On the Out-of-Distribution Coverage of Combining Split Conformal Prediction and Bayesian Deep Learning

Abstract

Bayesian deep learning and conformal prediction are two methods that have been used to convey uncertainty and increase safety in machine learning systems. We focus on combining Bayesian deep learning with split conformal prediction and how the addition of conformal prediction affects out-of-distribution coverage that we would otherwise see; particularly in the case of multiclass image classification. We suggest that if the model is generally underconfident on the calibration set, then the resultant conformal sets may exhibit worse out-of-distribution coverage compared to simple predictive credible sets (i.e. not using conformal prediction). Conversely, if the model is overconfident on the calibration set, the use of conformal prediction may improve out-of-distribution coverage. In particular, we study the extent to which the addition of conformal prediction increases or decreases out-of-distribution coverage for a variety of inference techniques. In particular, (i) stochastic gradient descent, (ii) deep ensembles, (iii) mean-field variational inference, (iv) stochastic gradient Hamiltonian Monte Carlo, and (v) Laplace approximation. Our results suggest that the application of conformal prediction to different predictive deep learning methods can have significantly different consequences.