Efficient set-valued prediction in multi-class classification

In cases of uncertainty, a multi-class classifier preferably returns set candidate classes instead predicting single class label with little guarantee. More precisely, the should strive for an optimal balance between correctness (the true is among candidates) and precision candidates are not too many) its prediction. We formalize this problem within general decision-theoretic framework that unifies most existing work in area. framework, uncertainty quantified terms conditional probabilities, quality predicted measured utility function. then address finding Bayes-optimal prediction, i.e., subset labels highest expected utility. For problem, which computationally challenging as there exponentially (in number classes) many predictions to choose from, we propose efficient algorithms can be applied broad family functions. Our theoretical results complemented by experimental studies, analyze proposed predictive accuracy runtime efficiency.