Learning Nonlinear Dynamical Systems Using an EM Algorithm

The Expectation Maximization EM algorithm is an iterative procedure for maximum likelihood parameter estimation from data sets with missing or hidden variables 2 . It has been applied to system identi cation in linear stochastic state-space models, where the state variables are hidden from the observer and both the state and the parameters of the model have to be estimated simultaneously 9 . We present a generalization of the EM algorithm for parameter estimation in nonlinear dynamical systems. The expectation" step makes use of Extended Kalman Smoothing to estimate the state, while the maximization" step re-estimates the parameters using these uncertain state estimates. In general, the nonlinear maximization step is di cult because it requires integrating out the uncertainty in the states. However, if Gaussian radial basis function RBF approximators are used to model the nonlinearities, the integrals become tractable and the maximization step can be solved via systems of li...

• Type: Conference
• Year: 1998
• Where: NIPS
• Authors: Zoubin Ghahramani, Sam T. Roweis
• Keywords: Expectation Maximization EM, Maximization Step, NIPS 1998, NIPS 2007, Nonlinear Dynamical Systems