Information Geometry

Information geometry studies the geometry of spaces of probability distributions, with particular focus to topics related to:

• the Fisher information metric (a Riemannian metric),
• the dually flat structure on these spaces,
• divergences between probability distributions,
• etc.

I. Notes

• Statistical manifolds
• Dual connections
• Dually flat manifolds
• Distributions:
  • Normal (univariate)

II. References

books

• Amari, Nagoka — Methods of Information Geometry (classic reference; great choice for a first reading; explains most of the basic ideas and the geometry needed; much focus on the dual connections)
• Calin, Udrişte — Geometric Modeling in Probability and Statistics (connects to information theory; full of examples; is divided in two parts: one about statistical models, and the other about abstract statistical manifolds)
• Ay, Jost, Lê, Schwachhöfer — Information Geometry (modern reference; explains geometric abstractions; shows many possible generalizations)
• Amari — Information Geometry and Its Applications (provides a overview of many applications of information geometry to different fields)

articles

• Nielsen — The Many Faces of Information Geometry (a good quick overview of the area)

journals

• Information Geometry (Springer)
• Entropy (MDPI)

useful webpages

• Frank Nielsen
• John Baez