Abstract. The existing methods of predicting with confidence give good accuracy and confidence values, but quite often are computationally inefficient. Some partial solutions have been suggested in the past. Both the original method and these solutions were based on transductive inference. In this paper we make a radical step of replacing transductive inference with inductive inference and define what we call the Inductive Confidence Machine (ICM); our main concern in this paper is the use of ICM in regression problems. The algorithm proposed in this paper is based on the Ridge Regression procedure (which is usually used for outputting bare predictions) and is much faster than the existing transductive techniques. The inductive approach described in this paper may be the only option available when dealing with large data sets.

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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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