  We formulate and prove an axiomatic characterization of conditional
information geometry, for both the normalized and the nonnormalized cases. This
characterization extends the axiomatic derivation of the Fisher geometry by
Cencov and Campbell to the cone of positive conditional models, and as a
special case to the manifold of conditional distributions. Due to the close
connection between the conditional I-divergence and the product Fisher
information metric the characterization provides a new axiomatic interpretation
of the primal problems underlying logistic regression and AdaBoost.
