About: Bayesian interpretation of kernel regularization

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Within bayesian statistics for machine learning, kernel methods arise from the assumption of an inner product space or similarity structure on inputs. For some such methods, such as support vector machines (SVMs), the original formulation and its regularization were not Bayesian in nature. It is helpful to understand them from a Bayesian perspective. Because the kernels are not necessarily positive semidefinite, the underlying structure may not be inner product spaces, but instead more general reproducing kernel Hilbert spaces. In Bayesian probability kernel methods are a key component of Gaussian processes, where the kernel function is known as the covariance function. Kernel methods have traditionally been used in supervised learning problems where the input space is usually a space of v

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rdfs:label	Bayesian interpretation of kernel regularization (en)
rdfs:comment	Within bayesian statistics for machine learning, kernel methods arise from the assumption of an inner product space or similarity structure on inputs. For some such methods, such as support vector machines (SVMs), the original formulation and its regularization were not Bayesian in nature. It is helpful to understand them from a Bayesian perspective. Because the kernels are not necessarily positive semidefinite, the underlying structure may not be inner product spaces, but instead more general reproducing kernel Hilbert spaces. In Bayesian probability kernel methods are a key component of Gaussian processes, where the kernel function is known as the covariance function. Kernel methods have traditionally been used in supervised learning problems where the input space is usually a space of v (en)
dcterms:subject	Machine learning Bayesian statistics
Wikipage page ID	35867897 (xsd:integer)
Wikipage revision ID	1109518986 (xsd:integer)
Link from a Wikipage to another Wikipage	Bayesian linear regression Bayesian probability Bayesian statistics Kernel methods Regularized least squares Bergman kernel Estimator Gaussian process Gramian matrix Multi-task learning Multivariate normal distribution Likelihood function Machine learning Kernel methods for vector output Machine learning Positive-definite function Posterior probability Prior probability Regularization (mathematics) Hilbert space Bayesian statistics Support vector machine Symmetry in mathematics Tikhonov regularization Supervised learning Gaussian processes
sameAs	Bayesian interpretation of kernel regularization Bayesian interpretation of kernel regularization Bayesian interpretation of kernel regularization
dbp:wikiPageUsesTemplate	dbt:Further dbt:NumBlk dbt:Reflist dbt:Technical dbt:EquationRef dbt:EquationNote
has abstract	Within bayesian statistics for machine learning, kernel methods arise from the assumption of an inner product space or similarity structure on inputs. For some such methods, such as support vector machines (SVMs), the original formulation and its regularization were not Bayesian in nature. It is helpful to understand them from a Bayesian perspective. Because the kernels are not necessarily positive semidefinite, the underlying structure may not be inner product spaces, but instead more general reproducing kernel Hilbert spaces. In Bayesian probability kernel methods are a key component of Gaussian processes, where the kernel function is known as the covariance function. Kernel methods have traditionally been used in supervised learning problems where the input space is usually a space of vectors while the output space is a space of scalars. More recently these methods have been extended to problems that deal with multiple outputs such as in multi-task learning. A mathematical equivalence between the regularization and the Bayesian point of view is easily proved in cases where the reproducing kernel Hilbert space is finite-dimensional. The infinite-dimensional case raises subtle mathematical issues; we will consider here the finite-dimensional case. We start with a brief review of the main ideas underlying kernel methods for scalar learning, and briefly introduce the concepts of regularization and Gaussian processes. We then show how both points of view arrive at essentially equivalent estimators, and show the connection that ties them together. (en)
prov:wasDerivedFrom	wikipedia-en:Bayesian_interpretation_of_kernel_regularization?oldid=1109518986&ns=0
page length (characters) of wiki page	17543 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Bayesian_interpretation_of_kernel_regularization
is Link from a Wikipage to another Wikipage of	Bayesian linear regression Bayesian interpretation of regularization List of things named after Thomas Bayes Outline of machine learning
is Wikipage redirect of	Bayesian interpretation of regularization
is foaf:primaryTopic of	wikipedia-en:Bayesian_interpretation_of_kernel_regularization

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