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arXiv · 1503.08478

Transversely Hessian foliations and information geometry

Michel Nguiffo Boyom·Robert A. Wolak
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Abstract

A family of probability distributions parametrized by an open domain $\Lambda$ in $R^n$ defines the Fisher information matrix on this domain which is positive semi-definite. In information geometry the standard assumption has been that the Fisher information matrix tensor is positive definite defining in this way a Riemannian metric on $\Lambda$. If we replace the "positive definite" assumption by the existence of a suitable torsion-free connection, a foliation with a transversely Hessian structure appears naturally. In the paper we develop the study of transversely Hessian foliations in view of applications in information geometry.

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Michel Nguiffo Boyom, Robert A. Wolak. 2015-03-29. Transversely Hessian foliations and information geometry. https://arxiv.org/abs/1503.08478

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