Related papers: Information geometry for Fermi-Dirac and Bose-Eins…
Information geometry and inductive inference methods can be used to model dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this article, we present a formal conceptual reexamination of the…
We develop an intrinsic information-theoretic approach for recovering Riemannian curvature from the small-time behaviour of heat diffusion. Given a point and a two-plane in the tangent space, we compare the heat mass transported along that…
This paper is about Information Geometry, a relatively new subject within mathematical statistics that attempts to study the problem of inference by using tools from modern differential geometry. This paper provides an overview of some of…
This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information…
In this paper we propose a unified statistics of Bose-Einstein and Fermi-Dirac statistics by suggesting that every particle can be associated with matter or fundamental forces with certain probability. The main Justification for this…
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…
Information geometry is a mathematical framework that elucidates the manifold structure of the probability distribution space (p-space), providing a systematic approach to transforming probability distributions (PDs). In this study, we…
Physical systems behave according to their underlying dynamical equations which, in turn, can be identified from experimental data. Explaining data requires selecting mathematical models that best capture the data regularities. Identifying…
This paper mainly contributes to a classification of statistical Einstein manifolds, namely statistical manifolds at the same time are Einstein manifolds. A statistical manifold is a Riemannian manifold, each of whose points is a…
This essay constitutes a review of the information geometric approach to renormalization developed in the recent works of B\'eny and Osborne as well as a detailed work-through of some of their contents. A noncommutative generalization of…
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of…
Growing network models have been shown to display emergent quantum statistics when nodes are associated to a fitness value describing the intrinsic ability of a node to acquire new links. Recently it has been shown that quantum statistics…
Classical Fisher-information asymptotics describe the covariance of regular efficient estimators through the local quadratic approximation of the log-likelihood, and thus capture first-order geometry only. In curved models, including…
Partial differential equations describing compressible fluids are prone to the formation of shock singularities, arising from faster upstream fluid particles catching up to slower, downstream ones. In geometric terms, this causes the…
The differential-geometric structure of the set of positive densities on a given measure space has raised the interest of many mathematicians after the discovery by C.R. Rao of the geometric meaning of the Fisher information. Most of the…
We examine the thermodynamic characteristics of unified quantum statistics as a novel framework that undergoes a crossover between Bose-Einstein and Fermi-Dirac statistics by varying a generalization parameter $\delta$. We find an…
We show that the relativistic energy-momentum relation can emerge as an effective ensemble-averaged structure from a multiplicative Hamiltonian when fluctuations of an auxiliary parameter are treated using maximum entropy inference. The…
Optimization in large language models (LLMs) unfolds over high-dimensional parameter spaces with non-Euclidean structure. Information geometry frames this landscape using the Fisher information metric, enabling more principled learning via…
In this work some advances in the theory of curvature of two-dimensional probability manifolds corresponding to families of distributions are proposed. It is proved that location-scale distributions are hyperbolic in the Information…