Normalized nonconformity measures for regression Conformal Prediction

In this paper we apply Conformal Prediction (CP) to the k-Nearest Neighbours Regression (k-NNR) algorithm and propose a way 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. When the regular regression nonconformity measure is used the resulting predictive regions have more or less the same width for all examples in the test set. However, it would be more natural for the size of the regions to vary according to how difficult to predict each example is. We define two new nonconformity measures, which produce predictive regions of variable width depending on the expected accuracy of the algorithm on each example. As a consequence, the resulting predictive regions are in most cases much tighter than those produced by the simple regression measure.