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Usually, the expected loss minimization criterion is used in order to look for the optimal model that expresses a certain response variable as a function of a collection of attributes. We generalize this criterion, in order to be able to deal also with those situations where a numerical loss function makes no sense or is not provided by the expert. In a first stage, we consider the new framework in standard situations, where both the collection of attributes and the response variables are observed with precision. In a second one, we assume that we are just provided with imprecise information about them (in terms of set-valued data sets). We cast some comparison criteria from the recent literature on learning methods from low-quality data as particular cases of our general approach.

Generalized stochastic orderings applied to the study of performance of machine learning algorithms for low quality data