| Literature DB >> 33286868 |
Abstract
In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. The exposition is self-contained by concisely introducing the necessary concepts of differential geometry. Proofs are omitted for brevity.Entities:
Keywords: Bayesian hypothesis testing; Fisher–Rao distance; Hessian manifolds; affine connection; conjugate connections; curvature and flatness; differential geometry; dual metric-compatible parallel transport; dually flat manifolds; exponential family; gauge freedom; information manifold; metric compatibility; metric tensor; mixed parameterization; mixture clustering; mixture family; parameter divergence; separable divergence; statistical divergence; statistical invariance; statistical manifold; α-embeddings
Year: 2020 PMID： 33286868 DOI： 10.3390/e22101100
Source DB: PubMed Journal: Entropy (Basel) ISSN： 1099-4300 Impact factor: 2.524