Nested Dichotomies with probability sets for multi-class classification

Binary decomposition techniques transform a multi-class problem into several simpler binary problems. In such techniques, a classical issue is to ensure the consistency between the binary assessments of conditional probabilities. Nested dichotomies, which consider tree-shaped decomposition, do not suffer from this issue. Yet, a wrong probability estimate in the tree can strongly biase the results and provide wrong predictions. To overcome this issue, we consider in this paper imprecise nested dichotomies, in which binary probabilities become imprecise. We show in experiments that the approach has many advantages: it provides cautious inferences when only little information is available, and allows to make efficient computations with imprecise probabilities even when considering generic cost functions.