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...

{\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...

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...

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

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...

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

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...

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

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

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

{X}},{\mathcal {B}}({\mathcal {X}}))} , the Markov chain ( X n ) {\displaystyle (X_{n})} with transition kernel K ( x , y ) {\displaystyle K(x,y)} is φ-irreducible...

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...

processes and potential theory Chapter I covers the Markov property and strong Markov property, Markov kernels, standard and Hunt processes, and measurability...

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

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

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

^{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...

(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...

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

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

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

measure spaces Category of Markov kernels – Category whose objects are measurable spaces and whose morphisms are Markov kernels Measurable space – Basic...

Artificial neural networks Game theory Bayesian probability Consciousness Markov kernels Signal-flow graphs Conjunctive queries Bidirectional transformations...

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...

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

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