Learning and classification of complex dynamics

Standard, exact techniques based on likelihood maximization are available f or learning Auto-Regressive Process models of dynamical processes. The unce rtainty of observations obtained from real sensors means that dynamics can be observed only approximately. Learning can still be achieved via "EM-K"-E xpectation-Maximization (EM) based on Kalman Filtering. This cannot handle more complex dynamics, however, involving multiple classes of motion. A pro blem arises also in the case of dynamical processes observed visually: back ground clutter arising for example, in camouflage, produces non-Gaussian ob servation noise. Even with a single dynamical class, non-Gaussian observati ons 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 r andom "particle-sets," can solve the learning problem. Here, learning in cl utter is studied experimentally using visual observations of a hand moving over a desktop. The resulting learned dynamical model is shown to have cons iderable predictive value: When used as a prior for estimation of motion, t he burden of computation in visual observation is significantly reduced. Mu lticlass dynamics are studied via visually observed juggling; plausible dyn amical models have been found to emerge from the learning process, and accu rate classification of motion has resulted. In practice, EM-C learning is c omputationally burdensome and the paper concludes with some discussion of c omputational complexity.