All articles starting with G

Gaussian filter

A Gaussian filter is a filter whose impulse response is a Gaussian function, used in signal processing as a low-pass smoothing filter with no overshoot.

Gaussian filtering

Gaussian filtering is a signal and image processing method that smooths data and suppresses noise by convolving it with a Gaussian kernel, at the cost of blurring fine detail.

Gaussian free field

The Gaussian free field is a centered Gaussian random field with covariance given by the Laplacian's Green function, described as a higher-dimensional analog of Brownian motion.

Gaussian function

The Gaussian function, also known as the Gaussian curve, is a function whose graph is a symmetric bell-shaped curve that falls off rapidly, named after Carl Friedrich Gauss.

Gaussian graphical model

A Gaussian graphical model, or covariance selection model, is a probabilistic graphical model for Gaussian variables whose graph edges correspond to nonzero entries of the inverse covariance matrix.

Gaussian integer

A Gaussian integer, also known as a complex integer, is a complex number a + bi where a and b are ordinary integers, named for Carl Friedrich Gauss.

Gaussian integral

The Gaussian integral, also known as the Euler-Poisson integral, is the integral of the Gaussian function over the whole real line, equal to the square root of pi.

Gaussian isoperimetric inequality

The Gaussian isoperimetric inequality, proven independently by Sudakov and Tsirelson and by Borell in the 1970s, states that half-spaces minimize Gaussian perimeter among sets of given measure, implying Gaussian concentration.

Gaussian Markov process

A Gaussian Markov process is a stochastic process that is both Gaussian and Markov, so its future depends only on its present value; examples include Brownian motion and the Ornstein–Uhlenbeck process.

Gaussian measure

A Gaussian measure is a probability measure on an infinite-dimensional space, such as a Banach or Hilbert space, where every continuous linear functional is a Gaussian random variable.

Gaussian mixture model

A Gaussian mixture model is a probabilistic model representing data as a weighted sum of Gaussian distributions, used for soft clustering and fitted with the EM algorithm.

Gaussian orthogonal ensemble

The Gaussian orthogonal ensemble (GOE) is a probability distribution on real symmetric matrices whose law is invariant under conjugation by orthogonal matrices, introduced by Eugene Wigner for nuclear level statistics.

Gaussian prime

A Gaussian prime is a Gaussian integer like 1 + i or 3 that cannot be factored except by units, classified by Carl Friedrich Gauss in 1832.

Gaussian process

A Gaussian process, also called a Gaussian stochastic process, is a stochastic process where every finite subset of variables has a joint multivariate Gaussian distribution.

Gaussian process regression

Gaussian process regression, developed in geostatistics as kriging, is a Bayesian method that places a Gaussian process prior over functions and predicts with calibrated uncertainty.

Gaussian quadrature

Gaussian quadrature, also called Gaussian integration, is a numerical integration method introduced by Carl Friedrich Gauss in 1814, exact for polynomials of degree 2n − 1 with n nodes.

Gaussian random field

A Gaussian random field is a collection of random variables over space where every finite set follows a normal distribution, the standard model of spatial uncertainty.

Gaussian Robotics (高仙机器人)

Gaussian Robotics (高仙机器人) is a Shanghai company founded in 2013 that makes autonomous commercial cleaning robots, sold abroad as Gausium; SoftBank co-led its $188 million Series C in 2021.

Gaussian Schell model

The Gaussian Schell model is a statistical model of partially coherent light beams in which intensity and spatial coherence follow Gaussian functions, used in free-space optical communication.

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.