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- Bayesian_interpretation_of_regularization abstract "In statistics and machine learning, a Bayesian interpretation of regularization for kernel methods is often useful. Kernel methods are central to both the regularization and the Bayesian point of view in machine learning. In regularization they are a natural choice for the hypothesis space and the regularization functional through the notion of reproducing kernel Hilbert spaces. In Bayesian probability they 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 Bayesian point of views for kernel methods in the case of scalar outputs. A mathematical equivalence between the regularization and the Bayesian point of views 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 point of views arrive at essentially equivalent estimators, and show the connection that ties them together.".
- Bayesian_interpretation_of_regularization wikiPageID "35867897".
- Bayesian_interpretation_of_regularization wikiPageRevisionID "603906789".
- Bayesian_interpretation_of_regularization hasPhotoCollection Bayesian_interpretation_of_regularization.
- Bayesian_interpretation_of_regularization subject Category:Machine_learning_algorithms.
- Bayesian_interpretation_of_regularization subject Category:Mathematical_analysis.
- Bayesian_interpretation_of_regularization comment "In statistics and machine learning, a Bayesian interpretation of regularization for kernel methods is often useful. Kernel methods are central to both the regularization and the Bayesian point of view in machine learning. In regularization they are a natural choice for the hypothesis space and the regularization functional through the notion of reproducing kernel Hilbert spaces.".
- Bayesian_interpretation_of_regularization label "Bayesian interpretation of regularization".
- Bayesian_interpretation_of_regularization sameAs m.0jw_0qr.
- Bayesian_interpretation_of_regularization sameAs Q4874475.
- Bayesian_interpretation_of_regularization sameAs Q4874475.
- Bayesian_interpretation_of_regularization wasDerivedFrom Bayesian_interpretation_of_regularization?oldid=603906789.
- Bayesian_interpretation_of_regularization isPrimaryTopicOf Bayesian_interpretation_of_regularization.