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.