Information Geometry: Geometrization of Science of Information
Abstract
Information geometry is an emerging mathematical framework for modeling the space of probability density functions as forming a (possibly infinite-dimensional) differentiable manifold equipped with a Riemannian metric and a pair of non-conjugate connections that need not be metrical. Information geometry has so far been applied to many disciplines such as asymptotic statistics, Bayesian inference, information theory and coding, machine learning, neural computation, econometrics, cognitive psychology, etc. It is seen by some as a potentially unifying framework for ÒgeometrizingÓ information in the same way that physics has been geometrized. Built on earlier works of the PI and his collaborators in information geometry, the current project will not only lead to a deeper understanding of the various geometric structures associated with the manifold of probability models (equiaffine structure, symplectic structure, Hermitian, Kahler structure, Einstein-Weyl structure), but also result in novel applications to information science (data compression, source and channel coding, etc) and Bayesian statistical inference (invariant prior, scoring function, estimating function etc) along with algorithmic developments. If successful, it will provide a solid mathematical foundation for information sciences when dealing with issues of coding, transmission, representation, learning, inference, etc.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Apr 22, 2019
- Source ID
- W911NF1610383
Entities
People
- Jun Zhang
Organizations
- Army Contracting Command
- Defense Advanced Research Projects Agency
- University of Michigan