Information Geometry

Dear Colleagues,

The mathematical field of information geometry originated from the observation that Fisher information can be used to define a Riemannian metric on manifolds of probability distributions. This led to a geometrical description of probability theory and statistics, allowing studies of the invariant properties of statistical manifolds. It was through the work of S.-I. Amari and others that it was later realized that the differential–geometric structure of a statistical manifold can be extended to families of dual affine connections and that such a structure can be derived from divergence functions.

Since then, information geometry has become a truly interdisciplinary field with applications in various domains. It enables a deeper and more intuitive understanding of the methods of statistical inference and machine learning, while providing a powerful framework for deriving new algorithms. As such, information geometry has many applications in optimization, signal and image processing, computer vision, neural networks, and other subfields of the information sciences. Furthermore, the methods of information geometry have been applied to a broad variety of topics in physics, mathematical finance, biology, and the neurosciences. In physics, there are many links with fields that have a natural probabilistic interpretation, including (nonextensive) statistical mechanics and quantum mechanics.

For this collection, we welcome submissions related to the foundations and applications of information geometry. We envisage contributions that aim at clarifying the connection of information geometry with both the information sciences and the physical sciences, so as to demonstrate the profound impact of the field in these disciplines. In addition, we hope to receive original papers illustrating the wide variety of applications of the methods of information geometry.

Prof. Dr. Geert Verdoolaege
Collection Editor

Manuscript Submission Information

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