Supervised Learning Recursive Filters for Optimal Structure and Parameter Adaptive Pattern Recognition. Case I: Continuous Data

摘要

Recursive filters for supervised learning Bayes-optimal adaptive pattern recognition with continuous data are derived. Both off-line (or prior to actual operation) and on-line (while in operation) supervised learning is considered. The concept of structure adaptation is introduced and both structure as well as parameter adaptive optimal pattern recognition systems are obtained. Specifically, for the class of supervised learning pattern recognition problems with gaussian process models and linear dynamics, the adaptive pattern recognition systems are shown to be decomposable ('partition theorem') into a linear, non-adaptive part consisting of recursive, matched Kalman filters, a nonlinear part--a set of probability computers--that incorporates the adaptive nature of the system, and finally a linear part of the correlator-estimator (Kailath) form. (Author)