马尔可夫模型中状态构建的数据驱动方法

中文摘要 AI 辅助

马尔可夫链是一种广泛用于对随时间变化的随机事件进行建模的随机过程。这类模型基于整个数据集的子集构建，这些子集被称为状态，且在转移概率方面被视为同质的。然而，这些状态的创建过程常被忽视或基于先验假设，可能会违反同质性要求，从而降低模型的有效性和预测能力。为填补这一空白，本文将有监督特征选择与无监督学习技术相结合，用于数据驱动的状态构建。研究考察了基于密度的聚类、谱聚类和Kohonen自组织映射在无需先验假设的情况下识别潜在群组的能力。本研究的贡献有两点：其一，本文提出了一种状态构建的方法框架，该框架融入了合适的无监督学习技术，并包含针对分类性能和马尔可夫模型准确性的适当度量；其二，该框架在实际应用中进行了测试，比较分析显示，谱聚类和Kohonen自组织映射最擅长捕捉固有结构。这些结果为改进应用马尔可夫建模中的状态定义提供了理论和方法指导的基础。

英文摘要

A Markov chain is a widely used stochastic process modelling random events over time. These models are built on subsets of the entire dataset, referred to as states, which are considered to be homogeneous regarding transition probabilities. However, the creation of these states is often disregarded or based on prior assumption, potentially violating the homogeneity requirement and thus decreasing the validity and predictive power of the model. In order to fill this gap, this paper combines supervised feature selection with unsupervised learning techniques for data-driven state construction. Density-based clustering, spectral clustering, and Kohonen self-organizing maps are examined for their ability to identify latent groups without prior assumptions. The contribution of this study is twofold. First, the paper presents a methodological framework for state construction incorporating suitable unsupervised learning techniques, with appropriate measures both for classification performance and Markov model accuracy. Secondly, the framework is tested on an application, resulting in a comparative analysis showing that spectral clustering and Kohonen self-organizing maps are best at capturing inherent structure. These results serve as a cornerstone in providing theoretical and methodological guidance for improving state definition in applied Markov modelling.

发表机构

• Vrije Universiteit Brussel（布鲁塞尔自由大学）

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