A Principled Approach to Bayesian Transfer Learning

TL;DR

This paper introduces a new framework for Bayesian transfer learning that enables principled comparison of methods using leave-one-out cross validation and presents an efficient implementation of power prior techniques.

Contribution

It proposes a transfer sequential Monte Carlo framework for Bayesian transfer learning and establishes a principled way to compare different methods on real data.

Findings

The new framework effectively compares Bayesian transfer methods.

Transfer sequential Monte Carlo efficiently implements power prior methods.

Simulation studies demonstrate the approach's effectiveness.

Abstract

Updating $\textit{a priori}$ information given some observed data is the core tenet of Bayesian inference. Bayesian transfer learning extends this idea by incorporating information from a related dataset to improve the inference on the observed target dataset which may have been collected under slightly different settings. The use of related information can be useful when the target dataset is scarce, for example. There exist various Bayesian transfer learning methods that decide how to incorporate the related data in different ways. Unfortunately, there is no principled approach for comparing Bayesian transfer methods in real data settings. Additionally, some Bayesian transfer learning methods, such as the so-called power prior approaches, rely on conjugacy or costly specialised techniques. In this paper, we find an effective approach to compare Bayesian transfer learning methods is to apply leave-one-out cross validation on the target dataset. Further, we introduce a new framework, $\textit{transfer sequential Monte Carlo}$, that efficiently implements power prior methods in an automated fashion. We demonstrate the performance of our proposed methods in two comprehensive simulation studies.