CONCERT: Covariate-Elaborated Robust Local Information Transfer with Conditional Spike-and-Slab Prior

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.