Last Layer Empirical Bayes
This work addresses uncertainty quantification in AI, which is crucial for reliable predictions in applications like safety-critical systems, but it is incremental as it builds on existing methods like BNNs and ensembles.
The paper tackled the challenge of quantifying uncertainty in neural network predictions by proposing Last Layer Empirical Bayes (LLEB), which uses a learnable prior as a normalizing flow on the last layer to interpolate between Bayesian neural networks and ensembles. The result shows that LLEB performs on par with existing approaches, indicating empirical Bayes as a promising direction for uncertainty quantification.
The task of quantifying the inherent uncertainty associated with neural network predictions is a key challenge in artificial intelligence. Bayesian neural networks (BNNs) and deep ensembles are among the most prominent approaches to tackle this task. Both approaches produce predictions by computing an expectation of neural network outputs over some distribution on the corresponding weights; this distribution is given by the posterior in the case of BNNs, and by a mixture of point masses for ensembles. Inspired by recent work showing that the distribution used by ensembles can be understood as a posterior corresponding to a learned data-dependent prior, we propose last layer empirical Bayes (LLEB). LLEB instantiates a learnable prior as a normalizing flow, which is then trained to maximize the evidence lower bound; to retain tractability we use the flow only on the last layer. We show why LLEB is well motivated, and how it interpolates between standard BNNs and ensembles in terms of the strength of the prior that they use. LLEB performs on par with existing approaches, highlighting that empirical Bayes is a promising direction for future research in uncertainty quantification.