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arXiv · 1401.3880

Regression Conformal Prediction with Nearest Neighbours

Harris Papadopoulos·Vladimir Vovk·Alex Gammerman
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Abstract

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.

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Harris Papadopoulos, Vladimir Vovk, Alex Gammerman. 2014-01-16. Regression Conformal Prediction with Nearest Neighbours. https://doi.org/10.1613/jair.3198

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