  This paper investigates the effectiveness of transfer learning based on
Mallows' Cp. We propose a procedure that combines transfer learning with
Mallows' Cp (TLCp) and prove that it outperforms the conventional Mallows' Cp
criterion in terms of accuracy and stability. Our theoretical results indicate
that, for any sample size in the target domain, the proposed TLCp estimator
performs better than the Cp estimator by the mean squared error (MSE) metric in
the case of orthogonal predictors, provided that i) the dissimilarity between
the tasks from source domain and target domain is small, and ii) the procedure
parameters (complexity penalties) are tuned according to certain explicit
rules. Moreover, we show that our transfer learning framework can be extended
to other feature selection criteria, such as the Bayesian information
criterion. By analyzing the solution of the orthogonalized Cp, we identify an
estimator that asymptotically approximates the solution of the Cp criterion in
the case of non-orthogonal predictors. Similar results are obtained for the
non-orthogonal TLCp. Finally, simulation studies and applications with real
data demonstrate the usefulness of the TLCp scheme.
