  Loss functions engineering and the assessment of forecasting performances are
two crucial and intertwined aspects of supervised machine learning. This paper
focuses on binary classification to introduce a class of loss functions that
are defined on probabilistic confusion matrices and that allow an automatic and
a priori maximization of the skill scores. The performances of these loss
functions are validated during the training phase of two experimental
forecasting problems, thus showing that the probability distribution function
associated with the confusion matrices significantly impacts the outcome of the
score maximization process.
