Regression Conformal Prediction with Nearest Neighbours

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 re...

• Type: Journal
• Year: 2011
• Where: JAIR
• Authors: Harris Papadopoulos, Vladimir Vovk, Alexander Gammerman
• Keywords: JAIR 2011, K-nearest Neighbours Regression, Nonconformity Measure, Predictive Region