Related papers: Extension of information geometry for modelling no…
Artificial neural networks (ANNs) are powerful tools capable of approximating any arbitrary mathematical function, but their interpretability remains limited, rendering them as black box models. To address this issue, numerous methods have…
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…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
Choosing the Fisher information as the metric tensor for a Riemannian manifold provides a powerful yet fundamental way to understand statistical distribution families. Distances along this manifold become a compelling measure of statistical…
We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the…
A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions,…
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 and a pair of torsion-free conjugate affine connections.…
Motivated by the increasing connections between information theory and high-energy physics, particularly in the context of the AdS/CFT correspondence, we explore the information geometry associated to a variety of simple systems. By…
In the application of Bayesian methods to metrology, pre-data probabilities play a critical role in the estimation of the model uncertainty. Following the observation that distributions form Riemann's manifolds, methods of differential…
The introduction of a metric onto the space of parameters in models in Statistical Mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrization, the scalar curvature, R, plays a central role. A…
A family of probability distributions parametrized by an open domain $\Lambda$ in $R^n$ defines the Fisher information matrix on this domain which is positive semi-definite. In information geometry the standard assumption has been that the…
We introduce generalized notions of a divergence function and a Fisher information matrix. We propose to generalize the notion of an exponential family of models by reformulating it in terms of the Fisher information matrix. Our methods are…
Imaging systems are represented as linear operators, and their singular value spectra describe the structure recoverable at the operator level. Building on an operator-based information-theoretic framework, this paper introduces a minimal…
Information geometry is the application of differential geometry in statistics, where the Fisher-Rao metric serves as the Riemannian metric on the statistical manifold, providing an intrinsic property for parameter sensitivity. In this…
Motivated by the engineering applications of uncertainty quantification, in this work we draw connections between the notions of random quantum states and operations in quantum information with probability distributions commonly encountered…
Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the…
The information geometry of the 2-manifold of gamma probability density functions provides a framework in which pseudorandom number generators may be evaluated using a neighbourhood of the curve of exponential density functions. The process…
For (2+2)-dimensional nonholonomic distributions, the physical information contained into a spacetime (pseudo) Riemannian metric can be encoded equivalently into new types of geometric structures and linear connections constructed as…
The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distributions on the real line, the parameter space has a…
Information geometry applies concepts in differential geometry to probability and statistics and is especially useful for parameter estimation in exponential families where parameters are known to lie on a Riemannian manifold. Connections…