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Abstract

In this paper, we extend the Hilbert space embedding approach to handle conditional distributions. We derive a kernel estimate for the conditional embedding, and show its connection to ordinary embeddings. Conditional embeddings largely extend our ability to manipulate distributions in Hibert spaces, and as an example, we derive a nonparametric method for modeling dynamical systems where the belief state of the system is maintained as a conditional embedding. Our method is very general in terms of both the domains and the types of distributions that it can handle, and we demonstrate the effectiveness of our method in various dynamical systems. We expect that conditional embeddings will have wider applications beyond modeling dynamical systems.

Notes

Text Reference

Le Song, Jonathan Huang, Alex Smola, and Kenji Fukumizu, "Hilbert Space Embeddings of Conditional Distributions with Applications to Dynamical Systems," International Conference on Machine Learning (ICML 2009), June, 2009.

BibTeX Reference

@inproceedings{Huang_2009_6472,
   author = "Le Song and Jonathan Huang and Alex Smola and Kenji Fukumizu",
   title = "Hilbert Space Embeddings of Conditional Distributions with Applications to Dynamical Systems",
   booktitle = "International Conference on Machine Learning (ICML 2009)",
   month = "June",
   year = "2009",
}

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