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Hilbert Space Embeddings of Conditional Distributions with Applications to Dynamical Systems

Hilbert Space Embeddings of Conditional Distributions with Applications to Dynamical Systems

This video was recorded at 26th International Conference on Machine Learning (ICML), Montreal 2009. In this paper, we extend the Hilbert space embedding approach to handle conditional distributions. This leads us to a nonparametric method for modeling dynamical systems, and allows us to update the belief state of a dynamical system by maintaining 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 Hilbert space embedding of {\em conditional} distributions will have wide applications beyond modeling dynamical systems.

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