A Bayesian approach to extracting meaning from system behavior
W.B. Dress · 2002
The modeling relation and its reformulation to include the semiotic hierarchy is essential for the understanding, control, and successful re-creation of natural systems. This presentation will argue for a careful application of Rosen's modeling relationship (1985, 1991) to the problems of intelligence and autonomy in natural and artificial systems. The methods of Bayesian and maximum entropy parameter estimation have been applied to measurements of system observables to directly infer the underlying differential equations generating system behavior. This is computationally efficient, since only location parameters enter into the maximum-entropy calculations; nonlinear parameters are unneeded. Such an approach more directly extracts the semantics inherent in a given system by going to the root of system meaning as expressed by abstract form or shape. Empirical models are embodied by the differential equations underlying, producing, or describing the behavior of a process as measured or tracked by a particular variable set. The a priori models are probability structures that capture syntactical relationships within the formal system that mirrors the natural system under observation. Inductive learning is a prescription for incorporating the current, and possibly changing, empirical model into an iterative syntactical relationship. The probabilistic nature of the model descriptions replaces rigid structures. The structures evolve with both new knowledge and temporal evolution of the system.