  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 {\em
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.
