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摘要翻译：
近年来，基于权向量的分布学习算法，如AROW，在各种问题上获得了最先进的性能，并有很强的理论保证。将这些算法推广到矩阵模型是一个挑战，因为分布尺度的协方差中自由参数的数目为$n^4$与矩阵的维数$n$，并且在实际应用中$n$往往很大。我们描述、分析和实验了两个学习矩阵模型分布的新算法。我们的第一个算法在参数上保持对角协方差，可以处理大的协方差矩阵。第二种算法利用协方差来捕捉特征间的相关性，同时保持参数个数与原始矩阵的大小成线性。在错误界模型下对两种算法进行了分析，在相似图像检索和相似文档排序两个任务中，我们的方法比其他算法具有更高的精度。结果表明，分解算法具有较快的收敛速度。
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英文标题：
《Adaptive Regularization for Weight Matrices》
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作者：
Koby Crammer (The Technion), Gal Chechik (Bar Ilan University and
Google research)
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最新提交年份：
2012
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分类信息：
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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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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英文摘要：
Algorithms for learning distributions over weight-vectors, such as AROW were recently shown empirically to achieve state-of-the-art performance at various problems, with strong theoretical guaranties. Extending these algorithms to matrix models pose challenges since the number of free parameters in the covariance of the distribution scales as $n^4$ with the dimension $n$ of the matrix, and $n$ tends to be large in real applications. We describe, analyze and experiment with two new algorithms for learning distribution of matrix models. Our first algorithm maintains a diagonal covariance over the parameters and can handle large covariance matrices. The second algorithm factors the covariance to capture inter-features correlation while keeping the number of parameters linear in the size of the original matrix. We analyze both algorithms in the mistake bound model and show a superior precision performance of our approach over other algorithms in two tasks: retrieving similar images, and ranking similar documents. The factored algorithm is shown to attain faster convergence rate.
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PDF链接：
https://arxiv.org/pdf/1206.4639
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