Kernel Bayesian inference is a principled approach to nonparametric inference in probabilistic graphical models, where probabilistic relationships between variables are learned from data in a nonparametric manner. Various algorithms of kernel Bayesian inference have been developed by combining kernelized basic probabilistic operations such as the kernel sum rule and kernel Bayes’ rule. However, the current framework is fully nonparametric, and it does not allow a user to flexibly combine nonparametric and model-based inferences. This is inefficient when there are good probabilistic models (or simulation models) available for some parts of a graphical model; this is in particular true in scientific fields where “models” are the central topic of study. Our contribution in this paper is to introduce a novel approach, termed the model-based kernel sum rule (Mb-KSR), to combine a probabilistic model and kernel Bayesian inference. By combining the Mb-KSR with the existing kernelized probabilistic rules, one can develop various algorithms for hybrid (i.e., nonparametric and model-based) inferences. As an illustrative example, we consider Bayesian filtering in a state space model, where typically there exists an accurate probabilistic model for the state transition process. We propose a novel filtering method that combines model-based inference for the state transition process and data-driven, nonparametric inference for the observation generating process. We empirically validate our approach with synthetic and real-data experiments, the latter being the problem of vision-based mobile robot localization in robotics, which illustrates the effectiveness of the proposed hybrid approach.

中文翻译：

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基于模型的核求和规则：使用概率模型进行核贝叶斯推理

核贝叶斯推理是概率图形模型中非参数推理的一种原则方法，其中以非参数方式从数据中学习变量之间的概率关系。核贝叶斯推理的各种算法已经通过结合核化的基本概率运算如核和规则和核贝叶斯规则而开发。然而，当前的框架是完全非参数的，它不允许用户灵活地结合非参数和基于模型的推理。当有良好的概率模型（或模拟模型）可用于图形模型的某些部分时，这是低效的；在以“模型”为研究中心主题的科学领域尤其如此。我们在本文中的贡献是介绍一种新颖的方法，称为基于模型的核总和规则 (Mb-KSR)，以结合概率模型和核贝叶斯推理。通过将 Mb-KSR 与现有的核化概率规则相结合，可以开发用于混合（即，非参数和基于模型）推理的各种算法。作为说明性示例，我们考虑状态空间模型中的贝叶斯滤波，其中通常存在用于状态转换过程的准确概率模型。我们提出了一种新的过滤方法，它结合了状态转换过程的基于模型的推理和观测生成过程的数据驱动的非参数推理。我们通过合成和真实数据实验凭经验验证了我们的方法，后者是机器人技术中基于视觉的移动机器人定位问题，