摘要翻译：
低秩矩阵近似常被用来帮助将标准机器学习算法扩展到大规模问题。近年来，矩阵一致性被用来描述在这些低秩近似和其他基于采样的算法（如矩阵组合、鲁棒PCA）的背景下从矩阵条目子集中提取全局信息的能力。由于相干性是由矩阵的奇异向量定义的，并且计算代价很高，这些结果的实际意义很大程度上取决于以下问题：我们能有效而准确地估计矩阵的相干性吗？在本文中，我们解决了这个问题。提出了一种新的从少量列估计相干性的算法，对其行为进行了形式化分析，并在此基础上导出了一个新的基于相干性的矩阵逼近界。然后，我们在合成数据集和真实数据集上给出了大量的实验结果，这些结果证实了我们的最坏情况理论分析，但在考虑低秩近似时，为我们提出的算法的使用提供了有力的支持。我们的算法有效而准确地估计了大范围数据集上的矩阵相干性，这些相干性估计是基于抽样的矩阵逼近在逐个案例基础上的有效性的优秀预测器。
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英文标题：
《On the Estimation of Coherence》
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作者：
Mehryar Mohri, Ameet Talwalkar
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最新提交年份：
2010
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分类信息：

一级分类：Statistics        统计学
二级分类：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类：Computer Science        计算机科学
二级分类：Machine Learning        机器学习
分类描述：Papers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.
关于机器学习研究的所有方面的论文（有监督的，无监督的，强化学习，强盗问题，等等），包括健壮性，解释性，公平性和方法论。对于机器学习方法的应用，CS.LG也是一个合适的主要类别。
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英文摘要：
  Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of matrix entries in the context of these low-rank approximations and other sampling-based algorithms, e.g., matrix com- pletion, robust PCA. Since coherence is defined in terms of the singular vectors of a matrix and is expensive to compute, the practical significance of these results largely hinges on the following question: Can we efficiently and accurately estimate the coherence of a matrix? In this paper we address this question. We propose a novel algorithm for estimating coherence from a small number of columns, formally analyze its behavior, and derive a new coherence-based matrix approximation bound based on this analysis. We then present extensive experimental results on synthetic and real datasets that corroborate our worst-case theoretical analysis, yet provide strong support for the use of our proposed algorithm whenever low-rank approximation is being considered. Our algorithm efficiently and accurately estimates matrix coherence across a wide range of datasets, and these coherence estimates are excellent predictors of the effectiveness of sampling-based matrix approximation on a case-by-case basis.
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PDF链接：
https://arxiv.org/pdf/1009.0861