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.

本文探讨了如何将 Conformal Prediction 应用于 k - 最近邻回归算法，提出了对于回归算法中所使用的非一致性度量进行扩展的方式，并定义了 6 种基于 k-NNR 算法的新型非一致性度量，得出相比典型回归度量相比，在预测区域密集程度方面突破性的改进。