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- Bayesian_interpretation_of_kernel_regularization abstract "In 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.In this article we analyze the connections between the regularization and the Bayesian point of view for kernel methods in the case of scalar outputs. 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.".
- Bayesian_interpretation_of_kernel_regularization wikiPageID "35867897".
- Bayesian_interpretation_of_kernel_regularization wikiPageLength "17241".
- Bayesian_interpretation_of_kernel_regularization wikiPageOutDegree "26".
- Bayesian_interpretation_of_kernel_regularization wikiPageRevisionID "704539900".
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Bayesian_probability.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Category:Bayesian_statistics.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Category:Machine_learning.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Category:Probability_theory.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Gaussian_process.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Gramian_matrix.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Hilbert_space.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Kernel_method.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Kernel_methods_for_vector_output.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Likelihood_function.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Machine_learning.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Multi-task_learning.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Multivariate_normal_distribution.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Positive-definite_function.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Posterior_probability.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Prior_probability.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Regularization_(mathematics).
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Reproducing_kernel_Hilbert_space.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Supervised_learning.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Support_vector_machine.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Symmetry_in_mathematics.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLink Tikhonov_regularization.
- Bayesian_interpretation_of_kernel_regularization wikiPageWikiLinkText "Bayesian interpretation of kernel regularization".
- Bayesian_interpretation_of_kernel_regularization wikiPageUsesTemplate Template:Context.
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- Bayesian_interpretation_of_kernel_regularization subject Category:Bayesian_statistics.
- Bayesian_interpretation_of_kernel_regularization subject Category:Machine_learning.
- Bayesian_interpretation_of_kernel_regularization subject Category:Probability_theory.
- Bayesian_interpretation_of_kernel_regularization type Field.
- Bayesian_interpretation_of_kernel_regularization type Page.
- Bayesian_interpretation_of_kernel_regularization comment "In 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.".
- Bayesian_interpretation_of_kernel_regularization label "Bayesian interpretation of kernel regularization".
- Bayesian_interpretation_of_kernel_regularization sameAs Q4874475.
- Bayesian_interpretation_of_kernel_regularization sameAs m.0jw_0qr.
- Bayesian_interpretation_of_kernel_regularization sameAs Q4874475.
- Bayesian_interpretation_of_kernel_regularization wasDerivedFrom Bayesian_interpretation_of_kernel_regularization?oldid=704539900.
- Bayesian_interpretation_of_kernel_regularization isPrimaryTopicOf Bayesian_interpretation_of_kernel_regularization.