2011
NIPS
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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Interdisciplinary Bridge
— Artificial Intelligence and Machine Learning
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Keyword Pioneer
— bayesian computation
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Cross-Pollinator
— Artificial Intelligence, Computer Science, Computer Vision, Data Science & Analytics, Deep Learning, Healthcare & Medicine, Interdisciplinary, Knowledge & Reasoning, Machine Learning, Mathematics & Optimization, Natural Language Processing, Reinforcement Learning, Robotics, Security & Privacy, Speech & Audio
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Trend Setter
— Kernel Methods
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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 > Bayesian & Probabilistic > Bayesian Inference
Machine Learning > Bayesian & Probabilistic > Kernel Methods