probability theory, a Markov kernel (also known as a stochastic kernel or probability kernel) is a map that in the general theory of Markov processes plays...

category of Markov kernels, often denoted Stoch, is the category whose objects are measurable spaces and whose morphisms are Markov kernels. It is analogous...

{\mathcal {F}},\mathbb {P} )} is called a time homogeneous Markov chain with Markov kernel p {\displaystyle p} and start distribution μ {\displaystyle...

equation Examples of Markov chains Category of Markov kernels Perrone (2024), pp. 10–11 Pavliotis, Grigorios A. (2014). "Markov Processes and the Chapman–Kolmogorov...

probability measures which depend measurably on a parameter (giving rise to Markov kernels), or when one has probability measures over probability measures (such...

{\displaystyle \Omega } . The discriminator's strategy set is the set of Markov kernels μ D : Ω → P [ 0 , 1 ] {\displaystyle \mu _{D}:\Omega \to {\mathcal {P}}[0...

measures or stochastic processes. The most important example of kernels are the Markov kernels. Let ( S , S ) {\displaystyle (S,{\mathcal {S}})} , ( T , T...

the Markov operator admits a kernel representation. Markov operators can be linear or non-linear. Closely related to Markov operators is the Markov semigroup...

permutation action on X N {\displaystyle X^{\mathbb {N} }} , as well as the Markov kernel X N → X N {\displaystyle X^{\mathbb {N} }\to X^{\mathbb {N} }} induced...

Hierarchical hidden Markov model Maximum-entropy Markov model Variable-order Markov model Markov renewal process Markov chain mixing time Markov kernel Piecewise-deterministic...

stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability...

In statistical classification, the Fisher kernel, named after Ronald Fisher, is a function that measures the similarity of two objects on the basis of...

process Markov information source Markov kernel Markov logic network Markov model Markov network Markov process Markov property Markov random field Markov renewal...

contains examples of Markov chains and Markov processes in action. All examples are in the countable state space. For an overview of Markov chains in general...

spaces Category of Markov kernels – Definition and properties of the category of Markov kernels, in more detail than at "Markov kernel". Measurable space –...

In machine learning, kernel machines are a class of algorithms for pattern analysis, whose best known member is the support-vector machine (SVM). These...

distribution is a parametrized family of probability measures called a Markov kernel. Consider two random variables X , Y : Ω → R {\displaystyle X,Y:\Omega...

theory are The category of measurable spaces; Markov categories such as the category of Markov kernels; Probability monads such as Giry monad. W. Lawvere...

probability kernels { Λ n } n = 1 N {\displaystyle \{\Lambda ^{n}\}_{n=1}^{N}} such that θ k 1 {\displaystyle \theta _{k}^{1}} is a Markov chain with transition...

^{i-1},{\mathcal {A}}^{i-1})\to (\Omega _{i},{\mathcal {A}}_{i})} be the Markov kernel derived from ( Ω i − 1 , A i − 1 ) {\displaystyle (\Omega ^{i-1},{\mathcal...

kernel machines such as support vector machines for regression and classification problems. Shogun also offers a full implementation of Hidden Markov...

called the kernel trick, representing the data only through a set of pairwise similarity comparisons between the original data points using a kernel function...

(1_{X\in B}|{\mathcal {H}})(\omega )} . It can be shown that they form a Markov kernel, that is, for almost all ω {\displaystyle \omega } , κ H ( ω , − ) {\displaystyle...

In machine learning, the kernel embedding of distributions (also called the kernel mean or mean map) comprises a class of nonparametric methods in which...

{\displaystyle 1_{T^{-1}(S)}} . Similarly, given a measure-preserving Markov kernel k : ( X , F , p ) → ( X , F , p ) {\displaystyle k:(X,{\mathcal {F}}...

processes there is the related concept of a stochastic kernel, probability kernel, Markov kernel. Define M ~ := { μ ∣ μ  is measure on  ( E , E ) } {\displaystyle...

LogitBoost Manifold alignment Markov chain Monte Carlo (MCMC) Minimum redundancy feature selection Mixture of experts Multiple kernel learning Non-negative matrix...

a protein fragment Heterogeneous memory management, in the Linux kernel Hidden Markov model, a statistical model Central Mashan Miao language (ISO 639-3...

balance in kinetics seem to be clear. A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary...

The Lempel–Ziv–Markov chain algorithm (LZMA) is an algorithm used to perform lossless data compression. It has been under development since either 1996...