18 citations · 126 across the 24 of their papers we have counts for
39 papers
A two-point approach to the inverse problem in information geometry
Florio M. Ciaglia, Giuseppe Marmo, Marco Pacelli +2
We formulate the inverse problem in information geometry within a two-point tensorial framework and solve it for general metric-affine manifolds, without imposing any curvature or…
Metric tensors and two-forms in information geometry from the GNS construction
Marco Castrillón López, Florio M. Ciaglia, Laura González-Bravo +1
We develop a GNS-based construction of geometric tensors on smooth parametric statistical models over -algebras. Since the state space of a -algebra is generally not a sm…
Potential functions in information geometry via bi-forms
Florio M. Ciaglia, Giuseppe Marmo, Marco Pacelli +2
In this paper we develop a general framework for potentials on Lauritzen manifolds, namely smooth manifolds equipped with a pseudo-Riemannian metric and a pair of conjugate affine…
Bi-forms Approach to Potential Functions in Information Geometry
Florio M. Ciaglia, Giuseppe Marmo, Marco Pacelli +2
Contrast functions play a fundamental role in information geometry, providing a means for generating the geometric structures of a statistical manifold: a pseudo-Riemannian metric…
Fields of covariances on non-commutative probability spaces in finite dimensions
Florio M. Ciaglia, Fabio Di Cosmo, Laura González-Bravo
We introduce the notion of a field of covariances, a contravariant functor from non-commutative probability spaces to Hilbert spaces, as a categorical analogue of statistical covar…
Towards a category-theoretic foundation of Classical and Quantum Information Geometry
Florio M. Ciaglia, Fabio Di Cosmo, Laura González-Bravo
We introduce the category , whose objects are pairs of W-algebras and normal states and whose morphisms are state-preserving unital completely positive (CPU) m…