  In this work, we study the transfer learning problem under high-dimensional
generalized linear models (GLMs), which aim to improve the fit on target data
by borrowing information from useful source data. Given which sources to
transfer, we propose a transfer learning algorithm on GLM, and derive its
$\ell_1/\ell_2$-estimation error bounds as well as a bound for a prediction
error measure. The theoretical analysis shows that when the target and source
are sufficiently close to each other, these bounds could be improved over those
of the classical penalized estimator using only target data under mild
conditions. When we don't know which sources to transfer, an algorithm-free
transferable source detection approach is introduced to detect informative
sources. The detection consistency is proved under the high-dimensional GLM
transfer learning setting. We also propose an algorithm to construct confidence
intervals of each coefficient component, and the corresponding theories are
provided. Extensive simulations and a real-data experiment verify the
effectiveness of our algorithms. We implement the proposed GLM transfer
learning algorithms in a new R package glmtrans, which is available on CRAN.
