Ricci curvature for parametric statistics via optimal transport

@article{Li2018RicciCF,
  title={Ricci curvature for parametric statistics via optimal transport},
  author={Wuchen Li and Guido Mont{\'u}far},
  journal={Information Geometry},
  year={2018},
  volume={3},
  pages={89-117}
}
We define the notion of a Ricci curvature lower bound for parametrized statistical models. Following the seminal ideas of Lott–Sturm–Villani, we define this notion based on the geodesic convexity of the Kullback–Leibler divergence in a Wasserstein statistical manifold, that is, a manifold of probability distributions endowed with a Wasserstein metric tensor structure. Within these definitions, which are based on Fisher information matrix and Wasserstein Christoffel symbols, the Ricci curvature… Expand
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