An Infinite-Dimensional Geometric Structure on the Space of all the Probability Measures Equivalent to a Given One

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Density Estimation in Infinite Dimensional Exponential Families (2013, background): “While various generalizations are possible for diﬀerent choices of F (e.g., Orlicz space as in [27]), the connection of P to the natural exponential family in (1) is particularly enlightening when H is an RKHS. reproducing This is due to the property of the kernel, f ( x ) = f, k ( , x ) H ,…”
Information geometry of divergence functions (2010, background): “See [13] for more delicate problems occurring in the function space.”
Information geometry on hierarchy of probability distributions (2001, background): “Mathematical foundations of information geometry in the function space were given by Pistone and his coworkers [35], [36] and are now developing further.”
Wasserstein Riemannian geometry of Gaussian densities (2018, background): “In view of the non-parametric approach first introduced in [33], and denoted byM the set of n-dimensional Gaussian densities with zero mean, the vector bundle”
Exponential statistical manifold (2007, methodology): “The following definition was introduced in Pistone and Sempi (1995).”