Robust Matrix Completion with Heavy-tailed Noise
重尾噪声下的稳健矩阵补全AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
本页为预印本版本；arXiv 收录、作者填写的期刊信息以及作者既有发表经历，都不单独证明本篇已接收。作者发表记录按 OpenAlex 身份与完整姓名、本站覆盖期刊 ISSN 及正式卷期核对，只展示已核实例，档案仍可能误合并。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要研究通用低秩矩阵恢复，未涉及因果面板、经济网络或其他指定应用方向。
反馈分类问题
正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
关注这篇论文的作者
重尾噪声下的稳健矩阵补全
- 研究问题
- 仅有少量带重尾且可能不对称噪声的矩阵元素时，如何恢复低秩矩阵，并控制算法收敛和统计估计误差？
- 方法与思路
- 作者结合自适应 Huber 损失、平衡低秩矩阵分解、稳健谱初始化与梯度下降，并用留一法分析算法迭代。
- 材料陈述的贡献
- 摘要称，在误差二阶矩有界及其他条件下，迭代误差几何下降至极小极大最优统计误差，其阶与次高斯情形相同。
- 阅读关注点
- 应核对采样机制、低秩矩阵条件、Huber 参数如何平衡偏差与稳健性，以及初始化和最优误差结论的适用范围。
- 阅读边界
- 所据为 arXiv 预印本，同行评审与期刊接收未核实；摘要未列出完整采样与矩阵条件，二阶矩有界并非全部要求。
原文摘要
This paper studies low-rank matrix completion in the presence of heavy-tailed and possibly asymmetric noise, where we aim to estimate an underlying low-rank matrix given a set of highly incomplete noisy entries. Though the matrix completion problem has attracted much attention in the past decade, there is still lack of theoretical understanding when the observations are contaminated by heavy-tailed noises. Prior theory falls short of explaining the empirical results and is unable to capture the optimal dependence of the estimation error on the noise level. In this paper, we adopt an adaptive Huber loss to accommodate heavy-tailed noise, which is robust against large and possibly asymmetric errors when the parameter in the loss function is carefully designed to balance the Huberization biases and robustness to outliers. Then, we propose an efficient nonconvex algorithm via a balanced low-rank Burer-Monteiro matrix factorization and gradient decent with robust spectral initialization. We prove that under merely bounded second moment condition on the error distributions, rather than the sub-Gaussian assumption, the Euclidean error of the iterates generated by the proposed algorithm decrease geometrically fast until achieving a minimax-optimal statistical estimation error, which has the same order as that in the sub-Gaussian case. The key technique behind this significant advancement is a powerful leave-one-out analysis framework. The theoretical results are corroborated by our simulation studies.