Nonlinear Time series filtering, smoothing and learning using the kernel Kalman filter
Liva Ralaivola and Florence d'Alché-Buc
Universite Pierre et Marie Curie, Paris, France.
In this paper, we propose a new model, the Kernel Kalman Filter, to perform various nonlinear time series processing. This model is based on the use of Mercer kernel functions in the framework of the Kalman Filter or Linear Dynamical Systems. Thanks to the kernel trick, all the equations involved in our model to perform filtering, smoothing and learning tasks, only require matrix algebra calculus whilst providing the ability to model complex time series. In particular, it is possible to learn dynamics from some nonlinear noisy time series implementing an exact EM procedure. When predictions in the original input space are needed, an efficient and original preimage learning strategy is proposed.
|EPrint Type:||Monograph (Technical Report)|
|Project Keyword:||Project Keyword UNSPECIFIED|
|Subjects:||Theory & Algorithms|
|Deposited By:||Liva Ralaivola|
|Deposited On:||30 December 2004|