![]() Amari’s Information Geometry and its Applications is a great book which has many of the important results and examples in IG. For information geometry, there isn’t a single standalone reference that I would recommend. The first one is more accessible, but the latter is a definitive reference which is extremely thorough, and they are both superbly well written. ![]() As such, this paper is probably not a great place to start if you are just getting into either of the two topics.įor a more complete background on optimal transport, both Santambrogio’s Optimal Transport for Applied Mathematics or Villani’s Optimal Transport: old and new are excellent references. Since our paper was written as an introduction for a special issue on optimal transport in Information Geometry, we did not include a background section on IG (and only wrote a short background section on OT). This induces a different geometry, but these two approaches have many connections and there is a wide range of research combining ideas from both areas. On the other hand, optimal transport studies the problem of transporting mass between probability distributions in the most economical way possible. Information geometry and optimal transport provide two distinct ways to study probability measures “geometrically.” As suggested by the name, IG uses ideas from information theory (e.g., relative entropy) to define geometric quantities (distances, angles, curvature, etc.) on statistical manifolds, which are spaces whose points correspond to probability distributions. ![]() The statistical manifold of multinomial distributions Jun Zhang and I have just published a survey paper “ When optimal transport meets information geometry” (also available on the arXiv), which is intended to give an overview of some ways in which these two fields interact.
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