Abstract
In this chapter we discuss positive results about probabilistic prediction in the case of classification. For that, we introduce a new kind of predictors, Venn predictors, which produce predictions satisfying a natural property of validity at the price of lowering the bar as compared with the previous chapter. To gain some wiggle room, Venn predictors are allowed to announce several probability distributions as their prediction, and the overall prediction is considered valid whenever any of its components is valid. Such a multiprobability prediction is useful if its components are close to each other, in which case we have an approximate probabilistic prediction; if not, we may be in a situation of Knightean uncertainty, and the multiprobability prediction may be considered as a useful warning.
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Vovk, V., Gammerman, A., Shafer, G. (2022). Probabilistic Classification: Venn Predictors. In: Algorithmic Learning in a Random World. Springer, Cham. https://doi.org/10.1007/978-3-031-06649-8_6
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