Regression conformal prediction produces prediction intervals that are valid, i.e., the probability of excluding the correct target value is bounded by a predefined confidence level. The most important criterion when comparing conformal regressors is efficiency; the prediction intervals should be as tight (informative) as possible. In this study, the use of random forests as the underlying model for regression conformal prediction is investigated and compared to existing state-of-the-art techniques, which are based on neural networks and k-nearest neighbors. In addition to their robust predictive performance, random forests allow for determining the size of the prediction intervals by using out-of-bag estimates instead of requiring a separate calibration set. An extensive empirical investigation, using 33 publicly available data sets, was undertaken to compare the use of random forests to existing stateof-the-art conformal predictors. The results show that the suggested approach, on almost all confidence levels and using both standard and normalized nonconformity functions, produced significantly more efficient conformal predictors than the existing alternatives.
Abstract. Conformal classifiers output confidence prediction regions, i.e., multi-valued predictions that are guaranteed to contain the true output value of each test pattern with some predefined probability. In order to fully utilize the predictions provided by a conformal classifier, it is essential that those predictions are reliable, i.e., that a user is able to assess the quality of the predictions made. Although conformal classifiers are statistically valid by default, the error probability of the prediction regions output are dependent on their size in such a way that smaller, and thus potentially more interesting, predictions are more likely to be incorrect. This paper proposes, and evaluates, a method for producing refined error probability estimates of prediction regions, that takes their size into account. The end result is a binary conformal confidence predictor that is able to provide accurate error probability estimates for those prediction regions containing only a single class label.
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