Question: What is the most beginner-friendly book for information geometry?
The book:
- Amari and Nagaoka, Methods of Information Geometry,
is often mentioned as a reference for information geometry.
However, Amari has also written several other books about the subject, at least two of which also seem like they are oriented towards beginners:
- Amari, Differential Geometric Methods in Statistics.
- Amari, Information Geometry and its Applications.
These two books by different authors also seem targeted towards beginners:
- Arwini, Dodson, Information Geometry.
- Murray, Differential Geometry and Statistics.
In case Amari is one of those geniuses who has so much to say about their ideas that they can't possibly explain it concisely/simply/straightforwardly, perhaps it might be better to start with something written secondhand by another author.
I also have access to these other books, which seem like they are more advanced monographs, but I am not really certain, so I am mentioning them here anyway:
- Cencov, Statistical Decision Rules and Optimal Inference.
- Kass, Vos, Geometrical Foundations of Asymptotic Inference.
This thesis (later published as a book) also seems relevant:
- Lebanon, Riemannian Geometry and Statistical Machine Learning.
What I often do is read a lot of books and get only a little out of each (because I don't spend any time thinking about any of them or doing any of the problems).
However, this time, instead of reading eight books, which would be exhausting anyway, I want to focus on one and only one but get a lot out of it.
Thus any informed suggestions or recommendations would be useful/helpful.
Note: Also there is the issue of there being other applications to statistics of differential geometry than just the field of information geometry itself, per se, although I am not knowledgeable about this distinction at all. All of the above books seem to reference Riemannian metrics and exponential families of random variables in some way, so I assume they are about information geometry, but if that is not the case for one of them, that would make for a simple and easy elimination criterion.
Best Answer
I also think these books are quite hard to read at the first place too (but I'm an applied guy). For me, it was simpler to start with scattered material/tutorial/applications using bits of IG such as: Pattern learning and recognition on statistical manifolds: An information-geometric review .