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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. 

ABSTRACT Individualized modeling has become increasingly popular in recent years with its growing application in fields such as personalized medicine and mobile health studies. With rich longitudinal measurements, it is of great interest to model certain subject‐specific time‐varying covariate effects. In this paper, we propose an individualized time‐varying nonparametric model by leveraging the subgroup information from the population. The proposed method approximates the time‐varying covariate effect using nonparametric B‐splines and aggregates the estimated nonparametric coefficients that share common patterns. Moreover, the proposed method can effectively handle various missing data patterns that frequently arise in mobile health data. Specifically, our method achieves subgrouping by flexibly accommodating varying dimensions of B‐spline coefficients due to missingness. This capability sets it apart from other fusion‐type approaches for subgrouping. The subgroup information can also potentially provide meaningful insight into the characteristics of subjects and assist in recommending an effective treatment or intervention. An efficient ADMM algorithm is developed for implementation. Our numerical studies and application to mobile health data on monitoring pregnant women's deep sleep and physical activities demonstrate that the proposed method achieves better performance compared to other existing methods.