An Extended Cencov-Campbell Characterization of Conditional Information Geometry
We formulate and prove an axiomatic characterization of conditional information geometry, for both the normalized and the non-normalized 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.