{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T07:07:06Z","timestamp":1774940826182,"version":"3.50.1"},"reference-count":54,"publisher":"MIT Press","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2016,2]]},"abstract":"<jats:p>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\u2019 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.<\/jats:p>","DOI":"10.1162\/neco_a_00806","type":"journal-article","created":{"date-parts":[[2015,12,14]],"date-time":"2015-12-14T20:53:04Z","timestamp":1450126384000},"page":"382-444","source":"Crossref","is-referenced-by-count":13,"title":["Filtering with State-Observation Examples via Kernel Monte Carlo Filter"],"prefix":"10.1162","volume":"28","author":[{"given":"Motonobu","family":"Kanagawa","sequence":"first","affiliation":[{"name":"SOKENDAI (Graduate University for Advanced Studies), Tokyo 190-8562, Japan, and Institute of Statistical Mathematics, Tokyo 190-8562, Japan"}]},{"given":"Yu","family":"Nishiyama","sequence":"additional","affiliation":[{"name":"University of Electro-Communications, Tokyo 182-8585, Japan"}]},{"given":"Arthur","family":"Gretton","sequence":"additional","affiliation":[{"name":"Gatsby Computational Neuroscience Unit, University College London, London"}]},{"given":"Kenji","family":"Fukumizu","sequence":"additional","affiliation":[{"name":"SOKENDAI (Graduate University for Advanced Studies), Tokyo 190-8562, Japan, and Institute of Statistical Mathematics, Tokyo 190-8562, Japan"}]}],"member":"281","reference":[{"key":"B1","volume-title":"Optimal filtering","author":"Anderson B.","year":"1979"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1950-0051437-7"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1162\/153244303768966085"},{"key":"B4","first-page":"1359","volume-title":"Proceedings of the 29th International Conference on Machine Learning (ICML2012)","author":"Bach F.","year":"2012"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-9096-9"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbu019"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2007.893250"},{"key":"B8","first-page":"109","volume-title":"Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence","author":"Chen Y.","year":"2010"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1145\/1553374.1553403"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3437-9"},{"key":"B11","first-page":"656","volume-title":"The Oxford handbook of nonlinear filtering","author":"Doucet A.","year":"2011"},{"key":"B12","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199641178.001.0001"},{"key":"B13","doi-asserted-by":"publisher","DOI":"10.1214\/12-EJS760"},{"key":"B14","doi-asserted-by":"publisher","DOI":"10.15607\/RSS.2006.II.039"},{"key":"B15","doi-asserted-by":"publisher","DOI":"10.1162\/15324430260185619"},{"key":"B17","first-page":"73","volume":"5","author":"Fukumizu K.","year":"2004","journal-title":"Journal of Machine Learning Research"},{"key":"B18","first-page":"489","volume-title":"Advances in neural information processing systems, 20","author":"Fukumizu K.","year":"2008"},{"key":"B19","first-page":"1737","volume-title":"Advances in neural information processing systems, 24","author":"Fukumizu K.","year":"2011"},{"key":"B20","first-page":"3753","volume":"14","author":"Fukumizu K.","year":"2013","journal-title":"Journal of Machine Learning Research"},{"key":"B21","first-page":"473","volume-title":"Advances in neural information processing systems, 21","author":"Fukumizu K.","year":"2009"},{"key":"B22","first-page":"107","volume":"140","author":"Gordon N. 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