking at the posterior: accuracy and uncertainty of neural-network predictions

TL;DR

This paper investigates how Bayesian posterior distributions can quantify uncertainty in neural network predictions, revealing complex relationships between uncertainty types, model architecture, and dataset properties, with implications for active learning.

Contribution

It demonstrates the intricate dependence of prediction accuracy on epistemic and aleatoric uncertainties and introduces a novel acquisition function for active learning.

Findings

Prediction accuracy depends on both epistemic and aleatoric uncertainty.

The relationship between uncertainty and accuracy varies with model architecture and dataset.

A new acquisition function outperforms existing uncertainty-based methods.

Abstract

Bayesian inference can quantify uncertainty in the predictions of neural networks using posterior distributions for model parameters and network output. By looking at these posterior distributions, one can separate the origin of uncertainty into aleatoric and epistemic contributions. One goal of uncertainty quantification is to inform on prediction accuracy. Here we show that prediction accuracy depends on both epistemic and aleatoric uncertainty in an intricate fashion that cannot be understood in terms of marginalized uncertainty distributions alone. How the accuracy relates to epistemic and aleatoric uncertainties depends not only on the model architecture, but also on the properties of the dataset. We discuss the significance of these results for active learning and introduce a novel acquisition function that outperforms common uncertainty-based methods. To arrive at our results, we approximated the posteriors using deep ensembles, for fully-connected, convolutional and attention-based neural networks.