Fast, Distribution-free Predictive Inference for Neural Networks with
  Coverage Guarantees
Yue Gao Garvesh Raskutti Rebecca Willet
This paper introduces a novel, computationally-efficient algorithm for
predictive inference (PI) that requires no distributional assumptions on the
data and can be computed faster than existing bootstrap-type methods for neural
networks. Specifically, if there are $n$ training samples, bootstrap methods
require training a model on each of the $n$ subsamples of size $n-1$; for large
models like neural networks, this process can be computationally prohibitive.
In contrast, our proposed method trains one neural network on the full dataset
with $(\epsilon, \delta)$-differential privacy (DP) and then approximates each
leave-one-out model efficiently using a linear approximation around the
differentially-private neural network estimate. With exchangeable data, we
prove that our approach has a rigorous coverage guarantee that depends on the
preset privacy parameters and the stability of the neural network, regardless
of the data distribution. Simulations and experiments on real data demonstrate
that our method satisfies the coverage guarantees with substantially reduced
computation compared to bootstrap methods.