论文标题
噪声矩阵完成的最佳无调凸松弛
Optimal tuning-free convex relaxation for noisy matrix completion
论文作者
论文摘要
本文涉及嘈杂的矩阵完成 - 从部分和嘈杂的条目中恢复低级矩阵的问题。在统一的采样和不一致的假设下，我们证明了无调的平方根矩阵完成估计器（Square-Root MC）实现了解决嘈杂矩阵完成问题的最佳统计性能。类似于高维线性回归中的平方根拉索估计器，方形 - 根MC不依赖于噪声大小的知识。求解Square-Root MC是一个凸面程序，但我们对Square-root MC的统计分析却取决于其与非convex级别受限估计器的紧密连接。
This paper is concerned with noisy matrix completion--the problem of recovering a low-rank matrix from partial and noisy entries. Under uniform sampling and incoherence assumptions, we prove that a tuning-free square-root matrix completion estimator (square-root MC) achieves optimal statistical performance for solving the noisy matrix completion problem. Similar to the square-root Lasso estimator in high-dimensional linear regression, square-root MC does not rely on the knowledge of the size of the noise. While solving square-root MC is a convex program, our statistical analysis of square-root MC hinges on its intimate connections to a nonconvex rank-constrained estimator.
