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 partial information is shared. In this paper, we propose a novel Bayesian transfer learning method named ``CONCERT'' to allow robust partial information transfer for high-dimensional data analysis. A 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 partial similarities and integrate source information collaboratively to improve the performance on the target. In contrast to existing work, the CONCERT is a one-step procedure which achieves variable selection and information transfer simultaneously. We establish variable selection consistency, as well as estimation and prediction error bounds for CONCERT. Our theory demonstrates the covariate-specific benefit of transfer learning. To ensure the scalability of the algorithm, we adopt the variational Bayes framework to facilitate implementation. Extensive experiments and two real data applications showcase the validity and advantages of CONCERT over existing cutting-edge transfer learning methods.

翻译：迁移学习的广泛应用源于其能够从有用的辅助数据集中借力。现有的统计迁移学习方法通常采用源数据与目标数据之间的全局相似性度量，当仅部分信息共享时，这种方法可能导致效率低下。本文提出了一种名为“CONCERT”的新型贝叶斯迁移学习方法，旨在实现高维数据分析中鲁棒的部分信息迁移。通过在目标与源参数的联合分布中引入条件尖峰-厚板先验，我们实现了信息迁移。通过纳入协变量特异性先验，我们能够刻画部分相似性，并协同整合源信息以提升目标任务的性能。与现有工作相比，CONCERT是一种单步流程，可同时实现变量选择与信息迁移。我们为CONCERT建立了变量选择一致性，以及估计与预测误差界。我们的理论揭示了迁移学习在协变量特异性方面的优势。为确保算法的可扩展性，我们采用变分贝叶斯框架以简化实现。大量实验及两个实际数据应用展示了CONCERT相较于现有前沿迁移学习方法的有效性和优越性。