  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.
