# Regression Conformal Prediction with Nearest Neighbours

arXiv: https://arxiv.org/abs/1401.3880 · HTML: https://mlsanity.com/paper/1401.3880/

## Key facts

- Cited by 59 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2014.

## Built on by (most cited first, 30 of 59)

- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Length Optimization in Conformal Prediction](https://mlsanity.com/paper/2406.18814/) (2024)
- [Predictive Inference with Feature Conformal Prediction](https://mlsanity.com/paper/2210.00173/) (2022)
- [Valid prediction intervals for regression problems](https://mlsanity.com/paper/2107.00363/) (2021)
- [A review of predictive uncertainty estimation with machine learning](https://mlsanity.com/paper/2209.08307/) (2022)
- [Probabilistic Conformal Prediction with Approximate Conditional Validity](https://mlsanity.com/paper/2407.01794/) (2024)
- [Improving Adaptive Conformal Prediction Using Self-Supervised Learning](https://mlsanity.com/paper/2302.12238/) (2023)
- [How Generalizable Is My Behavior Cloning Policy? A Statistical Approach to Trustworthy Performance Evaluation](https://mlsanity.com/paper/2405.05439/) (2024)
- [Guaranteed Coverage Prediction Intervals with Gaussian Process Regression](https://mlsanity.com/paper/2310.15641/) (2023)
- [Regression Trees for Fast and Adaptive Prediction Intervals](https://mlsanity.com/paper/2402.07357/) (2024)
- [Approximating Full Conformal Prediction at Scale via Influence Functions](https://mlsanity.com/paper/2202.01315/) (2022)
- [Conformal Methods for Quantifying Uncertainty in Spatiotemporal Data: A Survey](https://mlsanity.com/paper/2209.03580/) (2022)
- [Reliable Prediction Intervals with Regression Neural Networks](https://mlsanity.com/paper/2312.09606/) (2023)
- [Normalizing Flows for Conformal Regression](https://mlsanity.com/paper/2406.03346/) (2024)
- [Conformal Load Prediction with Transductive Graph Autoencoders](https://mlsanity.com/paper/2406.08281/) (2024)
- [Weighted Aggregation of Conformity Scores for Classification](https://mlsanity.com/paper/2407.10230/) (2024)
- [Exact Optimization of Conformal Predictors via Incremental and Decremental Learning](https://mlsanity.com/paper/2102.03236/) (2021)
- [PAC-Wrap: Semi-Supervised PAC Anomaly Detection](https://mlsanity.com/paper/2205.10798/) (2022)
- [Efficient Conformal Prediction under Data Heterogeneity](https://mlsanity.com/paper/2312.15799/) (2023)
- [TorchCP: A Python Library for Conformal Prediction](https://mlsanity.com/paper/2402.12683/) (2024)
- [Conformalized Unconditional Quantile Regression](https://mlsanity.com/paper/2304.01426/) (2023)
- [On training locally adaptive CP](https://mlsanity.com/paper/2306.04648/) (2023)
- [Multi-model Ensemble Conformal Prediction in Dynamic Environments](https://mlsanity.com/paper/2411.03678/) (2024)
- [Conformal Approach To Gaussian Process Surrogate Evaluation With Coverage Guarantees](https://mlsanity.com/paper/2401.07733/) (2024)
- [Reliable Prediction Intervals with Directly Optimized Inductive Conformal Regression for Deep Learning](https://mlsanity.com/paper/2302.00872/) (2023)
- [Conformalizing Machine Translation Evaluation](https://mlsanity.com/paper/2306.06221/) (2023)
- [Well-calibrated Confidence Measures for Multi-label Text Classification with a Large Number of Labels](https://mlsanity.com/paper/2312.09304/) (2023)
- [Extreme Conformal Prediction: Reliable Intervals for High-Impact Events](https://mlsanity.com/paper/2505.08578/) (2025)
- [Approximating Score-based Explanation Techniques Using Conformal Regression](https://mlsanity.com/paper/2308.11975/) (2023)
- [Efficient Robust Conformal Prediction via Lipschitz-Bounded Networks](https://mlsanity.com/paper/2506.05434/) (2025)

## Abstract (arXiv)

In this paper we apply Conformal Prediction (CP) to the k-Nearest Neighbours Regression (k-NNR) algorithm and propose ways of extending the typical nonconformity measure used for regression so far. Unlike traditional regression methods which produce point predictions, Conformal Predictors output predictive regions that satisfy a given confidence level. The regions produced by any Conformal Predictor are automatically valid, however their tightness and therefore usefulness depends on the nonconformity measure used by each CP. In effect a nonconformity measure evaluates how strange a given example is compared to a set of other examples based on some traditional machine learning algorithm. We define six novel nonconformity measures based on the k-Nearest Neighbours Regression algorithm and develop the corresponding CPs following both the original (transductive) and the inductive CP approaches. A comparison of the predictive regions produced by our measures with those of the typical regression measure suggests that a major improvement in terms of predictive region tightness is achieved by the new measures.