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.
Author supplied keywords
- Affine connection
- Bayesian hypothesis testing
- Conjugate connections
- Curvature and flatness
- Differential geometry
- Dual metric-compatible parallel transport
- Dually flat manifolds
- Exponential family
- Fisher–Rao distance
- Gauge freedom
- Hessian manifolds
- Information manifold
- Metric compatibility
- Metric tensor
- Mixed parameterization
- Mixture clustering
- Mixture family
- Parameter divergence
- Separable divergence
- Statistical divergence
- Statistical invariance
- Statistical manifold
- α-embeddings
Cite
CITATION STYLE
APA
Nielsen, F. (2020). An elementary introduction to information geometry. Entropy, 22(10), 1–61. https://doi.org/10.3390/e22101100
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