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Abstract : |
Standard, exact techniques, based on likelihood maximisation, are available for learning AutoRegressive 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-Maximisation (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. Learning in clutter is studied experimentally here using visual observations of a hand moving over a desk-top. 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. Multi-class 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. 1, |
