Incremental learning of spatio-temporal Markov chains: An introductory theoretical framework for composite domain Markov chains

Kumralbaş Z., Tümer B.

Information Sciences, cilt.721, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 721
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1016/j.ins.2025.122590
  • Dergi Adı: Information Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Library, Information Science & Technology Abstracts (LISTA), Metadex, MLA - Modern Language Association Database, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Incremental learning, Markov chains, Non-stationarity, Parameter estimation, Spatio-temporal Markov chains, Stochastic learning
  • Marmara Üniversitesi Adresli: Evet

Özet

Markov chains (MCs), capable of modeling real world systems' non-stationary behavior of sequential nature, exploit temporal dependence (TD) within data under analysis. Stochastic Learning Weak Estimator (SLWE) effectively learns the parameters of MCs modeling such systems' behaviors. Another data context, besides TD, that likely contributes to a more powerful analysis especially in recognition of complex patterns, is the data proximity, i.e., spatial dependence (SD). Regular MCs remain insensitive to information offered by SD of data. In this paper, we extend the mathematical definition of MCs to employ SD, besides TD. We present the theoretical framework, in particular, for spatio-temporal MCs (STMCs) (2 domains) considering the spatial domain differently from that in literature and, in general, for composite domain MCs (CDMCs) (≥2 domains). Furthermore, SLWE is extended to estimate the parameters of both of a discrete-time first-order homogeneous STMC and CDMC. Corresponding theorems regarding the asymptotic behavior of estimates are provided. We show that the proposed method SLWE of STMC (SLWESTMC) (i) outperforms MCs relying solely on temporal or spatial dependence, and the traditional estimation methods in synthetic experiments, (ii) has competitive forecasting performance with significantly less time complexity over Deep Learning methods in real-world experiments.