48 citations · 161 across the 26 of their papers we have counts for
34 papers
Affine statistical bundle modeled on a Gaussian Orlicz-Sobolev space
Giovanni Pistone
The dually flat structure of statistical manifolds can be derived in a non-parametric way from a particular case of affine space defined on a qualified set of probability measures.…
Dually affine Information Geometry modeled on a Banach space
Goffredo Chirco, Giovanni Pistone
In this chapter, we study Information Geometry from a particular non-parametric or functional point of view. The basic model is a probabilities subset usually specified by regulari…
A Lecture About the Use of Orlicz Spaces in Information Geometry
Giovanni Pistone
This is a revised version of a tutorial lecture that I presented at the Ècole de Physique des Houches on July 26-31 2020. Topics include Non-parametric Information Geometry, the St…
Lagrangian and Hamiltonian Mechanics for Probabilities on the Statistical Manifold
Goffredo Chirco, Luigi Malagò, Giovanni Pistone
We provide an Information-Geometric formulation of Classical Mechanics on the Riemannian manifold of probability distributions, which is an affine manifold endowed with a dually-fl…
Information Geometry of smooth densities on the Gaussian space: Poincaré inequalities
Giovanni Pistone
We derive bounds for the Orlicz norm of the deviation of a random variable defined on from its Gaussian mean value. The random variables are assumed to be smooth and…
Finite space Kantorovich problem with an MCMC of table moves
Giovanni Pistone, Fabio Rapallo, Maria Piera Rogantin
In Optimal Transport (OT) on a finite metric space, one defines a distance on the probability simplex that extends the distance on the ground space. The distance is the value of a…