Nonparametric Information Geometry: From Divergence Function to Referential-Representational Biduality on Statistical Manifolds

@article{Zhang2013NonparametricIG,
  title={Nonparametric Information Geometry: From Divergence Function to Referential-Representational Biduality on Statistical Manifolds},
  author={Jing Zhang},
  journal={Entropy},
  year={2013},
  volume={15},
  pages={5384-5418}
}
Divergence functions are the non-symmetric “distance” on the manifold,Mθ, of parametric probability density functions over a measure space, (X,μ). Classical information geometry prescribes, on Mθ: (i) a Riemannian metric given by the Fisher information; (ii) a pair of dual connections (giving rise to the family of α-connections) that preserve the metric under parallel transport by their joint actions; and (iii) a family of divergence functions (α-divergence) defined on Mθ × Mθ, which induce the… CONTINUE READING

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