论文标题
预算上的建议：从一部分观察到的随机或主动采样的条目中恢复列的空间空间
Recommendation on a Budget: Column Space Recovery from Partially Observed Entries with Random or Active Sampling
论文作者
论文摘要
我们分析了交替的最小化，以供部分观察到的部分观察到的柱空间回收，大约较低的等级矩阵，每列越来越多的列和固定的观测预算。在这项工作中，我们证明，如果预算大于矩阵的等级，则列空间恢复成功 - 随着列的数量的增长，从交替最小化收敛到真实列空间的估计值，概率趋向于一个。从我们的证明技术中，我们自然制定了一种主动采样策略，用于选择一条列的条目，该列在理论上和经验上（在合成和真实数据上）比常见研究的统一随机抽样策略更好。
We analyze alternating minimization for column space recovery of a partially observed, approximately low rank matrix with a growing number of columns and a fixed budget of observations per column. In this work, we prove that if the budget is greater than the rank of the matrix, column space recovery succeeds -- as the number of columns grows, the estimate from alternating minimization converges to the true column space with probability tending to one. From our proof techniques, we naturally formulate an active sampling strategy for choosing entries of a column that is theoretically and empirically (on synthetic and real data) better than the commonly studied uniformly random sampling strategy.
