Related papers: Geometry of Information Integration
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is…
Recently, there has been considerable interest in the application of information geometry to quantum many body physics. This interest has been driven by three separate lines of research, which can all be understood as different facets of…
Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random…
Layered architecture represents the software structure in the form of layers. Every element in the software is assigned to one of the layers such that the relationship amongst the elements is maintained. A set of design principles rules the…
A framework for a quantum information theory is introduced that is based on the measure of quantum information associated with probability distribution predicted by quantum measuring of state. The entanglement between states of measured…
Merge trees, a type of topological descriptor, serve to identify and summarize the topological characteristics associated with scalar fields. They present a great potential for the analysis and visualization of time-varying data. First,…
Relevance of key quantum information measures for analysis of quantum systems is discussed. It is argued that possible ways of measuring quantum information are based on compatibility/incompatibility of the quantum states of a quantum…
Multivariate mutual information provides a conceptual framework for characterizing higher-order interactions in complex systems. Two well-known measures of multivariate information---total correlation and dual total correlation---admit a…
We propose a unified information-geometric framework that formalizes understanding in learning as a trade-off between informativeness and geometric simplicity. An encoder phi is evaluated by U(phi) = I(phi(X); Y) - beta * C(phi), where…
In this work we: (1) review likelihood-based inference for parameter estimation and the construction of confidence regions; and, (2) explore the use of techniques from information geometry, including geodesic curves and Riemann scalar…
We consider probabilistic theories in which the most elementary system, a two-dimensional system, contains one bit of information. The bit is assumed to be contained in any complete set of mutually complementary measurements. The…
We investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a comparative analysis based upon Riemannian…
Measures of dependence among variables, and measures of information content and shared information have become valuable tools of multi-variable data analysis. Information measures, like marginal entropies, mutual and multi-information, have…
In the contemporary era, the importance of information is undisputed, but there has never been a common understanding of information, nor a unanimous conclusion to the researches on information metrics. Based on the previous studies, this…
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…
We introduce the notion of information ratio $\text{Ir}(H/G)$ between two (simple, undirected) graphs $G$ and $H$, defined as the supremum of ratios $k/n$ such that there exists a mapping between the strong products $G^k$ to $H^n$ that…
We examine data-processing of Markov chains through the lens of information geometry. We first establish a theory of congruent Markov morphisms within the framework of stochastic matrices. Specifically, we introduce and justify the concept…
Quantifying entanglement is an important issue in quantum information theory. Here we consider the entanglement measures through the trace norm in terms of two methods, the modified measure and the extended measure for bipartite states. We…
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…