AI 2012 - LNAI 7691

Simultaneous Interval Regression for K-Nearest Neighbor

Mohammad Ghasemi Hamed^{1, 2}, Mathieu Serrurier¹, and Nicolas Durand^{1, 2}

¹IRIT - Université Paul Sabatier, 118 route de Narbonne 31062, Toulouse Cedex 9, France

²ENAC/MAIAA, 7 Avenue Edouard Belin 31055, Toulouse, France

Abstract. In some regression problems, it may be more reasonable to predict intervals rather than precise values. We are interested in finding intervals which simultaneously for all input instances contain a proportion of the response values. We name this problem simultaneous interval regression. This is similar to simultaneous tolerance intervals for regression with a high confidence level 1 and several authors have already treated this problem for linear regression. Such intervals could be seen as a form of confidence envelop for the prediction variable given any value of predictor variables in their domain. Tolerance intervals and simultaneous tolerance intervals have not yet been treated for the K-nearest neighbor (KNN) regression method. The goal of this paper is to consider the simultaneous interval regression problem for KNN and this is done without the homoscedasticity assumption. In this scope, we propose a new interval regression method based on KNN which takes advantage of tolerance intervals in order to choose, for each instance, the value of the hyper-parameter K which will be a good trade-off between the precision and the uncertainty due to the limited sample size of the neighborhood around each instance. In the experiment part, our proposed interval construction method is compared with a more conventional interval approximation method on six benchmark regression data sets.

LNAI 7691, p. 602 ff.

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