Conditionality is discussed in Section 1.4 of Vovk et al. (2005). It is a general desideratum in statistical inference. A classical paper on this topic is Cox (1958). It was a major concern for Ronald Fisher.

For an in-depth study of conditionality for (inductive) conformal predictors, see Vovk (2103). According to that paper (Figure 1), three important kinds of conditionality are:

  • object conditionality
  • label conditionality
  • training conditionality

In the case of classification, label conditionality can be achieved by Mondrian conformal predictors (namely, label-conditional conformal predictors). Object conditionality is most flagrantly violated by empty predictions, which occasionally happen, especially in the case of classification. Partial object conditionality can also be achieved by Mondrian conformal predictors (such as separate analysis for males and females given in that article). A degree of training conditional validity is achieved by inductive conformal predictors automatically (Vovk, 2013, Section 3).