Bayesian Transfer Learning Between Uniformly Modelled Bayesian Filters

Abstract

We investigate sensor network nodes that sequentially infer states with bounded values, and affected by noise that is also bounded. The transfer of knowledge between such nodes is the principal focus of this chapter. A fully Bayesian framework is adopted, in which the source knowledge is represented by a bounded data predictor, the specification of a formal conditioning mechanism between the filtering nodes is avoided, and the optimal knowledge-conditioned target state predictor is designed via optimal Bayesian decision-making (fully probabilistic design). We call this framework Bayesian transfer learning, and derive a sequential algorithm for pairs of interacting, bounded filters. To achieve a tractable, finite-dimensional flow, the outputs of the time step, transfer step and data step are locally projected onto parallelotopic supports. An informal variant of the transfer algorithm demonstrates both strongly positive transfer of high-quality (low variance) source knowledge—improving on a former orthotopically supported variant—as well as rejection of low-quality (high variance) source knowledge, which we call robust transfer.