Optimizing pred(25) Is NP-Hard

Abstract

Usually, in data processing, to find the parameters of the models that best fits the data, people use the Least Squares method. One of the advantages of this method is that for linear models, it leads to an easy-to-solve system of linear equations. A limitation of this method is that even a single outlier can ruin the corresponding estimates; thus, more robust methods are needed. In particular, in software engineering, often, a more robust pred(25) method is used, in which we maximize the number of cases in which the model’s prediction is within the 25% range of the observations. In this paper, we show that even for linear models, pred(25) parameter estimation is NP-hard.