Filtering with State-Observation Examples via Kernel Monte Carlo Filter

By Motonobu Kanagawa, Yu Nishiyama, Arthur Gretton, Kenji Fukumizu. 2013

22 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Probabilistic & Bayesian Methods, Signal Processing

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “See also Kar and Karnick (2012), Vedaldi and Zisserman (2012), Le et al. (2013), Pham and Pagh (2013) and references therein for a generalization of this idea. Theoretical results on the preservation of kernel evaluation can be found in, e.g., Sutherland and Schneider (2015) and Sriperumbudur and Sz”