Threshold optimization for classification in imbalanced data in a problem of gamma-ray astronomy

We introduce a method to minimize the mean square error (MSE) of an estimator which is derived from a classification. The method chooses an optimal discrimination threshold in the outcome of a classification algorithm and deals with the problem of unequal and unknown misclassification costs and class imbalance. The approach is applied to data from the MAGIC experiment in astronomy for choosing an optimal threshold for signal-background-separation. In this application one is interested in estimating the number of signal events in a dataset with very unfavorable signal to background ratio. Minimizing the MSE of the estimation is a rather general approach which can be adapted to various other applications, in which one wants to derive an estimator from a classification. If the classification depends on other or additional parameters than the discrimination threshold, MSE minimization can be used to optimize these parameters as well. We illustrate this by optimizing the parameters of logistic regression, leading to relevant improvements of the current approach used in the MAGIC experiment.