HIERARCHICAL BAYESIAN-KALMAN MODELS FOR REGULARISATION AND ARD IN SEQUENTIAL LEARNING
J.F.G. de Freitas, M. Niranjan and A.H. Gee
December 1997
In this paper, we show that a hierarchical Bayesian modelling approach to sequential learning leads to many interesting attributes such as regularisation and automatic relevance determination. We identify three inference levels within this hierarchy, namely model selection, parameter estimation and noise estimation. In environments where data arrives sequentially, techniques such as cross-validation to achieve regularisation or model selection are not possible. The Bayesian approach, with extended Kalman filtering at the parameter estimation level, allows for regularisation within a minimum variance framework.A multi-layer perceptron is used to generate the extended Kalman filter nonlinear measurements mapping. We describe several algorithms at the noise estimation level, which allow us to implement adaptive regularisation and automatic relevance determination of model inputs and basis functions. An important contribution of this paper is to show the theoretical links between adaptive noise estimationin extended Kalman filtering, multiple adaptive learning rates and multiple smoothing regularisation coefficients.
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