In physics and mathematics, a random field is a random function over an arbitrary domain (usually a multi-dimensional space such as R n {\displaystyle...

physics and probability, a Markov random field (MRF), Markov network or undirected graphical model is a set of random variables having a Markov property...

In statistics, a Gaussian random field (GRF) is a random field involving Gaussian probability density functions of the variables. A one-dimensional GRF...

Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured...

theory and related fields, a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random variables in a probability...

functions, processes, fields, series, transformations, and also sets or collections of sets.” The modern-day usage of “random element” frequently assumes...

are nowhere differentiable. Random fields are indexed sets of random variables; a continuous random field is a random field that has a set of functions...

statistics and related fields, a Poisson point process (also known as: Poisson random measure, Poisson random point field and Poisson point field) is a type of...

and information entropy. The fields of mathematics, probability, and statistics use formal definitions of randomness, typically assuming that there...

by a Markov network (also known as a Markov random field). It is the fundamental theorem of random fields. It states that a probability distribution that...

Random forests or random decision forests is an ensemble learning method for classification, regression and other tasks that works by creating a multitude...

case of a random field on a lattice. The idea of a Gibbs measure is, however, much more general than this. The definition of a Gibbs random field on a lattice...

a Markov random field, each state depends on its neighbors in any of multiple directions. A Markov random field may be visualized as a field or graph...

hidden Markov random field is a generalization of a hidden Markov model. Instead of having an underlying Markov chain, hidden Markov random fields have an underlying...

function is defined is a time interval (time series) or a region of space (random field). Familiar examples of time series include stock market and exchange...

statistical mechanics, the Gaussian free field (GFF) is a Gaussian random field, a central model of random surfaces (random height functions). The discrete version...

distribution. Random matrix theory (RMT) is the study of properties of random matrices, often as they become large. RMT provides techniques like mean-field theory...

the occurrence of a set of measured values is random. Randomization is widely applied in various fields, especially in scientific research, statistical...

chain random field theory, which extends a single Markov chain into a multi-dimensional random field for geostatistical modeling. A Markov chain random field...

exploited in a sequence model such as a hidden Markov model or conditional random field that predicts the entire tag sequence for a sentence (rather than just...

describes how much two random variables change together (their covariance) with varying spatial or temporal separation. For a random field or stochastic process...

distributions are commonly used, namely, Bayesian networks and Markov random fields. Both families encompass the properties of factorization and independences...

hardware random number generator (HRNG), true random number generator (TRNG), non-deterministic random bit generator (NRBG), or physical random number generator...

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which...

such as a hidden Markov model. A Markov random field extends this property to two or more dimensions or to random variables defined for an interconnected...

the context of cognitive science. It is also classified as a Markov random field. Boltzmann machines are theoretically intriguing because of the locality...

temporary random change in the amount of energy in a point in space, as prescribed by Werner Heisenberg's uncertainty principle. They are minute random fluctuations...

and the financial status of a gambler. Random walks have applications to engineering and many scientific fields including ecology, psychology, computer...

model is the linear-chain conditional random field. This uses an undirected graphical model (aka Markov random field) rather than the directed graphical...

such as through use of a noncausal nonparametric multiscale Markov random field. Patch-based texture synthesis creates a new texture by copying and stitching...