We present a Bayesian formulation of locally weighted learning (LWL)
using the novel concept of a randomly varying coefficient model.
Based on this, we propose a mechanism for multivariate non-linear
regression using spatially localised linear models that learns
completely independent of each other, uses only local
information and adapts the local model complexity in a data driven
fashion. We derive online updates for the model parameters
based on variational Bayesian EM. The evaluation of the proposed
algorithm against other state-of-the-art methods reveal the
excellent, robust generalization performance beside surprisingly
efficient time and space complexity properties. This paper, for the
first time, brings together the computational efficiency and the
adaptability of `non-competitive' locally weighted learning schemes
and the modelling guarantees of the Bayesian formulation.