Kernel Bayes' rule: Bayesian inference with positive definite kernels
Kernel Bayes' rule: Bayesian inference with positive definite kernels
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DOI：
10.5555/2567709.2627677
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
K. Fukumizu;Le Song;A. Gretton
中科院分区：
文献类型：
--
作者：
K. Fukumizu;Le Song;A. Gretton
基于再生核Hilbert空间中概率的表示，提出了一种实现贝叶斯规则的核方法。概率唯一地由到RKHS的典型映射的平均值来表征。先验概率和条件概率用经验样本的RKHS函数表示：这些量不需要明确的参数模型。后验同样是加权样本的RKHS均值。估计的期望函数的后验推导，并显示率的一致性。介绍了核贝叶斯规则的一些典型应用，包括无似然贝叶斯计算和非参数状态空间模型的滤波。
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.