Information Geometry
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Information geometry of warped product spaces
Information Geometry - Tập 6 - Trang 127-155 - 2022
Information geometry is an important tool to study statistical models. There are some important examples in statistical models which are regarded as warped products. In this paper, we study information geometry of warped products. We consider the case where the warped product and its fiber space are equipped with dually flat connections and, in the particular case of a cone, characterize the conne......
Anomaly detection in the probability simplex under different geometries
Information Geometry - Tập 6 - Trang 385-412 - 2023
An open problem in data science is that of anomaly detection. Anomalies are instances that do not maintain a certain property that is present in the remaining observations in a dataset. Several anomaly detection algorithms exist, since the process itself is ill-posed mainly because the criteria that separates common or expected vectors from anomalies are not unique. In the most extreme case, data ......
The Bonnet theorem for statistical manifolds
Information Geometry - Tập 4 - Trang 363-376 - 2021
We prove the Bonnet theorem for statistical manifolds, which states that if a statistical manifold admits tensors satisfying the Gauss–Codazzi–Ricci equations, then it is locally embeddable to a flat statistical manifold (or a Hessian manifold). The proof is based on the notion of statistical embedding to the product of a vector space and its dual space introduced by Lauritzen. As another applicat......
Transport information geometry: Riemannian calculus on probability simplex
Information Geometry - Tập 5 - Trang 161-207 - 2021
We formulate the Riemannian calculus of the probability set embedded with
$$L^2$$
-Wasserstein metric. This is an initial work of transport information geometry. Our investigation starts with the probability simplex (probability manifold) supported on vertices of a finite graph. The main idea is to......
Parametric models and information geometry on W*-algebras
Information Geometry - Tập 7 - Trang 329-354 - 2023
We introduce the notion of smooth parametric model of normal positive linear functionals on possibly infinite-dimensional
$$W^{\star }$$
-algebras generalizing the notions of parametric models used in classical and quantum information geometry. We then use the Jordan product naturally available in ......
G-dual Teleparallel Connections in Information Geometry
Information Geometry - Tập 7 - Trang 587-608 - 2023
Given a real, finite-dimensional, smooth parallelizable Riemannian manifold
$$(\mathcal {N},G)$$
endowed with a teleparallel connection
$$\nabla $$
determined by a choice of a global basis of vect......
Geometric thermodynamics for the Fokker–Planck equation: stochastic thermodynamic links between information geometry and optimal transport
Information Geometry - - Trang 1-43 - 2023
We propose a geometric theory of non-equilibrium thermodynamics, namely geometric thermodynamics, using our recent developments of differential-geometric aspects of entropy production rate in non-equilibrium thermodynamics. By revisiting our recent results on geometrical aspects of entropy production rate in stochastic thermodynamics for the Fokker–Planck equation, we introduce a geometric framewo......
The information geometry of two-field functional integrals
Information Geometry - Tập 5 - Trang 427-492 - 2022
Two-field functional integrals (2FFI) are an important class of solution methods for generating functions of dissipative processes, including discrete-state stochastic processes, dissipative dynamical systems, and decohering quantum densities. The stationary trajectories of these integrals describe a conserved current by Liouville’s theorem, despite the absence of a conserved kinematic phase space......
Publisher Correction: The Fisher–Rao loss for learning under label noise
Information Geometry - Tập 6 - Trang 379-379 - 2022
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