Related papers: Information geometry and sufficient statistics
Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…
A statistic on a statistical model is sufficient if it has no information loss, namely, the Fisher metric of the induced model coincides with that of the original model due to Kullback and Ay-Jost-L\^e-Schwachh\"ofer. We introduce a…
A novel information-geometrodynamical approach to chaotic dynamics (IGAC) on curved statistical manifolds based on Entropic Dynamics (ED) is presented and a new definition of information geometrodynamical entropy (IGE) as a measure of…
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…
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 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…
After a review of the pure state case, we discuss from a geometrical point of view the meaning of the quantum Fisher metric in the case of mixed states for a two-level system, i.e. for a q-bit, by examining the structure of the fiber bundle…
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…
I review recent works showing that information geometry is a useful framework to characterize quantum coherence and entanglement. Quantum systems exhibit peculiar properties which cannot be justified by classical physics, e.g. quantum…
Using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the Information Geometry based on these entropies. Our aim, at this stage, is modest, as we are first constructing…
Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of…
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…
We build information geometry for a partially ordered set of variables and define the orthogonal decomposition of information theoretic quantities. The natural connection between information geometry and order theory leads to efficient…
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…
Information theory is a powerful framework to capture aspects of dynamical systems with multiple degrees of freedom. Mathematically, the dynamics can be represented as a continuous curve $\mathcal{C}$ on a suitable hyperplane in flat space…
We study a differential geometric construction, the warped product, on the background geometry for information theory. Divergences, dual structures and symmetric 3-tensor are studied under this construction, and we show that warped product…
This paper is a strongly geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. The Fisher distance, as well as other divergence measures, are also used in many…
The Fisher information matrix can be used to characterize the local geometry of the parameter space of neural networks. It elucidates insightful theories and useful tools to understand and optimize neural networks. Given its high…
The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the…
Real-world signals typically span across multiple dimensions, that is, they naturally reside on multi-way data structures referred to as tensors. In contrast to standard ``flat-view'' multivariate matrix models which are agnostic to data…