# Approximating Full Conformal Prediction at Scale via Influence Functions

arXiv: https://arxiv.org/abs/2202.01315 · HTML: https://mlsanity.com/paper/2202.01315/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 47 references that are in the map.
- First posted on arXiv 2 Feb 2022.

## Builds on (most cited first, 19 of 19)

- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Pruning neural networks without any data by iteratively conserving synaptic flow](https://mlsanity.com/paper/2006.05467/) (2020)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [On the Accuracy of Influence Functions for Measuring Group Effects](https://mlsanity.com/paper/1905.13289/) (2019)
- [On Second-Order Group Influence Functions for Black-Box Predictions](https://mlsanity.com/paper/1911.00418/) (2019)
- [Regression Conformal Prediction with Nearest Neighbours](https://mlsanity.com/paper/1401.3880/) (2014)
- [A Swiss Army Infinitesimal Jackknife](https://mlsanity.com/paper/1806.00550/) (2018)
- [Criteria of efficiency for conformal prediction](https://mlsanity.com/paper/1603.04416/) (2016)
- [Discriminative Jackknife: Quantifying Uncertainty in Deep Learning via Higher-Order Influence Functions](https://mlsanity.com/paper/2007.13481/) (2020)
- [Locally Valid and Discriminative Prediction Intervals for Deep Learning Models](https://mlsanity.com/paper/2106.00225/) (2021)
- [Fast Exact Conformalization of Lasso using Piecewise Linear Homotopy](https://mlsanity.com/paper/1708.00427/) (2017)
- [Computing Full Conformal Prediction Set with Approximate Homotopy](https://mlsanity.com/paper/1909.09365/) (2019)
- [Stable Conformal Prediction Sets](https://mlsanity.com/paper/2112.10224/) (2021)
- [Exact Optimization of Conformal Predictors via Incremental and Decremental Learning](https://mlsanity.com/paper/2102.03236/) (2021)

## Built on by (most cited first, 11 of 11)

- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Towards Modeling Uncertainties of Self-explaining Neural Networks via Conformal Prediction](https://mlsanity.com/paper/2401.01549/) (2024)
- [A novel Deep Learning approach for one-step Conformal Prediction approximation](https://mlsanity.com/paper/2207.12377/) (2022)
- [Quantifying Uncertainty in Natural Language Explanations of Large Language Models for Question Answering](https://mlsanity.com/paper/2509.15403/) (2025)
- [Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distributions to Multivariate Settings](https://mlsanity.com/paper/2511.15146/) (2025)
- [Interpretable Multivariate Conformal Prediction with Fast Transductive Standardization](https://mlsanity.com/paper/2512.15383/) (2025)
- [A Confidence Machine for Sparse High-Order Interaction Model](https://mlsanity.com/paper/2205.14317/) (2022)
- [Approximating Full Conformal Prediction for Neural Network Regression with Gauss-Newton Influence](https://mlsanity.com/paper/2507.20272/) (2025)
- [Orthogonal Bootstrap: Efficient Simulation of Input Uncertainty](https://mlsanity.com/paper/2404.19145/) (2024)
- [Accelerating Conformal Prediction via Approximate Leave-One-Out](https://mlsanity.com/paper/2606.31915/) (2026)
- [Scaling Full Conformal Image Classifiers](https://mlsanity.com/paper/2609.37298/) (2026)

## Abstract (arXiv)

Conformal prediction (CP) is a wrapper around traditional machine learning models, giving coverage guarantees under the sole assumption of exchangeability; in classification problems, for a chosen significance level varepsilon, CP guarantees that the error rate is at most varepsilon, irrespective of whether the underlying model is misspecified. However, the prohibitive computational costs of "full" CP led researchers to design scalable alternatives, which alas do not attain the same guarantees or statistical power of full CP. In this paper, we use influence functions to efficiently approximate full CP. We prove that our method is a consistent approximation of full CP, and empirically show that the approximation error becomes smaller as the training set increases; e.g., for 103 training points the two methods output p-values that are <10-3 apart: a negligible error for any practical application. Our methods enable scaling full CP to large real-world datasets. We compare our full CP approximation (ACP) to mainstream CP alternatives, and observe that our method is computationally competitive whilst enjoying the statistical predictive power of full CP.