title: Filtering with State-Observation Examples via Kernel Monte Carlo Filter.
abstract: This letter addresses the problem of filtering with a state-space model. Standard approaches for filtering assume that a probabilistic model for observations (i.e., the observation model) is given explicitly or at least parametrically. We consider a setting where this assumption is not satisfied; we assume that the knowledge of the observation model is provided only by examples of state-observation pairs. This setting is important and appears when state variables are defined as quantities that are very different from the observations. We propose kernel Monte Carlo filter, a novel filtering method that is focused on this setting. Our approach is based on the framework of kernel mean embeddings, which enables nonparametric posterior inference using the state-observation examples. The proposed method represents state distributions as weighted samples, propagates these samples by sampling, estimates the state posteriors by kernel Bayes' rule, and resamples by kernel herding. In particular, the sampling and resampling procedures are novel in being expressed using kernel mean embeddings, so we theoretically analyze their behaviors. We reveal the following properties, which are similar to those of corresponding procedures in particle methods: the performance of sampling can degrade if the effective sample size of a weighted sample is small, and resampling improves the sampling performance by increasing the effective sample size. We first demonstrate these theoretical findings by synthetic experiments. Then we show the effectiveness of the proposed filter by artificial and real data experiments, which include vision-based mobile robot localization.
authors.affiliation: SOKENDAI (Graduate University for Advanced Studies), Tokyo 190-8562, Japan, and Institute of Statistical Mathematics, Tokyo 190-8562, Japan motonobu.kanagawa@gmail.com.
authors.forename: Motonobu
authors.initials: M
authors.lastname: Kanagawa
authors.affiliation: University of Electro-Communications, Tokyo 182-8585, Japan yu.nishiyama@ai.is.uec.ac.jp.
authors.forename: Yu
authors.initials: Y
authors.lastname: Nishiyama
authors.affiliation: Gatsby Computational Neuroscience Unit, University College London, London arthur.gretton@gmail.com.
authors.forename: Arthur
authors.initials: A
authors.lastname: Gretton
authors.affiliation: SOKENDAI (Graduate University for Advanced Studies), Tokyo 190-8562, Japan, and Institute of Statistical Mathematics, Tokyo 190-8562, Japan fukumizu@ism.ac.jp.
authors.forename: Kenji
authors.initials: K
authors.lastname: Fukumizu
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006801:Humans; D008962:Models, Theoretical; D009010:Monte Carlo Method; D011336:Probability; D012815:Signal Processing, Computer-Assisted