Fast Predictive Uncertainty for Classification with Bayesian Deep Networks
This work addresses the problem of slow uncertainty estimation in Bayesian deep networks for practitioners, though it is incremental as it builds on existing Laplace Bridge methods.
The paper tackles the computational cost of approximating output distributions in Bayesian deep learning for classification by proposing a Dirichlet approximation via the Laplace Bridge, which enables efficient uncertainty estimation and scales to large datasets like ImageNet and DenseNet.
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.