论文标题
与混合数据类型的强大矩阵完成
Robust Matrix Completion with Mixed Data Types
论文作者
论文摘要
我们考虑恢复结构化低级矩阵的矩阵完成问题，其部分观察到的条目具有混合的数据类型。对于矩阵中数据的基本分布是连续的，绝大多数解决方案都提出了具有强大统计保证的计算可行估计器。最近的一些方法使用类似的想法扩展了这些估计量，即基础分布属于指数家族的情况。这些方法中的大多数都假定只有一个基本分布，并且低等级约束是由矩阵Schatten Norm正规化的。我们提出了一种具有强大恢复保证的计算可行统计方法，以及适合并行化算法框架，以恢复一个低级矩阵，一方面观察到了部分混合数据类型的条目。我们还提供了广泛的模拟证据，以证实我们的理论结果。
We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong statistical guarantees for the case where the underlying distribution of data in the matrix is continuous. A few recent approaches have extended using similar ideas these estimators to the case where the underlying distributions belongs to the exponential family. Most of these approaches assume that there is only one underlying distribution and the low rank constraint is regularized by the matrix Schatten Norm. We propose a computationally feasible statistical approach with strong recovery guarantees along with an algorithmic framework suited for parallelization to recover a low rank matrix with partially observed entries for mixed data types in one step. We also provide extensive simulation evidence that corroborate our theoretical results.
