Kernel Bayes' Rule
Kernel Bayes' Rule
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发表时间：
2010-09
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通讯作者：
K. Fukumizu;Le Song;A. Gretton
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作者：
K. Fukumizu;Le Song;A. Gretton
基于再生核希尔伯特空间中概率的核表示，提出了一种实现贝叶斯规则的非参数核方法。先验和条件概率分别表示为经验核均值和协方差算子，后验分布的核均值以加权样本的形式计算。核贝叶斯的规则可以应用于各种各样的贝叶斯推理问题：我们证明贝叶斯计算没有可能性，过滤与非参数状态空间模型。建立了后验估计的一致率。
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.