The Discriminative Jackknife: Quantifying Uncertainty in Deep Learning via Higher-Order Influence Functions
Authors: Ahmed M. Alaa, Mihaela van der Schaar
Abstract: Deep learning models achieve high predictive accuracy in a broad spectrum of tasks, but rigorously quantifying their predictive uncertainty remains challenging. Usable estimates of predictive uncertainty should (1) cover the true prediction target with a high probability, and (2) discriminate between high- and low-confidence prediction instances. State-of-the-art methods for uncertainty quantification are based predominantly on Bayesian neural networks. However, Bayesian methods may fall short of (1) and (2) — i.e., Bayesian credible intervals do not guarantee frequentist coverage, and approximate posterior inference may undermine discriminative accuracy. To this end, this paper tackles the following question: can we devise an alternative frequentist approach for uncertainty quantification that satisfies (1) and (2)? 

To address this question, we develop the discriminative jackknife (DJ), a formal inference procedure that constructs predictive confidence intervals for a wide range of deep learning models, is easy to implement, and provides rigorous theoretical guarantees on (1) and (2). The DJ procedure uses higher-order influence functions (HOIFs) of the trained model parameters to construct a jackknife (leave-one-out) estimator of predictive confidence intervals. DJ computes HOIFs using a recursive formula that requires only oracle access to loss gradients and Hessian-vector products, hence it can be applied in a post-hoc fashion without compromising model accuracy or interfering with model training. Experiments demonstrate that DJ performs competitively compared to existing Bayesian and non-Bayesian baselines.