The Nonparametric Kernel Bayes Smoother
The Nonparametric Kernel Bayes Smoother
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发表时间：
2016-05
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通讯作者：
Yu Nishiyama;A. Afsharinejad;Shunsuke Naruse;Byron Boots;Le Song
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作者：
Yu Nishiyama;A. Afsharinejad;Shunsuke Naruse;Byron Boots;Le Song
近年来，贝叶斯推理的核均值表达式的研究取得了重大进展。非参数核贝叶斯滤波(NKB-Filter)是这一领域的一个重要成功，它可用于状态空间模型中的序贯推理。在此基础上，提出了一种基于核和规则和核贝叶斯规则的非参数核贝叶斯光滑器(NKB-Smoster)算法。我们推导了光滑化方程，分析了计算代价，并证明了光滑化的一致性。我们总结了该算法，该算法实现简单，只需要矩阵乘法和NKB滤波器的输出。最后，我们报告了将NKB-平滑器与以前的参数和非参数贝叶斯滤波和平滑方法进行比较的实验结果。在补充材料中，我们证明了NKB-滤子和NKB-光滑器的组合允许边缘核平均计算，这给出了核信任传播的另一种选择。
Recently, significant progress has been made developing kernel mean expressions for Bayesian inference. An important success in this domain is the nonparametric kernel Bayes’ filter (nKB-filter), which can be used for sequential inference in state space models. We expand upon this work by introducing a smoothing algorithm, the nonparametric kernel Bayes’ smoother (nKB-smoother) which relies on kernel Bayesian inference through the kernel sum rule and kernel Bayes’ rule. We derive the smoothing equations, analyze the computational cost, and show smoothing consistency. We summarize the algorithm, which is simple to implement, requiring only matrix multiplications and the output of the nKB-filter. Finally, we report experimental results that compare the nKB-smoother to previous parametric and nonparametric approaches to Bayesian filtering and smoothing. In the supplementary materials, we show that the combination of the nKB-filter and the nKB-smoother allows marginal kernel mean computation, which gives an alternative to kernel belief propagation.