Representational Transfer Learning for Matrix Completion
This work addresses matrix completion tasks in noisy settings, which is incremental as it builds on existing transfer learning and matrix completion methods.
The authors tackled the problem of noisy matrix completion by transferring representational knowledge from multiple sources to improve statistical efficiency, achieving significant performance gains in simulations and real data cases.
We propose to transfer representational knowledge from multiple sources to a target noisy matrix completion task by aggregating singular subspaces information. Under our representational similarity framework, we first integrate linear representation information by solving a two-way principal component analysis problem based on a properly debiased matrix-valued dataset. After acquiring better column and row representation estimators from the sources, the original high-dimensional target matrix completion problem is then transformed into a low-dimensional linear regression, of which the statistical efficiency is guaranteed. A variety of extensional arguments, including post-transfer statistical inference and robustness against negative transfer, are also discussed alongside. Finally, extensive simulation results and a number of real data cases are reported to support our claims.