Multi-domain performance analysis with scores tailored to user preferences

The performance of algorithms, methods, and models tends to depend heavily on the distribution of cases on which they are applied, this distribution being specific to the applicative domain. After performing an evaluation in several domains, it is highly informative to compute a (weighted) mean performance and, as shown in this paper, to scrutinize what happens during this averaging. To achieve this goal, we adopt a probabilistic framework and consider a performance as a probability measure (e.g., a normalized confusion matrix for a classification task). It appears that the corresponding weighted mean is known to be the summarization, and that only some remarkable scores assign to the summarized performance a value equal to a weighted arithmetic mean of the values assigned to the domain-specific performances. These scores include the family of ranking scores, a continuum parameterized by user preferences, and that the weights to consider in the arithmetic mean depend on the user preferences. Based on this, we rigorously define four domains, named easiest, most difficult, preponderant, and bottleneck domains, as functions of user preferences. After establishing the theory in a general setting, regardless of the task, we develop new visual tools for two-class classification.