[Math] Self-studying Information Geometry

Question

I was recently exposed to the topic of Information Geometry by a friend of mine, and was looking for a good book to begin self-studying this topic. Any suggestions?

Also, what subject matter would one need to have a handle on to begin self-studying this? I have an undergraduate-level background in real analysis, some basic point-set topology, as well as algebra up to the level of Galois Theory.

Answer 1

The most famous book on the subject is probably:

Amari, 2007, Methods of Information Geometry

But there are few other ones that look quite nice:

Amari, 2016, Information Geometry and Its Applications

Murray & Rice, 1993, Differential Geometry and Statistics

Ay et al, 2017, Information Geometry

The last one mentioned is quite new.

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This question has been asked quite a few times in different ways on the SE network. Let me link to a few here:

• Applications of information geometry to the natural sciences [MathSE]
• Research situation in the field of Information Geometry [MathOverflow]
• Information geometry tutorial [CrossValidated]
• What is the most beginner-friendly book for information geometry? [CrossValidated]
• Does differential geometry have anything to do with statistics? [CrossValidated]

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For the background/prerequisites, I would say they are:

1. Differential geometry: manifold theory (differential forms, connections, etc) and Riemannian geometry (metric and curvature tensors, geodesics, etc)

2. Probability and statistics: probability distributions, statistical estimation, basic measure theory, and information theory