通过融合多个源数据的奇异子空间信息，提升噪声矩阵补全的准确性。
Representational Transfer Learning for Matrix Completion
- 利用多源数据的奇异子空间信息进行表征迁移。
- 将高维矩阵补全转为低维线性回归，提升统计效率。
- 适用于存在噪声且数据量不足的矩阵补全场景。
我们提出一种表征迁移学习方法，通过聚合多个来源的奇异子空间信息，用于目标噪声矩阵补全任务。在表征相似性框架下，首先基于去偏矩阵数据集求解双向主成分分析问题，整合线性表征信息。由此获得更优的列与行表征估计器后，原高维矩阵补全问题被转化为低维线性回归，其统计效率得到保证。同时讨论了转移后的统计推断及对负迁移的鲁棒性等扩展问题。最后，通过大量模拟实验和真实数据案例验证了方法的有效性。
原文摘要 · Abstract (English)
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.
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