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基于约束矩阵补全的广义加权自动机谱学习
Spectral Learning of General Weighted Automata via Constrained Matrix Completion |
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| 课程网址: |
http://videolectures.net/nips2012_balle_spectral_learning/
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| 主讲教师: |
Borja Balle
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| 开课单位: |
加泰罗尼亚技术大学
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| 开课时间: |
2013-01-16
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| 课程语种: |
英语
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| 中文简介: |
文本和语音处理以及计算生物学中的许多任务涉及从可变长度字符串到实数编号的函数。可以通过加权自动机来计算一大类这样的函数。最近已经提出了基于Hankel矩阵的奇异值分解的谱方法用于学习可以通过加权自动机计算的字符串上的概率分布。在本文中，我们展示了如何将这种方法应用于从任意分布生成的字符串标签对样本中学习一般加权自动机的问题。这种方法的主要障碍是，一般来说，需要分解的Hankel矩阵的某些条目可能会丢失。我们提出了一种基于求解约束矩阵完成问题的解决方案。结合这两种成分，获得了用于学习一般加权自动机的全新算法族。给出了该类中特定算法的泛化边界。防护依赖于矩阵完成和光谱学习的稳定性分析。
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| 课程简介: |
Many tasks in text and speech processing and computational biology involve functions from variable-length strings to real numbers. A wide class of such functions can be computed by weighted automata. Spectral methods based on singular value decompositions of Hankel matrices have been recently proposed for learning probability distributions over strings that can be computed by weighted automata. In this paper we show how this method can be applied to the problem of learning a general weighted automata from a sample of string-label pairs generated by an arbitrary distribution. The main obstruction to this approach is that in general some entries of the Hankel matrix that needs to be decomposed may be missing. We propose a solution based on solving a constrained matrix completion problem. Combining these two ingredients, a whole new family of algorithms for learning general weighted automata is obtained. Generalization bounds for a particular algorithm in this class are given. The proofs rely on a stability analysis of matrix completion and spectral learning.
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| 关 键 词: |
文本; 语音处理; 函数
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| 课程来源: |
视频讲座网
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| 最后编审: |
2019-09-06：lxf
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| 阅读次数: |
71
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