Regularisation in Sequential Learning Algorithms

João F. G. de Freitas, Mahesan Niranjan, Andrew H. Gee

Abstract: In this paper, we discuss regularisation in online/sequential learn(cid:173) ing algorithms. In environments where data arrives sequentially, techniques such as cross-validation to achieve regularisation or model selection are not possible. Further, bootstrapping to de(cid:173) termine a confidence level is not practical. To surmount these problems, a minimum variance estimation approach that makes use of the extended Kalman algorithm for training multi-layer percep(cid:173) trons is employed. The novel contribution of this paper is to show the theoretical links between extended Kalman filtering, Sutton's variable learning rate algorithms and Mackay's Bayesian estima(cid:173) tion framework. In doing so, we propose algorithms to overcome the need for heuristic choices of the initial conditions and noise covariance matrices in the Kalman approach.