  The popularity of transfer learning stems from the fact that it can borrow
information from useful auxiliary datasets. Existing statistical transfer
learning methods usually adopt a global similarity measure between the source
data and the target data, which may lead to inefficiency when only local
information is shared. In this paper, we propose a novel Bayesian transfer
learning method named "CONCERT" to allow robust local information transfer for
high-dimensional data analysis. A novel conditional spike-and-slab prior is
introduced in the joint distribution of target and source parameters for
information transfer. By incorporating covariate-specific priors, we can
characterize the local similarities and make the sources work collaboratively
to help improve the performance on the target. Distinguished from existing
work, CONCERT is a one-step procedure, which achieves variable selection and
information transfer simultaneously. Variable selection consistency is
established for our CONCERT. To make our algorithm scalable, we adopt the
variational Bayes framework to facilitate implementation. Extensive experiments
and a genetic data analysis demonstrate the validity and the advantage of
CONCERT over existing cutting-edge transfer learning methods. We also extend
our CONCERT to the logistical models with numerical studies showing its
superiority over other methods.
