6,052 articles
Gaussian simulation
Gaussian simulation is a computational method that generates samples from Gaussian distributions, multivariate normal vectors, and Gaussian process realizations, typically by transforming independent standard normal draws to match a required mean and covariance.
Gaussian symplectic ensemble
The Gaussian symplectic ensemble (GSE) is a random matrix ensemble introduced by Freeman Dyson in 1962 for quantum systems with time-reversal invariance but no rotational symmetry.
GCD domain
A GCD domain, also known as an HCF domain, is an integral domain in which every pair of elements has a greatest common divisor, a generalization of unique factorization domains.
Gegenbauer polynomials
Gegenbauer polynomials, also called ultraspherical polynomials, are classical orthogonal polynomials on (-1,1), introduced by Leopold Gegenbauer in 1875, generalizing the Legendre polynomials and arising as zonal spherical harmonics.
Gelfand representation
The Gelfand representation, also called the Gelfand transform or Gelfand duality, sends each element of a commutative Banach algebra to a function on its character space, introduced by Gelfand in 1941.
Gelfand–Naimark theorem
The Gelfand–Naimark theorem, also called the Gelfand–Naimark representation theorem, is a 1943 result stating that every commutative C-algebra is a function algebra C₀(X) and every C-algebra is a -algebra of bounded operators on a Hilbert space.
Gelfand–Naimark–Segal construction
The Gelfand–Naimark–Segal construction, also called the GNS construction or GNS theorem, converts a state on a C-algebra into a Hilbert-space representation with a cyclic vector, a correspondence Segal completed in 1947.
Gelfond's constant
Gelfond's constant is the transcendental number e^π, approximately 23.1407, proven transcendental in 1934 by Aleksandr Gelfond and independently by Theodor Schneider in 1935, settling Hilbert's seventh problem.
Gen (probabilistic programming system)
Gen is an open-source probabilistic programming system embedded in the Julia language, introduced by MIT researchers at PLDI in 2019 and known for programmable inference, which lets users write custom inference algorithms as ordinary Julia programs.
General Dirichlet series
A general Dirichlet series is a series of the form sum a_n e^{-lambda_n s} that generalizes ordinary Dirichlet series and power series through a chosen frequency sequence.
General linear group
The general linear group GL_n(R) is the group of all invertible n by n matrices over a ring R, forming a group under matrix multiplication.
General linear model
The general linear model, or multivariate linear regression, is the statistical framework Y = Xβ + ε that underlies t-tests, ANOVA, ANCOVA, and regression, estimated by ordinary least squares.
General number field sieve
The general number field sieve (GNFS) is the fastest known classical algorithm for factoring arbitrary large integers, generalized by Buhler, Lenstra, and Pomerance in 1993 and used for RSA-250.
General recursive function
A general recursive function, also called a μ-recursive or partial recursive function, is built from basic functions using composition, primitive recursion, and unbounded minimization, formalizing effective computability.
General theory of Banach algebras
The general theory of Banach algebras, which began in 1941, examines complete normed algebras with submultiplicative norms. It details concepts like closed ideals, quotients, and the Gelfand transform.
Generalizability theory
Generalizability theory is a statistical framework that estimates the reliability of measurements by separating multiple sources of error, introduced by Cronbach, Rajaratnam, and Gleser in 1963.
Generalization
Generalization is extending a finding from the studied sample to a broader population, a component of external validity in research and a key goal in machine learning.
Generalizations of Fibonacci numbers
Generalizations of Fibonacci numbers, including the k-bonacci or k-step Fibonacci numbers, are integer sequences that extend the Fibonacci recurrence by summing more preceding terms, giving tribonacci and tetranacci numbers.
Generalized additive model
A generalized additive model (GAM) is a regression model in which each covariate enters through a smooth function estimated from the data, introduced by Hastie and Tibshirani in 1986.
Generalized Approximate Message Passing
Generalized approximate message passing (GAMP) is an iterative Bayesian estimation algorithm introduced by Sundeep Rangan in 2010 that recovers signals through linear transforms, widely used in compressed sensing.
Generalized Cartan matrix
A generalized Cartan matrix, plural Cartan matrices, is a square integer matrix with diagonal entries 2 and non-positive off-diagonal entries; each one determines a Kac-Moody Lie algebra.
Generalized continuum hypothesis
The generalized continuum hypothesis (GCH) is the set-theoretic statement that each infinite cardinal's power set has the next larger cardinality; Gödel and Cohen proved it independent of ZFC.
Generalized cross-validation
Generalized cross-validation (GCV) is a criterion for choosing a smoothing or regularization parameter in linear models, introduced by Craven and Wahba in 1979 and computable from a single fit without retraining.
Generalized eigenvector
A generalized eigenvector of a matrix A is a nonzero vector v with (A − λI)^p v = 0 for some p; ordinary eigenvectors are the case p = 1.
Generalized estimating equation
A generalized estimating equation (GEE) is a statistical method for estimating regression coefficients when observations are correlated, as in repeated measurements, introduced by Liang and Zeger in 1986.
Generalized estimating equations
Generalized estimating equations (GEE) is a statistical method introduced by Liang and Zeger in 1986 for fitting regression models to correlated or longitudinal data, robust to misspecified within-cluster correlation.
Generalized extreme value distribution
The generalized extreme value (GEV) distribution is a three-parameter family of probability distributions that models the largest value in blocks, such as annual maxima of floods.
Generalized Kac–Moody algebra
A generalized Kac–Moody algebra, also called a Borcherds or BKM algebra, is an infinite-dimensional Lie algebra introduced by Richard Borcherds in 1988, generalizing Kac–Moody algebras by allowing imaginary simple roots.
Generalized least squares
Generalized least squares (GLS) is a method for estimating linear regression coefficients when errors are correlated or have unequal variance, introduced by A. T. Aitken in 1935.
Generalized likelihood ratio test
The generalized likelihood ratio test (GLRT) is a statistical hypothesis test that compares maximized likelihoods under null and alternative models, calibrated by Wilks' chi-square theorem.