Data analysis in high energy physics has to deal with data samples produced from different sources. One of the most widely used ways to unfold their contributions is the sPlot technique. It uses the results of a maximum likelihood fit to assign weights to events. Some weights produced by sPlot are by design negative. Negative weights make it difficult to apply machine learning methods. The loss function becomes unbounded. This leads to divergent neural network training. In this paper we propose a mathematically rigorous way to transform the weights obtained by sPlot into class probabilities conditioned on observables, thus enabling to apply any machine learning algorithm out-of-the-box.

Abstract: Data analysis in high energy physics often deals with data samples consisting of a mixture of signal and background events. The sPlot technique is a common method to subtract the contribution of the background by assigning weights to events. Part of the weights are by design negative. Negative weights lead to the divergence of some machine learning algorithms training due to absence of the lower bound in the loss function. In this paper we propose a mathematically rigorous way to train machine learning algorithms on data samples with background described by sPlot to obtain signal probabilities conditioned on observables, without encountering negative event weight at all. This allows usage of any out-of-the-box machine learning methods on such data.