主动学习多矩阵补全，自适应处理不同秩的未知矩阵。
Active multiple matrix completion with adaptive confidence sets
- 通过自适应置信集选择采样目标矩阵，动态优化查询策略。
- 算法在合成数据上表现优异，达到理论最优下界。
- 适合市场细分等多区域偏好建模场景，可处理异构数据规模。
本文提出一种新的多任务主动学习框架，旨在同时解决多个矩阵补全问题。每轮中，学习者可从任意一个矩阵中随机选取一个条目进行观测。实际动机来自市场细分场景，各矩阵代表不同区域的客户偏好。挑战在于各矩阵大小和秩均不同且未知。我们提出并分析了一种新算法 MAlocate，能够自适应不同矩阵的未知秩。进一步给出了下界证明，表明该策略为最小最大最优。通过合成实验验证了其性能。
原文摘要 · Abstract (English)
In this work, we formulate a new multi-task active learning setting in which the learner's goal is to solve multiple matrix completion problems simultaneously. At each round, the learner can choose from which matrix it receives a sample from an entry drawn uniformly at random. Our main practical motivation is market segmentation, where the matrices represent different regions with different preferences of the customers. The challenge in this setting is that each of the matrices can be of a different size and also of a different rank which is unknown. We provide and analyze a new algorithm, MAlocate that is able to adapt to the unknown ranks of the different matrices. We then give a lower-bound showing that our strategy is minimax-optimal and demonstrate its performance with synthetic experiments.
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