Related papers: Information Geometry via the Q-Root Transform
We show a relationship between the entropy production in stochastic thermodynamics and the stochastic interaction in the information integrated theory. To clarify this relationship, we newly introduce an information geometric interpretation…
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…
The concept of distinguishability lies at the heart of quantum information theory. We introduce \textit{left-right relative entropy} as a quantitative measure of distinguishability within the space of boundary states in two-dimensional…
We provide an explicit connection between the differential generation of entanglement entropy in a tensor network representation of the ground states of two field theories, and a geometric description of these states based on the Fisher…
We study a curve of Gibbsian families of complex 3x3-matrices and point out new features, absent in commutative finite-dimensional algebras: a discontinuous maximum-entropy inference, a discontinuous entropy distance and non-exposed faces…
The purpose of this thesis is to convey the basic concepts of information geometry and its applications to non-specialists and those in applied fields, assuming only a first-year undergraduate background in calculus, linear algebra, and…
Optimal transport and information geometry both study geometric structures on spaces of probability distributions. Optimal transport characterizes the cost-minimizing movement from one distribution to another, while information geometry…
The idea that a spacetime metric emerges as a Fisher-Rao `information metric' of instanton moduli space has been examined in several field theories such as the Yang-Mills theories and nonlinear sigma models. In this brief paper, we report…
In this paper, we develop a framework for information theoretic learning based on infinitely divisible matrices. We formulate an entropy-like functional on positive definite matrices based on Renyi's axiomatic definition of entropy and…
Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are equipped with…
We formulate a geometric framework in which physical laws emerge from restricted access to microscopic information. Measurement constraints are modeled as a gauge symmetry acting on density operators, inducing a gauge-reduced space of…
In the recent years, information theory of quantum-mechanical systems have aroused the interest of many Theoretical Physicist. This due to the fact that it provides a deeper insight into the internal structure of the systems. Also, It is…
The maximum entropy principle (MEP) is one of the most prominent methods to investigate and model complex systems. Despite its popularity, the standard form of the MEP can only generate Boltzmann-Gibbs distributions, which are ill-suited…
Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose,…
In the elastic shape analysis approach to shape matching and object classification, plane curves are represented as points in an infinite-dimensional Riemannian manifold, wherein shape dissimilarity is measured by geodesic distance. A…
Causal inference is perhaps one of the most fundamental concepts in science, beginning originally from the works of some of the ancient philosophers, through today, but also weaved strongly in current work from statisticians, machine…
We develop a family of infinite-dimensional Banach manifolds of measures on an abstract measurable space, employing charts that are "balanced" between the density and log-density functions. The manifolds, $(\tilde{M}_{\lambda},\lambda\in…
It is well known that the Fisher information induces a Riemannian geometry on parametric families of probability density functions. Following recent work, we consider the nonparametric generalization of the Fisher geometry. The resulting…
Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and…
Three steps in the development of the maximum likelihood (ML) method are presented. At first, the application of the ML method and Fisher information notion in the model selection analysis is described (Chapter 1). The fundamentals of…