Hierarchical Bayesian models for regularization in sequential learning

We show that a hierarchical Bayesian modeling approach allows us to perform regularization in sequential learning. We identify three inference levels within this hierarchy: model selection, parameter estimation, and noise est imation. In environments where data arrive sequentially, techniques such as cross validation to achieve regularization or model selection are not poss ible. The Bayesian approach, with extended Kalman filtering at the paramete r estimation level, allows for regularization within a minimum variance fra mework. A multilayer perceptron is used to generate the extended Kalman fil ter nonlinear measurements mapping. We describe several algorithms at the n oise estimation level that allow us to implement on-line regularization. We also show the theoretical links between adaptive noise estimation in exten ded Kalman filtering, multiple adaptive learning rates, and multiple smooth ing regularization coefficients.