# Fast Predictive Uncertainty for Classification with Bayesian Deep Networks Source: [Fast Predictive Uncertainty for Classification with Bayesian Deep Networks]() Collection index: [llms.txt]() Data updated: 2025-10-26T00:14:46.163Z Authors: Marius Hobbhahn, Agustinus Kristiadi, Philipp Hennig Published: 2020-03-02T22:29:03.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()