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This paper introduces a novel, computationally-efficient algorithm forpredictive inference (PI) that requires no distributional assumptions on thedata and can be computed faster than existing bootstrap-type methods for neuralnetworks. Specifically, if there are $n$ training samples, bootstrap methodsrequire training a model on each of the $n$ subsamples of size $n-1$; for largemodels like neural networks, this process can be computationally prohibitive.In contrast, our proposed method trains one neural network on the full datasetwith $(\epsilon, \delta)$-differential privacy (DP) and then approximates eachleave-one-out model efficiently using a linear approximation around thedifferentially-private neural network estimate. With exchangeable data, weprove that our approach has a rigorous coverage guarantee that depends on thepreset privacy parameters and the stability of the neural network, regardlessof the data distribution. Simulations and experiments on real data demonstratethat our method satisfies the coverage guarantees with substantially reducedcomputation compared to bootstrap methods.

Fast, Distribution-free Predictive Inference for Neural Networks with Coverage Guarantees