Robust importance sampling for error estimation in the context of optimal Bayesian transfer learning

Classification has been a major task for building intelligent systems because it enables decision-making under uncertainty. Classifier design aims at building models from training data for representing feature-label distributions—either explicitly or implicitly. In many scientific or clinical settings, training data are typically limited, which impedes the design and evaluation of accurate classifiers. Atlhough transfer learning can improve the learning in target domains by incorporating data from relevant source domains, it has received little attention for performance assessment, notably in error estimation. Here, we investigate knowledge transferability in the context of classification error estimation within a Bayesian paradigm. We introduce a class of Bayesian minimum mean-square error estimators for optimal Bayesian transfer learning, which enables rigorous evaluation of classification error under uncertainty in small-sample settings. Using Monte Carlo importance sampling, we illustrate the outstanding performance of the proposed estimator for a broad family of classifiers that span diverse learning capabilities.