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arXiv 2103.11238stat.MLcs.LG
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基于符号分析的时间序列数据的马尔可夫建模

Markov Modeling of Time-Series Data using Symbolic Analysis

MERL（三菱电机研究实验室）

Devesh K. Jha

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摘要：

马尔可夫模型经常被用来捕捉时序数据的时间模式，用于统计学习应用。虽然隐马尔可夫模型为基础的学习机制在文献中得到了很好的研究，我们分析了一个符号动力学启发的方法。在这个保护伞下，时间序列数据的马尔可夫建模包括两个主要步骤--连续属性的离散化，然后估计离散化序列的时间记忆的大小。这两个步骤对于在离散空间中精确和简洁地表示时间序列数据是至关重要的。离散化控制所得到的离散化序列的信息内容。另一方面，符号序列的记忆估计有助于从离散化数据中提取预测模式。显然，信号表示为离散马尔可夫过程的有效性取决于这两个步骤。在本文中，我们将回顾离散随机过程的离散化和记忆估计的不同技术。特别是，我们将集中在离散随机过程的离散化和阶估计的个别问题。我们将提出一些结果，从文献中的划分动力系统理论和阶估计使用信息论和统计学习的概念。本文还提出了一些相关的问题公式，这将是有用的机器学习和统计学习应用程序使用的符号框架的数据分析。我们提出了一些统计分析的结果复杂的热声不稳定现象在稀薄预混燃烧的喷气涡轮发动机使用建议的马尔可夫建模方法。

英文摘要：

Markov models are often used to capture the temporal patterns of sequential data for statistical learning applications. While the Hidden Markov modeling-based learning mechanisms are well studied in literature, we analyze a symbolic-dynamics inspired approach. Under this umbrella, Markov modeling of time-series data consists of two major steps -- discretization of continuous attributes followed by estimating the size of temporal memory of the discretized sequence. These two steps are critical for the accurate and concise representation of time-series data in the discrete space. Discretization governs the information content of the resultant discretized sequence. On the other hand, memory estimation of the symbolic sequence helps to extract the predictive patterns in the discretized data. Clearly, the effectiveness of signal representation as a discrete Markov process depends on both these steps. In this paper, we will review the different techniques for discretization and memory estimation for discrete stochastic processes. In particular, we will focus on the individual problems of discretization and order estimation for discrete stochastic process. We will present some results from literature on partitioning from dynamical systems theory and order estimation using concepts of information theory and statistical learning. The paper also presents some related problem formulations which will be useful for machine learning and statistical learning application using the symbolic framework of data analysis. We present some results of statistical analysis of a complex thermoacoustic instability phenomenon during lean-premixed combustion in jet-turbine engines using the proposed Markov modeling method.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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