Regularized Bayesian transfer learning for population level etiological distributions

Computer-coded verbal autopsy (CCVA) algorithms predict cause of death from high-dimensional family questionnaire data (verbal autopsies) of a deceased individual. CCVA algorithms are typically trained on non-local data, then used to generate national and regional estimates of cause-specific mortality fractions. These estimates may be inaccurate if the non-local training data is different from the local population of interest. This problem is a special case of transfer learning. However, most transfer learning classification approaches are concerned with individual (e.g. a person's) classification within a target domain (e.g. a particular population) with training performed in data from a source domain. Epidemiologists are often more interested in estimating population-level etiological distributions, using datasets much smaller than those used in common transfer learning applications. We present a parsimonious hierarchical Bayesian transfer learning framework to directly estimate population-level class probabilities in a target domain. To address small sample sizes, we introduce a novel shrinkage prior for the transfer error rates guaranteeing that, in absence of any labeled target domain data or when the baseline classifier has zero transfer error, the calibrated estimate of class probabilities coincides with the naive estimates from the baseline classifier, thereby subsuming the default practice as a special case. A novel Gibbs sampler using data-augmentation enables fast implementation. We extend our approach to use not one, but an ensemble of baseline classifiers. Theoretical and empirical results demonstrate how the ensemble model favors the most accurate baseline classifier. We present extensions allowing class probabilities to vary with covariates, and an EM-algorithm-based MAP estimation. An R-package implementing this method is developed.