Fully probabilistic design for knowledge fusion between Bayesian filters under uniform disturbances

TL;DR

This paper introduces a fully probabilistic design approach for Bayesian transfer learning between linear state-space models with uniform noise, enhancing robustness and avoiding the need for joint source-target modeling.

Contribution

It proposes a novel FPD-based Bayesian transfer learning method that is robust to poor source quality and model misspecification, without requiring joint source-target models.

Findings

The proposed method effectively rejects poor-quality source knowledge.

It demonstrates robustness to model misspecification.

Simulation results outperform two contemporary alternatives.

Abstract

This paper considers the problem of Bayesian transfer learning-based knowledge fusion between linear state-space processes driven by uniform state and observation noise processes. The target task conditions on probabilistic state predictor(s) supplied by the source filtering task(s) to improve its own state estimate. A joint model of the target and source(s) is not required and is not elicited. The resulting decision-making problem for choosing the optimal conditional target filtering distribution under incomplete modelling is solved via fully probabilistic design (FPD), i.e. via appropriate minimization of Kullback-Leibler divergence (KLD). The resulting FPD-optimal target learner is robust, in the sense that it can reject poor-quality source knowledge. In addition, the fact that this Bayesian transfer learning (BTL) scheme does not depend on a model of interaction between the source and target tasks ensures robustness to the misspecification of such a model. The latter is a problem that affects conventional transfer learning methods. The properties of the proposed BTL scheme are demonstrated via extensive simulations, and in comparison with two contemporary alternatives.