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.

翻译：本文提出了一种通过聚合奇异子空间信息，将多个源领域的表示知识迁移至目标噪声矩阵补全任务的方法。在我们的表示相似性框架下，首先通过求解基于适当去偏矩阵值数据集的双向主成分分析问题，整合线性表示信息。在从源领域获得更优的列与行表示估计量后，原始高维目标矩阵补全问题被转化为低维线性回归问题，其统计效率得到理论保证。文中还进一步探讨了多种扩展性议题，包括迁移后的统计推断方法以及对负迁移的鲁棒性分析。最后，通过大量仿真实验与多个真实数据案例验证了所提方法的有效性。