2011
NeurIPS
NeurIPS 2011
Kernel Bayes' Rule
Abstract
A nonparametric kernel-based method for realizing Bayes' rule is proposed, based on kernel representations of probabilities in reproducing kernel Hilbert spaces. The prior and conditional probabilities are expressed as empirical kernel mean and covariance operators, respectively, and the kernel mean of the posterior distribution is computed in the form of a weighted sample. The kernel Bayes' rule can be applied to a wide variety of Bayesian inference problems: we demonstrate Bayesian computation without likelihood, and filtering with a nonparametric state-space model. A consistency rate for the posterior estimate is established.
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Hot Topic Early Bird
- reproducing kernel hilbert space
Authors
Topics
Artificial Intelligence > Bayesian & Probabilistic > Bayesian Learning
Machine Learning > Core Methods > Representation Learning
Machine Learning > Optimization & Theory > Bayesian Inference
Machine Learning > Bayesian & Probabilistic > Probabilistic Modeling
Machine Learning > Core Methods > Kernel Methods