6,052 articles
Variational autoencoder
A variational autoencoder, or VAE, is a deep generative model introduced by Diederik P. Kingma and Max Welling in their December 2013 paper "Auto-Encoding Variational Bayes."
Variational Bayesian inference
Variational Bayesian inference (VI) approximates an intractable posterior distribution by optimization, maximizing the ELBO to find the closest density in KL divergence; it is faster than MCMC but generally underestimates posterior variance.
Variational Bayesian methods
Variational Bayesian methods, also called variational Bayes or variational inference, approximate intractable Bayesian posteriors by optimization, typically maximizing the evidence lower bound as a faster alternative to MCMC sampling.
Variational iteration method
The variational iteration method (VIM) is a semi-analytical technique for solving nonlinear differential and integral equations, introduced by Jihuan He in 1997, needing no linearization or small parameters.
Variety (universal algebra)
In universal algebra, a variety, also known as an equational class, is a class of algebras defined by identities; Birkhoff introduced the concept in 1935.
Varimax rotation
Varimax rotation is an orthogonal rotation method in factor analysis, introduced by Henry F. Kaiser in 1958, that maximizes the variance of squared loadings to simplify factors.
Variogram
The variogram is a function in spatial statistics that measures how dissimilar pairs of values of a random field become as the distance between their locations increases.
Varying coefficient model
A varying coefficient model is a regression method where coefficients vary smoothly with a covariate such as time, credited to Hastie and Tibshirani's 1993 paper.
VC dimension
The Vapnik–Chervonenkis (VC) dimension is a measure of the complexity of a family of sets: the largest number of points on which the family realizes every possible labeling.
Vector
A vector is a quantity characterized by magnitude and direction, such as displacement, velocity, or electric field strength, defined in modern mathematics as an element of a vector space.
Vector (mathematics and physics)
In mathematics and physics, a vector, also called a physical vector, is an object with magnitude and direction, representing displacement, velocity, force, and torque, and in mathematics an element of a vector space.
Vector bundle
A vector bundle is a family of vector spaces attached to a base space, glued locally like a product; the tangent bundle of a manifold is the standard example.
Vector calculus
Vector calculus, also called vector analysis, studies vector fields through the gradient, divergence, and curl operators, and is the standard language of mechanics, electromagnetism, and fluid dynamics.
Vector calculus identities
Vector calculus identities, also known as vector identities, are equations relating the gradient, divergence, and curl, used as algebraic shortcuts in electromagnetism, fluid mechanics, and other field theories.
Vector field
A vector field, also called a vector point function, assigns a tangent vector to every point of a space, used for velocities, forces, and electric and magnetic fields.
Vector notation
Vector notation is the conventions for representing vectors in writing, most commonly a bold letter in print or an arrow above the letter in handwritten work.
Vector projection
Vector projection, also called perpendicular projection, is the linear-algebra operation that gives the component of a vector along a direction or subspace, computed with the dot product and underlying least squares.
Vector space
A vector space, also called a linear space, is a set of vectors that can be added together and multiplied by scalars, forming the central structure of linear algebra.
Vectorization (mathematics)
Vectorization, written vec, is the linear-algebra operation that stacks a matrix's columns into a single column vector, connecting matrix algebra to ordinary vector calculus.
Vedic Mathematics
Vedic Mathematics is a system of mental calculation set out in a 1965 book by Bharati Krishna Tirtha, built on 16 Sanskrit sutras of disputed Vedic origin.
Venn diagram
A Venn diagram, also called a set diagram, represents sets as overlapping closed curves that divide the plane into all 2^n possible intersections; John Venn named and defined it in 1880.
Verlet integration
Verlet integration, also called Störmer's method, is a numerical method for solving Newton's equations of motion introduced by the French physicist Loup Verlet in 1967 for molecular dynamics simulations.
Verma module
A Verma module is an infinite-dimensional highest-weight module for a complex semisimple Lie algebra, induced from a Borel subalgebra; Daya-Nand Verma introduced it in 1966.
Vertex (geometry)
A vertex (plural: vertices) is a point where two or more curves, lines, edges, or rays meet, such as the corner of a polygon, the point of a cone, or the sides of an angle.
Vertex (graph theory)
In graph theory, a vertex (plural vertices), also called a node, is one of the discrete objects connected pairwise by edges that a graph is built from.
Vertex coloring
Vertex coloring is a graph algorithm assigning colors to vertices so adjacent vertices differ, minimizing colors used; it is NP-complete and models scheduling, register allocation, and frequency assignment.
Vertex connectivity
Vertex connectivity (also called node connectivity) is the minimum number of vertices whose removal disconnects a graph, the standard measure of network robustness against node failures.
Vertex cover
A vertex cover, also called a node cover, is a set of graph vertices containing at least one endpoint of every edge; finding a minimum one is NP-complete.
Vertex enumeration problem
The vertex enumeration problem is the computational problem of listing all vertices of a convex polyhedron described by linear inequalities, converting its H-representation to a vertex list.
Vertex operator algebra
A vertex operator algebra, also called a vertex algebra, is an algebraic structure axiomatized by Richard Borcherds in 1986 that encodes the operator products of two-dimensional conformal field theory.