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Technique in statistics
Information geometry is an interdisciplinary field that applies the techniques of differential geometry to study probability theory and statistics. It
Information_geometry
Posits ability to interpolate within latent manifolds
128–129. ISBN 978-1-61729-686-4. Caticha, Ariel (2015). Geometry from Information Geometry. MaxEnt 2015, the 35th International Workshop on Bayesian
Manifold_hypothesis
Branch of mathematics
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is
Geometry
Mathematical statistics distance measure
contrast to variation of information), and does not satisfy the triangle inequality. Instead, in terms of information geometry, it is a type of divergence
Kullback–Leibler_divergence
Japanese scholar (born 1936)
is a Japanese engineer and neuroscientist, known as a pioneer of information geometry and artificial intelligence. He majored in Mathematical Engineering
Shun'ichi_Amari
Notion in statistics
Observed information Fisher information metric Formation matrix Information geometry Jeffreys prior Cramér–Rao bound Minimum Fisher information Quantum
Fisher_information
Shape with three sides
three sides connected at three corners. It is one of the basic shapes in geometry and the simplest of polygons. The corners, also called vertices, are zero-dimensional
Triangle
Branch of mathematics
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.
Differential_geometry
Facts provided or learned about something or someone
broker Information continuum Information ecology Information engineering Information geometry Information inequity Information infrastructure Information management
Information
Metric on a smooth statistical manifold
In information geometry, the Fisher information metric is a particular Riemannian metric which can be defined on a smooth statistical manifold, i.e., a
Fisher_information_metric
Measure of difference between two points
In mathematics, specifically statistics and information geometry, a Bregman divergence or Bregman distance is a measure of difference between two points
Bregman_divergence
Geometric system used in thermodynamics
Ruppeiner geometry is thermodynamic geometry (a type of information geometry) using the language of Riemannian geometry to study thermodynamics. George
Ruppeiner_geometry
In information geometry, Chentsov's theorem states that the Fisher information metric is, up to rescaling, the unique Riemannian metric on a statistical
Chentsov's_theorem
Study of geometry using a coordinate system
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts
Analytic_geometry
2013 video game
Geometry Dash is a 2013 rhythm video game developed by Swedish game developer Robert Topala and published by his company RobTop Games. It was released
Geometry_Dash
French computer scientist and information geometer
computational and information geometry. He became an IEEE Fellow in 2026 for his "contributions to geometric information theory and information measures". He
Frank Nielsen (computer scientist)
Frank_Nielsen_(computer_scientist)
Number taken as representative of a list of numbers
notion of a "center" as minimizing variation can be generalized in information geometry as a distribution that minimizes divergence (a generalized distance)
Average
Computer markup language
representing vector geometry objects. A binary equivalent, known as well-known binary (WKB), is used to transfer and store the same information in a more compact
Well-known text representation of geometry
Well-known_text_representation_of_geometry
Skeletonized version of algebraic geometry
some geometric information about the original variety, it can be used to help prove and generalize classical results from algebraic geometry, such as the
Tropical_geometry
Mathematical model of the physical space
Euclidean geometry is a mathematical system attributed to Euclid, an ancient Greek mathematician, which he described in his textbook on geometry, Elements
Euclidean_geometry
Overview of and topical guide to geometry
geometry Information geometry Integral geometry Inversive geometry Inversive ring geometry Klein geometry Lie sphere geometry Non-Euclidean geometry Noncommutative
Outline_of_geometry
Function that measures dissimilarity between two probability distributions
In information geometry, a divergence is a kind of statistical distance: a binary function which establishes the separation from one probability distribution
Divergence_(statistics)
Branch of computer science
problems), geographic information systems (GIS) (geometrical location and search, route planning), integrated circuit design (IC geometry design and verification)
Computational_geometry
Theory within consciousness research
Shun-ichi (20 December 2016). "Unified framework for information integration based on information geometry". Proceedings of the National Academy of Sciences
Integrated_information_theory
Study of random spatial patterns
statistics Stochastic geometry models of wireless networks Mathematical morphology Information geometry Stochastic differential geometry Chayes, J. T.; Chayes
Stochastic_geometry
Generalization of the concept from statistical mechanics
provides a natural setting for the information geometry approach to information theory, where the Fisher information metric can be understood to be a correlation
Partition function (mathematics)
Partition_function_(mathematics)
Scientific study of digital information
Estimation theory Fisher information Information algebra Information asymmetry Information field theory Information geometry Information theory and measure
Information_theory
Type of manifold
Statistical manifolds provide a setting for the field of information geometry. The Fisher information metric provides a metric on these manifolds. Following
Statistical_manifold
Two geometries based on axioms closely related to those specifying Euclidean geometry
non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the
Non-Euclidean_geometry
Hungarian mathematical physicist and quantum information theorist (1953–2018)
statistical inference, quantum Fisher information, and the related concept of monotone metrics in quantum information geometry. He proposed the first quantum
Dénes_Petz
Relationship between two figures of the same shape and size, or mirroring each other
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the
Congruence_(geometry)
Branch of differential geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds. An example of a Riemannian manifold is a surface, on which
Riemannian_geometry
This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics. List of curves topics
List of differential geometry topics
List_of_differential_geometry_topics
Straight figure with zero width and depth
In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature. It is a special case of a curve
Line_(geometry)
Average uncertainty in variable's states
information Graph entropy Hamming distance History of entropy History of information theory Information fluctuation complexity Information geometry Kolmogorov–Sinai
Entropy_(information_theory)
Concept in information theory
the distributions in P. The I-projection is useful in setting up information geometry, notably because of the following inequality, valid when P is convex:
Information_projection
Aspect of theoretical physics
Quantum geometry in condensed matter physics refers to gauge-invariant geometric properties of quantum states as functions of external parameters—most
Quantum geometry (condensed matter)
Quantum_geometry_(condensed_matter)
British applied mathematician and physicist
thermodynamics and quantum mechanics in another. Brody's work has covered information geometry and geometric quantum theory as well as foundational issues in quantum
Dorje_C._Brody
Riemannian metric on the space of mixed states of a quantum system
In mathematics, in the area of quantum information geometry, the Bures metric (named after Donald Bures) or Helstrom metric (named after Carl W. Helstrom)
Bures_metric
Data and information having an implicit or explicit association with a location
and multi-temporal data. Spatial data or spatial information is a broader class of data whose geometry is relevant but it is not necessarily georeferenced
Geographic data and information
Geographic_data_and_information
Branch of mathematics
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems
Algebraic_geometry
Geometry of the surface of a sphere
Spherical geometry or spherics (from Ancient Greek σφαιρικά) is the geometry of the two-dimensional surface of a sphere or the n-dimensional surface of
Spherical_geometry
Field of scientific study
a change is called a thermodynamic process. Ruppeiner geometry is a type of information geometry used to study thermodynamics. It claims that thermodynamic
Equilibrium_thermodynamics
Concept in statistical science
WAIC", in Ay, Nihat; Gibilisco, Paolo; Matúš, František (eds.), Information Geometry and Its Applications, vol. 252, Cham: Springer International Publishing
Widely applicable information criterion
Widely_applicable_information_criterion
Point where two or more curves, lines, or edges meet
In geometry, a vertex (pl.: vertices or vertexes), also called a corner, is a point where two or more curves, lines, or line segments meet or intersect
Vertex_(geometry)
Professor of theoretical physics
Mechanics and General Relativity), Entropic and Bayesian Inference, and Information Geometry. Ph.D. California Institute of Technology B.Sc. and M.Sc. UNICAMP
Ariel_Caticha
Branch of mathematics
Noncommutative geometry (NCG) is a branch of mathematics that studies geometric ideas through noncommutative algebras. In ordinary geometry, a space can
Noncommutative_geometry
Biometric identification
Hand geometry is a biometric that identifies users from the shape of their hands. Hand geometry readers measure a user's palm and fingers along many dimensions
Hand_geometry
XML grammar for geographical features
specific schemas or application languages. These primitives include: Feature Geometry Coordinate reference system Topology Time Dynamic feature Coverage (including
Geography_Markup_Language
name of Ricci calculus Absolute geometry Also called neutral geometry, a synthetic geometry similar to Euclidean geometry but without the parallel postulate
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Theory in number theory
number theory, algebraic geometry, and low-dimensional topology. The "anabelian question" has been formulated as How much information about the isomorphism
Anabelian_geometry
Separation between two points
similar objects. This page gives a few examples. In statistics and information geometry, statistical distances measure the degree of difference between two
Distance
Russian mathematician (1930–1992)
important contributions to stochastic processes, convergence theory and information geometry. Chentsov was born in Moscow and showed an early interest in mathematics
Nikolai_Chentsov
Mathematics journal
"Editorial board", Journal of Geometry, Springer Science+Business Media, retrieved 2023-06-02 "Journal of Geometry", MIAR: Information Matrix for the Analysis
Journal_of_Geometry
Field in mathematics
inverse problems. Inverse problems seek to identify features of the geometry from information about the eigenvalues of the Laplacian. One of the earliest results
Spectral_geometry
Set of mathematical concepts in quantum gravity
In quantum gravity, quantum geometry is the set of mathematical concepts that generalize geometry to describe physical phenomena at distance scales comparable
Quantum_geometry
Type of program in computer graphics
pipeline. Geometry shader programs are executed after vertex shaders. They take as input a whole primitive, possibly with adjacency information. For example
Shader
Straight path on a curved surface or a Riemannian manifold
In geometry, a geodesic (/ˌdʒiː.əˈdɛsɪk, -oʊ-, -ˈdiːsɪk, -zɪk/) is a curve representing in some sense the locally shortest path (arc) between two points
Geodesic
Numerical algebraic geometry is a field of computational mathematics, particularly computational algebraic geometry, which uses methods from numerical
Numerical_algebraic_geometry
Application of geometry in number theory
fundamental information on algebraic numbers. Hermann Minkowski (1896) initiated this line of research at the age of 26 in his work The Geometry of Numbers
Geometry_of_numbers
Probability distribution of random variable
geometric distribution (called the Chernoff point in information geometry) induced by the Chernoff information. Groeneboom, Lalley and Temme state that the first
Chernoff's_distribution
Model parameters in mathematical finance
sensitivities can be interpreted as spreads in expected returns. Information geometry offers another (trigonometric) interpretation. Gamma, Γ {\displaystyle
Greeks_(finance)
Generalization of centroids to metric spaces
1007/BF01214029. Nielsen, Frank; Bhatia, Rajendra (2012), Matrix Information Geometry, Springer, p. 171, ISBN 9783642302329. Nielsen & Bhatia (2012), p
Fréchet_mean
Length of a line segment
ancient Greek mathematicians Euclid and Pythagoras. In the Greek deductive geometry exemplified by Euclid's Elements, distances were not represented as numbers
Euclidean_distance
Danish statistician (1935–2022)
Generalized inverse Gaussian distribution Hyperbolic distribution Information geometry List of mathematicians Kaarsted, Tage; Alfred Larsen, eds. (1963)
Ole_Barndorff-Nielsen
Geometric system with a finite number of points
A finite geometry is any geometric system that has only a finite number of points. The familiar Euclidean geometry is not finite, because a Euclidean
Finite_geometry
Historical development of geometry
Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") arose as the field of knowledge dealing with spatial relationships. Geometry
History_of_geometry
Smooth approximation to the maximum function
Networks for Visual Recognition. Nielsen, Frank; Hadjeres, Gaetan (2018). "Monte Carlo Information Geometry: The dually flat case". arXiv:1803.07225 [cs.LG].
LogSumExp
Ancient Greek mathematician (fl. 300 BC)
Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated
Euclid
System to capture, manage, and present geographic data
software or information technology architectures. One example is a spatial extension to Object-relational database software, which defines a geometry datatype
Geographic_information_system
Type of technical drawing used to define requirements for engineered items
drawing is a type of technical drawing. A common use is to specify the geometry necessary for the construction of a component and is called a detail drawing
Engineering_drawing
Russian mathematician (born 1966)
for his contributions to the fields of geometric analysis, Riemannian geometry, and geometric topology. In 2005, Perelman resigned from his research post
Grigori_Perelman
Property of a mathematical space
back to René Descartes, substantial development of a higher-dimensional geometry only began in the 19th century, via the work of Arthur Cayley, William
Dimension
Area of research
Institutions Geometric Modeling and Industrial Geometry Städelschule Architecture Class SIAL - The Spatial Information Architecture Laboratory Companies Evolute
Architectural_geometry
Irish theoretical physicist
1038/s41567-025-03144-9. Bettmann, Laetitia P.; Goold, John (2025-01-20). "Information geometry approach to quantum stochastic thermodynamics". Physical Review E
John_Goold_(physicist)
Bayesian diagnostic threshold derived from the geometry of screening curves
value of disease prevalence, or pre-test probability, associated with the geometry of the curve that maps prior probability to positive predictive value for
Prevalence_threshold
Geospatial vector data format
format with a wide variety of software. The shapefile format stores the geometry as primitive geometric shapes like points, lines, and polygons. These shapes
Shapefile
Academic journal
geometry: in computer graphics, pattern recognition, image processing, robotics, electronic design automation, CAD/CAM, and geographical information systems
Computational Geometry (journal)
Computational_Geometry_(journal)
Dutch computer scientist
seminal monograph Information Retrieval and of the textbook The Geometry of Information Retrieval. He was born in Rotterdam, and educated in the Netherlands
C._J._van_Rijsbergen
Mathematics of varieties with integer coordinates
geometry. The extensive development of algebraic geometry in the 20th century produced powerful tools to study these equations. Diophantine geometry is
Diophantine_geometry
Area of mathematics
Discrete differential geometry is the study of discrete counterparts of notions in differential geometry. Instead of smooth curves and surfaces, there
Discrete differential geometry
Discrete_differential_geometry
Branch of mathematics
Asymptotic geometry, also known as asymptotic geometric analysis or high-dimensional geometry, is a field of mathematics that investigates the geometric
Asymptotic_geometry
In geometry, a slab is a region between two parallel lines in the Euclidean plane, or between two parallel planes in three-dimensional Euclidean space
Slab_(geometry)
Branch of geometry
In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying
Contact_geometry
Property of objects which are scaled or mirrored versions of each other
In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. More precisely
Similarity_(geometry)
German mathematician (born 1956)
Jürgen Jost (born 9 June 1956) is a German mathematician specializing in geometry. He has been a director of the Max Planck Institute for Mathematics in
Jürgen_Jost
Branch of algebraic geometry concerned with counting solutions
In mathematics, enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions, mainly by
Enumerative_geometry
Peak or top of a geometric figure
In geometry, an apex (pl.: apices) is the vertex which is in some sense the "highest" of the figure to which it belongs. The term is typically used to
Apex_(geometry)
Study of the 3D shapes of molecules
molecular geometry can be determined by various spectroscopic methods and diffraction methods. IR, microwave and Raman spectroscopy can give information about
Molecular_geometry
mathematics, a web permits an intrinsic characterization in terms of Riemannian geometry of the additive separation of variables in the Hamilton–Jacobi equation
Web_(differential_geometry)
Mathematical treatise by Euclid
Sinclair, Nathalie (2008). The History of the Geometry Curriculum in the United States. Information Age Publishing. ISBN 9781607527305. Siu, Man-Keung
Euclid's_Elements
Field of knowledge
properties), algebra (the study of operations and the structures they form), geometry (the study of shapes and spaces that contain them), analysis (the quantitative
Mathematics
Mathematical abstraction of objects being "visible"
In geometry, visibility is a mathematical abstraction of the real-life notion of visibility. Given a set of obstacles in the Euclidean space, two points
Visibility_(geometry)
Branch of algebraic geometry
arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around
Arithmetic_geometry
Mathematician
the differential geometric approach to statistics, also related to information geometry. This work was part of Brigo's Ph.D. studies, appearing in his Ph
Damiano_Brigo
Cylinder with hemispherical ends
This elementary geometry-related article is a stub. You can help Wikipedia by adding missing information.
Capsule_(geometry)
Non-informative prior distribution
partial differential equation involving the Fisher information. Using tools from information geometry, the Jeffreys prior can be generalized in pursuit
Jeffreys_prior
Battery-powered mid-size sedan produced by Chinese auto brand Geometry
The Geometry C is a battery electric compact crossover SUV produced by Chinese manufacturer Geely Auto under the Geometry brand. The Geometry C is the
Geometry_C
symplectic geometry in mathematics. The terms listed here cover the occurrences of symplectic geometry both in topology as well as in algebraic geometry (over
Glossary of symplectic geometry
Glossary_of_symplectic_geometry
Form of an object
properties, such as color, texture, or material type. In geometry, shape excludes information about the object's position, size, orientation and chirality
Shape
travel, tourism, insurance
INFORMATION GEOMETRY
INFORMATION GEOMETRY
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INFORMATION GEOMETRY
INFORMATION GEOMETRY
INFORMATION GEOMETRY
INFORMATION GEOMETRY
INFORMATION GEOMETRY
INFORMATION GEOMETRY
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