Regression Conformal Prediction with Nearest Neighbours
This work addresses the need for more precise uncertainty quantification in regression tasks, particularly for applications requiring reliable confidence intervals, though it is incremental as it builds on existing conformal prediction methods.
The paper tackles the problem of improving predictive region tightness in conformal prediction for regression by proposing six novel nonconformity measures based on k-nearest neighbours regression, achieving a major improvement in tightness compared to typical measures.
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.