In set theory, the kernel of a function f {\displaystyle f} (or equivalence kernel) may be taken to be either the equivalence relation on the function's...

to the zero vector Kernel (category theory), a generalization of the kernel of a homomorphism Kernel (set theory), an equivalence relation: partition...

In mathematics, and specifically in potential theory, the Poisson kernel is an integral kernel, used for solving the two-dimensional Laplace equation,...

subalgebra of B {\displaystyle B} ). Kernel (category theory) Kernel of a function Equalizer (mathematics) Zero set Some sources do not include the multiplicative...

theory (for example, using Rademacher complexity). Kernel methods can be thought of as instance-based learners: rather than learning some fixed set of...

In 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...

In operator theory, a branch of mathematics, a positive-definite kernel is a generalization of a positive-definite function or a positive-definite matrix...

mathematics of probability, a transition kernel or kernel is a function in mathematics that has different applications. Kernels can for example be used to define...

equation. In certain contexts, a difference kernel is the equaliser of exactly two functions. Let X and Y be sets. Let f and g be functions, both from X to...

In functional analysis, a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional...

in the reproducing kernel Hilbert space theory where it characterizes a symmetric positive-definite kernel as a reproducing kernel. To explain Mercer's...

parameterized complexity theory, it is often possible to prove that a kernel with guaranteed bounds on the size of a kernel (as a function of some parameter...

kernel is a computer program at the core of a computer's operating system that always has complete control over everything in the system. The kernel is...

In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method...

without kernels and/or cokernels. There is a convenient relationship between the kernel and cokernel and the abelian group structure on the hom-sets. Given...

Mach (/mɑːk/) is an operating system kernel developed at Carnegie Mellon University by Richard Rashid and Avie Tevanian to support operating system research...

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

much collective payoff a set of players can gain by forming a coalition. Cooperative game theory is a branch of game theory that deals with the study...

mathematics, specifically in category theory, a pre-abelian category is an additive category that has all kernels and cokernels. Spelled out in more detail...

functor Hom functor Product (category theory) Equaliser (mathematics) Kernel (category theory) Pullback (category theory)/fiber product Inverse limit Pro-finite...

study of artificial neural networks (ANNs), the neural tangent kernel (NTK) is a kernel that describes the evolution of deep artificial neural networks...

defined by the kernel, such that closer points are given higher weights. The estimated function is smooth, and the level of smoothness is set by a single...

abstract structure of Fredholm's theory is given in terms of the spectral theory of Fredholm operators and Fredholm kernels on Hilbert space. It therefore...

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

manifolds, dynamical systems, and other structured objects. The theory behind kernel embeddings of distributions has been primarily developed by Alex...

Bayesian interpretation of kernel regularization examines how kernel methods in machine learning can be understood through the lens of Bayesian statistics...

In mathematics, the Carathéodory kernel theorem is a result in complex analysis and geometric function theory established by the Greek mathematician Constantin...

example being the neighborhood filter. Filters appear in order theory, model theory, and set theory, but can also be found in topology, from which they originate...

analytics VC dimension VIGRA Validation set Vapnik–Chervonenkis theory Variable-order Bayesian network Variable kernel density estimation Variable rules analysis...

reproducing kernel Hilbert space can be represented as a finite linear combination of kernel products evaluated on the input points in the training set data...