Fast Predictive Uncertainty for Classification with Bayesian Deep Networks

Abstract

In Bayesian Deep Learning, distributions over the output of classification neural networks are often approximated by first constructing a Gaussian distribution over the weights, then sampling from it to receive a distribution over the softmax outputs. This is costly. We reconsider old work (Laplace Bridge) to construct a Dirichlet approximation of this softmax output distribution, which yields an analytic map between Gaussian distributions in logit space and Dirichlet distributions (the conjugate prior to the Categorical distribution) in the output space. Importantly, the vanilla Laplace Bridge comes with certain limitations. We analyze those and suggest a simple solution that compares favorably to other commonly used estimates of the softmax-Gaussian integral. We demonstrate that the resulting Dirichlet distribution has multiple advantages, in particular, more efficient computation of the uncertainty estimate and scaling to large datasets and networks like ImageNet and DenseNet. We further demonstrate the usefulness of this Dirichlet approximation by using it to construct a lightweight uncertainty-aware output ranking for ImageNet.

Updated version. Accepted for publication at UAI2022

References in corpus (5)

• Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift
• Evidential Deep Learning to Quantify Classification Uncertainty
• Evaluating Uncertainty Quantification in End-to-End Autonomous Driving Control
• One-vs-Each Approximation to Softmax for Scalable Estimation of Probabilities
• On Last-Layer Algorithms for Classification: Decoupling Representation from Uncertainty Estimation

Cited by in corpus (5)

• A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges
• Laplace Redux -- Effortless Bayesian Deep Learning
• Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimation
• SafeML: Safety Monitoring of Machine Learning Classifiers through Statistical Difference Measure
• Deep Classifiers with Label Noise Modeling and Distance Awareness