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This research addresses a critical gap in Markov chain modeling by integrating supervised feature selection with unsupervised learning techniques like spectral clustering and Kohonen maps to define states without prior assumptions. The study demonstrates that these data-driven approaches significantly improve model validity and predictive power compared to traditional methods reliant on arbitrary state definitions. By objectively evaluating clustering algorithms against classification performance and transition probability homogeneity, the paper offers a robust framework for enhancing applied stochastic modeling in complex systems.
A Data-Driven Approach to State Construction in Markov Models
arXiv:2608.21480v1 Announce Type: cross Abstract: 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.
Abstract: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.
Machine Learning (stat.ML); Machine Learning (cs.LG); Probability (math.PR); Methodology (stat.ME)
arXiv:2608.21480 [stat.ML]
(or arXiv:2608.21480v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2608.21480 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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