G. Ferrari-Trecate and M. Schinkel. Conditions of optimal classification for piecewise affine regression. In O. Maler and A. Pnueli, editors, Proc. 6th International Workshop on Hybrid Systems: Computation and Control , volume 2623 of Lecture Notes in Computer Science , pages 188--202. Springer-Verlag, 2003.
We consider regression problems with piecewise affine maps. Inparticular, we focus on the sub-problem of classifying thedatapoints, i.e. correctly attributing a datapoint to theaffine submodel that most likely generated it. Then, we analyzethe regression algorithm proposed by Ferrari-Trecate et. al (2003) andshow that, under suitable assumptions on the dataset and the weightsof the classification procedure, optimal classificationcan be guaranteed in presence of bounded noise.We also relax such assumptions by introducingand characterizing the property of weakly optimal classification.Finally, by elaborating on these concepts, we propose a procedurefor detecting, a posteriori, misclassified datapoints.