Related papers: The Information Geometry of UMAP
In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information…
In this paper, we show how information geometry, the natural geometry of discrete probability distributions, can be used to derive the quantum formalism. The derivation rests upon three elementary features of quantum phenomena, namely…
We use the method of maximum entropy to model physical space as a curved statistical manifold. It is then natural to use information geometry to explain the geometry of space. We find that the resultant information metric does not describe…
In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic…
Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information,…
Information Geometry has been used to inspire efficient algorithms for stochastic optimization, both in the combinatorial and the continuous case. We give an overview of the authors' research program and some specific contributions to the…
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…
Information is the basic concept of information theory. However, there is no definition of this concept that can encompass all uses of the term information in information theories and beyond. Many question a possibility of such a…
It is shown that the geometry of quantum theory can be derived from geometrical structure that may be considered more fundamental. The basic elements of this reconstruction of quantum theory are the natural metric on the space of…
In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…
Information geometry provides differential geometric concepts like a Riemannian metric, connections and covariant derivatives on spaces of probability distributions. We discuss here how these concepts apply to quantum field theories in the…
In this work, we study generalized entropies and information geometry in a group-theoretical framework. We explore the conditions that ensure the existence of some natural properties and at the same time of a group-theoretical structure for…
Information geometry is used to quantify the amount of information integration within multiple terminals of a causal dynamical system. Integrated information quantifies how much information is lost when a system is split into parts and…
To what extent can we distinguish one probability distribution from another? Are there quantitative measures of distinguishability? The goal of this tutorial is to approach such questions by introducing the notion of the "distance" between…
This paper is devoted to the mathematical study of some divergences based on the mutual information well-suited to categorical random vectors. These divergences are generalizations of the "entropy distance" and "information distance". Their…
In this paper a class of dynamical systems describing expectation variables exactly derived from continuous-time master equations is introduced and studied from the viewpoint of differential geometry, where such master equations consist of…
We describe a categorical approach to finite noncommutative geometries. Objects in the category are spectral triples, rather than unitary equivalence classes as in other approaches. This enables to treat fluctuations of the metric and…
We highlight the underlying category-theoretic structure of measures of information flow. We present an axiomatic framework in which communication systems are represented as morphisms, and information flow is characterized by its behavior…
As one type of incidence theory, the geometry of pentagram map seems quite classical at first. However, this is an excellent example of such a classical idea developed into a marvellous insight by some modern approach. We introduce an…
Perceptual geometry refers to the interdisciplinary research whose objectives focuses on study of geometry from the perspective of visual perception, and in turn, applies such geometric findings to the ecological study of vision. Perceptual…