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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
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
Notion in statistics
Observed information Fisher information metric Formation matrix Information geometry Jeffreys prior Cramér–Rao bound Minimum Fisher information Quantum
Fisher_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
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
Japanese scholar (born 1936)
neuroscientist born in 1936 in Tokyo, Japan. He was a pioneer in information geometry and artificial intelligence. He majored in Mathematical Engineering
Shun'ichi_Amari
Facts provided or learned about something or someone
broker Information continuum Information ecology Information engineering Information geometry Information inequity Information infrastructure Information management
Information
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
2013 video game
Geometry Dash is a 2013 side-scrolling rhythm platform video game developed by Swedish game developer Robert Topala and published by his company RobTop
Geometry_Dash
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
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
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
Shape with three sides
polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero-dimensional points while the
Triangle
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
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
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
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
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
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
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)
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
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
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)
Scientific study of digital information
Estimation theory Fisher information Information algebra Information asymmetry Information field theory Information geometry Information theory and measure
Information_theory
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
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)
Statistical value representing the center or average of a distribution
notion of a "center" as minimizing variation can be generalized in information geometry as a distribution that minimizes divergence (a generalized distance)
Central_tendency
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)
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)
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
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
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
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
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
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
Generalized version of the Akaike information criterion
WAIC", in Ay, Nihat; Gibilisco, Paolo; Matúš, František (eds.), Information Geometry and Its Applications, vol. 252, Cham: Springer International Publishing
Watanabe–Akaike information criterion
Watanabe–Akaike_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)
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
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
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
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
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
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)
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
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
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
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
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
Data and information having an implicit or explicit association with a location
and multi-temporal data. Spatial data or spatial information is broader class of data whose geometry is relevant but it is not necessarily georeferenced
Geographic data and information
Geographic_data_and_information
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)
Cylinder with hemispherical ends
This elementary geometry-related article is a stub. You can help Wikipedia by adding missing information.
Capsule_(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
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
Area of research
Institutions Geometric Modeling and Industrial Geometry Städelschule Architecture Class SIAL - The Spatial Information Architecture Laboratory Companies Evolute
Architectural_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
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
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
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
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
Numerical algebraic geometry is a field of computational mathematics, particularly computational algebraic geometry, which uses methods from numerical
Numerical_algebraic_geometry
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
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)
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
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
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
Littlewood–Offord problem Inclusion–exclusion principle Impossible event Information geometry Talagrand's concentration inequality Probability theory Probability
List_of_probability_topics
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
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
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
Danish statistician (1935–2022)
Generalized inverse Gaussian distribution Hyperbolic distribution Information geometry List of mathematicians "Creates". Barndorff-Nielsen, Ole. 1984. Blown
Ole_Barndorff-Nielsen
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
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
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
Mathematical treatise by Euclid
and theorems with their proofs that covers plane and solid Euclidean geometry, elementary number theory, and incommensurability. These include the Pythagorean
Euclid's_Elements
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
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
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
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
Academic journal
Journal of Geometry and Physics is a scientific journal in mathematical physics. Its scope is to stimulate the interaction between geometry and physics
Journal of Geometry and Physics
Journal_of_Geometry_and_Physics
Artificial intelligence (AI) program
AlphaGeometry is an artificial intelligence (AI) program that can solve hard problems in Euclidean geometry. The system comprises a data-driven large language
AlphaGeometry
Mathematician
mathematical finance, filtering theory, stochastic analysis with differential geometry, probability theory and statistics, authoring more than 130 research publications
Damiano_Brigo
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)
Generalization of the standard Boltzmann–Gibbs entropy
q-exponential function have been widely explored in statistical physics and information geometry. In the machine learning literature, the q-exponential family has
Tsallis_entropy
Technique used in realtime rendering
In real-time computer graphics, geometry instancing is the practice of rendering multiple copies of the same mesh in a scene at once. This technique is
Geometry_instancing
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
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
Chinese/British statistician (born 1944)
model selection, likelihood-free statistics, gradient-based entropy, information geometry and other areas. Commenting on Howell Tong's contributions to nonlinear
Howell_Tong
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)
Geometric space with four dimensions
ordinary space is called Euclidean space because it corresponds to Euclid's geometry, which was originally abstracted from the spatial experiences of everyday
Four-dimensional_space
Theorem about orthocenter and polars in circle geometry
known as Brocard's theorem) is a theorem on poles and polars in projective geometry commonly used in Olympiad mathematics. It is named after French mathematician
Brokard's_theorem
de facto standard for handling much of the so-called observation geometry information on NASA's planetary missions, and it is now widely used in support
SPICE (observation geometry system)
SPICE_(observation_geometry_system)
Concept in mathematics
Bregman divergence. Mirror descent is related to natural gradient in information geometry and Riemannian gradient descent. Mirror descent in the online optimization
Mirror_descent
Interactive geometry software
Cabri Geometry is a commercial interactive geometry software produced by the French company Cabrilog for teaching and learning geometry and trigonometry
Cabri_Geometry
Points and lines with equal incidences
In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such
Configuration_(geometry)
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
Mathematical linear code
Algebraic geometry codes, often abbreviated AG codes, are a type of linear code that generalize Reed–Solomon codes. The Russian mathematician V. D. Goppa
Algebraic_geometry_code
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
general mathematical disciplines such as geometry, probability theory, stochastic processes, queueing theory, information theory, and Fourier analysis. In the
Stochastic geometry models of wireless networks
Stochastic_geometry_models_of_wireless_networks
INFORMATION GEOMETRY
INFORMATION GEOMETRY
Girl/Female
Arabic, Bengali, Gujarati, Hindu, Indian, Kannada, Marathi, Muslim, Mythological, Sanskrit, Tamil, Telugu
Maiden; Without Any Deformation; Wife of Gautam Rishi; A Woman who was Saved by Lord Rama
Surname or Lastname
English
English : nickname for a Roman Catholic, a comparatively late formation. Most surnames originated before the Reformation, with its schism between the Roman Catholic and Protestant Churches.
Girl/Female
Indian, Telugu
Formation of Stars
Girl/Female
Indian, Telugu
Good Information
Girl/Female
Indian
Knowledge; Information; Experience; Thought
Surname or Lastname
Jewish (Ashkenazic)
Jewish (Ashkenazic) : metronymic from the Yiddish female personal name brayne (a back formation of the Yiddish female personal name brayndl, which is a diminutive of Yiddish broyn ‘brown’) + the genitive ending -s.English : variant of Brine.
Girl/Female
British, Christian, English
Temperance; One of the Qualities Adopted as a First Name by the Puritans After the Reformation; Moderation; Self Restraint
Girl/Female
Indian, Marathi
Information; News
Boy/Male
Gujarati, Indian
Musical Instrument; Used in Medieval Time to Gather People for Informantion
Boy/Male
Hindu, Indian, Sanskrit
Address; Information
Surname or Lastname
English (Northumberland and Durham)
English (Northumberland and Durham) : unexplained; just possibly a late formation from the plant name, although tulips were not introduced into western Europe until the 16th century.
Girl/Female
Australian, British, Christian, English, Latin
Prudence; One of the Many Qualities and Virtues that the Puritans Adopted as Names After the Reformation; Caution; Discretion; Diminutive of Prudence; Cautious
Surname or Lastname
English
English : unexplained; perhaps from either of two medicinal and edible plants commonly known by this name (Arctium lappa and A. minus). However, the word is not recorded in OED before 1597, rather too late for surname formation.
Girl/Female
Gujarati, Hindu, Indian, Kannada, Marathi, Tamil, Telugu
One Star; Formation of Stars; Modern; Name of a Bright Star; Nakshaktra
Girl/Female
Indian, Tamil
Formation of Stars
Boy/Male
Indian
Information on Origin
Girl/Female
American, Australian, British, Chinese, Christian, English, French, German, Latin, Shakespearean
To Endure; Patience; One of the Many Qualities and Virtues that the Puritans Adopted as Names After the Reformation; Enduring; To Suffer
Girl/Female
English
Temperance. One of the qualities adopted as a first name by the Puritans after the Reformation.
Girl/Female
Gujarati, Hindu, Indian, Telugu
Information
Boy/Male
Hindu, Indian, Marathi
Information
INFORMATION GEOMETRY
INFORMATION GEOMETRY
Boy/Male
Arabic, Muslim
Worshipper
Girl/Female
Australian, British, English
Garden of Heaven
Girl/Female
African, Australian, Swahili
Peace; Safety; Unharmed
Girl/Female
Hindu, Indian, Malayalam, Tamil
Prosperous
Girl/Female
Indian
Goddess Durga
Female
Babylonian
, wife of Merodach; she is the Succoth-benoth of the Bible.
Female
English
Variant spelling of English Erin, ARIN means "Ireland." Compare with masculine Arin.
Boy/Male
Tamil
Sugunesh | ஸà¯à®•à¯à®¨à¯‡à®·
Girl/Female
American, Australian
Grace by the Lake
Boy/Male
Tamil
Gourishankar | கௌரீஷஂகர
Peak of the himalayas, Mt everest
INFORMATION GEOMETRY
INFORMATION GEOMETRY
INFORMATION GEOMETRY
INFORMATION GEOMETRY
INFORMATION GEOMETRY
n.
Precept; information; teachings.
n.
The act of forming anew; a second forming in order; as, the reformation of a column of troops into a hollow square.
n.
Notification; information; intelligence.
n.
Notice; information.
n.
The act of reforming, or the state of being reformed; change from worse to better; correction or amendment of life, manners, or of anything vicious or corrupt; as, the reformation of manners; reformation of the age; reformation of abuses.
n.
The manner in which a thing is formed; structure; construction; conformation; form; as, the peculiar formation of the heart.
n.
The information so acquired.
n.
Ill formation; irregular or anomalous formation; abnormal or wrong conformation or structure.
n.
Information; advice.
v. t.
The act of informing, or communicating knowledge or intelligence.
n.
Discovery made; information.
v. t.
A proceeding in the nature of a prosecution for some offens against the government, instituted and prosecuted, really or nominally, by some authorized public officer on behalt of the government. It differs from an indictment in criminal cases chiefly in not being based on the finding of a grand juri. See Indictment.
n.
Counsel; advice; information.
v. t.
News, advice, or knowledge, communicated by others or obtained by personal study and investigation; intelligence; knowledge derived from reading, observation, or instruction.
n.
The information communicated.
n.
Specifically (Eccl. Hist.), the important religious movement commenced by Luther early in the sixteenth century, which resulted in the formation of the various Protestant churches.
n.
Mineral deposits and rock masses designated with reference to their origin; as, the siliceous formation about geysers; alluvial formations; marine formations.
n.
A group of beds of the same age or period; as, the Eocene formation.
n.
Wrong information; misinformation.
n.
Intelligence; information.