摘要翻译:
隐马尔可夫模型是离散时间序列建模中最基本、应用最广泛的统计工具之一。一般来说,从数据中学习HMM在计算上是困难的(在密码学假设下),从业者通常求助于搜索启发式,这受到通常的局部最优问题的困扰。我们证明了在一个自然分离条件下(HMM参数的最小奇异值为界),存在一个高效且可证明正确的HMM学习算法。该算法的样本复杂度并不显式地依赖于不同(离散)观测值的数量--它通过底层HMM的光谱特性隐式地依赖于这个数量。这使得该算法特别适用于具有大量观察的设置,例如自然语言处理中的观察空间有时是语言中的单词。该算法简单,只需进行奇异值分解和矩阵乘法。
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英文标题:
《A Spectral Algorithm for Learning Hidden Markov Models》
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作者:
Daniel Hsu, Sham M. Kakade, Tong Zhang
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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:
Hidden Markov Models (HMMs) are one of the most fundamental and widely used statistical tools for modeling discrete time series. In general, learning HMMs from data is computationally hard (under cryptographic assumptions), and practitioners typically resort to search heuristics which suffer from the usual local optima issues. We prove that under a natural separation condition (bounds on the smallest singular value of the HMM parameters), there is an efficient and provably correct algorithm for learning HMMs. The sample complexity of the algorithm does not explicitly depend on the number of distinct (discrete) observations---it implicitly depends on this quantity through spectral properties of the underlying HMM. This makes the algorithm particularly applicable to settings with a large number of observations, such as those in natural language processing where the space of observation is sometimes the words in a language. The algorithm is also simple, employing only a singular value decomposition and matrix multiplications.
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PDF链接:
https://arxiv.org/pdf/0811.4413