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

arXiv: https://arxiv.org/abs/2306.06582 · HTML: https://mlsanity.com/paper/2306.06582/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 26 references that are in the map.
- First posted on arXiv 11 Jun 2023.

## Builds on (most cited first, 11 of 11)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Convergence Analysis of Two-layer Neural Networks with ReLU Activation](https://mlsanity.com/paper/1705.09886/) (2017)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Recovery Guarantees for One-hidden-layer Neural Networks](https://mlsanity.com/paper/1706.03175/) (2017)
- [Stability and Generalization of Graph Convolutional Neural Networks](https://mlsanity.com/paper/1905.01004/) (2019)
- [Max-Information, Differential Privacy, and Post-Selection Hypothesis Testing](https://mlsanity.com/paper/1604.03924/) (2016)
- [Optimality of the Laplace Mechanism in Differential Privacy](https://mlsanity.com/paper/1504.00065/) (2015)
- [The Bounded Laplace Mechanism in Differential Privacy](https://mlsanity.com/paper/1808.10410/) (2018)
- [Lazy Estimation of Variable Importance for Large Neural Networks](https://mlsanity.com/paper/2207.09097/) (2022)

## Abstract (arXiv)

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 (ε, δ)-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.