In mathematics, information geometry is the study of probability and information by way of differential geometry. It reached maturity through the work of Shun'ichi Amari in the 1980's, with what is currently the canonical reference book: Differential-geometrical methods in statistics.
Information geometry is based primarily on the Fisher information metric:
Substiting i = -ln(p) from information theory, the formula becomes:
Which can be thought of intuitively as: "The distance between two points on a statistical differential manifold is the amount of information between them, i.e. the informational difference between them."
References
- Shun'ichi Amari - Differential-geometrical methods in statistics, Lecture notes in statistics, Springer-Verlag, Berlin, 1985
- Shun'ichi Amari, Hiroshi Nagaoka - Methods of information geometry, Transactions of mathematical monographs; v. 191, American Mathematical Society, 2000
