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Hidden Abstract Stack Markov Models with Learning Process

Author

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  • Mete Özbaltan

    (Department of Computer Engineering, Faculty of Engineering and Architecture, Erzurum Technical University, 25050 Erzurum, Türkiye)

Abstract

We present hidden abstract stack Markov models (HASMMs) with their learning process. The HASMMs we offer carry the more expressive nature of probabilistic context-free grammars (PCFGs) while allowing faster parameter fitting of hidden Markov models (HMMs). Both HMMs and PCFGs are widely utilized structured models, offering an effective formalism capable of describing diverse phenomena. PCFGs are better accommodated than HMMs such as for expressing natural language processing; however, HMMs outperform PCFGs for parameter fitting. We extend HMMs towards PCFGs for such applications, by associating each state of an HMM with an abstract stack, which can be thought of as the single-stack alphabet of pushdown automata (PDA). As a result, we leverage the expressive capabilities of PCFGs for such applications while mitigating the cubic complexity of parameter learning in the observation sequence length of PCFGs by adopting the bilinear complexity of HMMs.

Suggested Citation

  • Mete Özbaltan, 2024. "Hidden Abstract Stack Markov Models with Learning Process," Mathematics, MDPI, vol. 12(13), pages 1-19, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2144-:d:1431183
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    References listed on IDEAS

    as
    1. Fanping Wei & Jingjing Wang & Xiaobing Ma & Li Yang & Qingan Qiu, 2023. "An Optimal Opportunistic Maintenance Planning Integrating Discrete- and Continuous-State Information," Mathematics, MDPI, vol. 11(15), pages 1-19, July.
    2. Xiaoyue Wang & Jingxuan Wang & Ru Ning & Xi Chen, 2023. "Joint Optimization of Maintenance and Spare Parts Inventory Strategies for Emergency Engineering Equipment Considering Demand Priorities," Mathematics, MDPI, vol. 11(17), pages 1-18, August.
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