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Standard, exact techniques based on likelihood maximization are available for learning Auto-Regressive Process models of dynamical processes. The uncertainty of observations obtained from real sensors means that dynamics can be observed only approximately. Learning can still be achieved via 'EM-K'-Expectation-Maximization (EM) based on Kalman Filtering. This cannot handle more complex dynamics, however, involving multiple classes of motion. A problem arises also in the case of dynamical processes observed visually: background clutter arising for example, in camouflage, produces non-Gaussian observation noise. Even with a single dynamical class, non-Gaussian observations put the learning problem beyond the scope of EM-K. For those cases, we show here how 'EM-C' - based on the Condensation algorithm which propagates random 'particle-sets', can solve the learning problem. Here, learning in clutter is studied experimentally using visual observations of a hand moving over a desktop. The resulting learned dynamical model is shown to have considerable predictive value: When used as a prior for estimation of motion, the burden of computation in visual observation is significantly reduced. Multiclass dynamics are studied via visually observed juggling; plausible dynamical models have been found to emerge from the learning process, and accurate classification of motion has resulted. In practice, EM-C learning is computationally burdensome and the paper concludes with some discussion of computational complexity.

Original publication




Journal article


IEEE Transactions on Pattern Analysis and Machine Intelligence

Publication Date





1016 - 1034