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2013 JMLR JMLR 2013

Kernel Bayes' Rule: Bayesian Inference with Positive Definite Kernels

Abstract

A kernel method for realizing Bayes' rule is proposed, based on representations of probabilities in reproducing kernel Hilbert spaces. Probabilities are uniquely characterized by the mean of the canonical map to the RKHS. The prior and conditional probabilities are expressed in terms of RKHS functions of an empirical sample: no explicit parametric model is needed for these quantities. The posterior is likewise an RKHS mean of a weighted sample. The estimator for the expectation of a function of the posterior is derived, and rates of consistency are shown. Some representative applications of the kernel Bayes' rule are presented, including Bayesian computation without likelihood and filtering with a nonparametric state-space model. [abs] [ pdf ][ bib ] © JMLR 2013. (edit, beta)

🌉 Interdisciplinary Bridge — Artificial Intelligence and Machine Learning
🐣 Hot Topic Early Bird — probabilistic modeling
🐝 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

Authors

Kenji Fukumizu , Le Song , Arthur Gretton

Topics

Artificial Intelligence > Bayesian & Probabilistic > Probabilistic Modeling Machine Learning > Optimization & Theory > Bayesian Inference Machine Learning > Bayesian & Probabilistic > Probabilistic Modeling Machine Learning > Bayesian & Probabilistic > Bayesian Inference

Keywords

bayesian computation probabilistic modeling bayesian inference reproducing kernel hilbert space nonparametric inference kernel methods
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