An Extended Cencov-Campbell Characterization of Conditional Information Geometry

Abstract

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.

Cite

Text

Lebanon. "An Extended Cencov-Campbell Characterization of Conditional Information Geometry." Conference on Uncertainty in Artificial Intelligence, 2004.

Markdown

[Lebanon. "An Extended Cencov-Campbell Characterization of Conditional Information Geometry." Conference on Uncertainty in Artificial Intelligence, 2004.](https://mlanthology.org/uai/2004/lebanon2004uai-extended/)

BibTeX

@inproceedings{lebanon2004uai-extended,
  title     = {{An Extended Cencov-Campbell Characterization of Conditional Information Geometry}},
  author    = {Lebanon, Guy},
  booktitle = {Conference on Uncertainty in Artificial Intelligence},
  year      = {2004},
  pages     = {341-345},
  url       = {https://mlanthology.org/uai/2004/lebanon2004uai-extended/}
}