Talker: Kenji Fukumizu (ISM)
(Joint work with M. Kanagawa, Y. Nishiyama, and A. Gretton)

Title: Monte Carlo filter with kernel mean embedding

Abstract: Recently, nonparametric inference methods with positive definite kernels and associated reproducing kernel Hilbert spaces have been developed, employing representation of distributions with kernel mean embedding.  In this approach, the distribution of a variable is represented by the mean element of the random feature vector defined with the mapping of the variable by the kernel function, and the relation between variables is expressed by a covariance operator.  In this work, we consider a filtering problem in a partly-nonparametric state space model, where sampling is possible with a known state-transition but the observation model is neither known nor estimable with a simple parametric model.  Alternatively, we assume that a set of paired data of state and observation is available in the training phase. Based on combination of Monte Carlo sampling from the state transition and the kernel Bayes rule with a new observation, a sequential filtering algorithm is proposed for this partly-nonparametric state-space model.  As a typical example, the method is applied to a vision-based robot localization problem, where the state-transition of robot location is well modeled, but it is difficult to assume a suitable parametric model for the conditional probability of an image given location.