Alpha-Beta HMM: Hidden Markov Model Filtering with Equal Exit Probabilities and a Step-Size Parameter
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913885721722880 |
|---|---|
| author | Sui, Dongyan Pu, Haotian Leng, Siyang Vlaski, Stefan |
| author_facet | Sui, Dongyan Pu, Haotian Leng, Siyang Vlaski, Stefan |
| contents | The hidden Markov model (HMM) provides a powerful framework for inference in time-varying environments, where the underlying state evolves according to a Markov chain. To address the optimal filtering problem in general dynamic settings, we propose the $αβ$-HMM algorithm, which simplifies the state transition model to a Markov chain with equal exit probabilities and introduces a step-size parameter to balance the influence of observational data and the model. By analyzing the algorithm's dynamics in stationary environments, we uncover a fundamental trade-off between inference accuracy and adaptation capability, highlighting how key parameters and observation quality impact performance. A comprehensive theoretical analysis of the nonlinear dynamical system governing the evolution of the log-belief ratio, along with supporting numerical experiments, demonstrates that the proposed approach effectively balances adaptability and inference performance in dynamic environments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01759 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Alpha-Beta HMM: Hidden Markov Model Filtering with Equal Exit Probabilities and a Step-Size Parameter Sui, Dongyan Pu, Haotian Leng, Siyang Vlaski, Stefan Systems and Control Applications The hidden Markov model (HMM) provides a powerful framework for inference in time-varying environments, where the underlying state evolves according to a Markov chain. To address the optimal filtering problem in general dynamic settings, we propose the $αβ$-HMM algorithm, which simplifies the state transition model to a Markov chain with equal exit probabilities and introduces a step-size parameter to balance the influence of observational data and the model. By analyzing the algorithm's dynamics in stationary environments, we uncover a fundamental trade-off between inference accuracy and adaptation capability, highlighting how key parameters and observation quality impact performance. A comprehensive theoretical analysis of the nonlinear dynamical system governing the evolution of the log-belief ratio, along with supporting numerical experiments, demonstrates that the proposed approach effectively balances adaptability and inference performance in dynamic environments. |
| title | Alpha-Beta HMM: Hidden Markov Model Filtering with Equal Exit Probabilities and a Step-Size Parameter |
| topic | Systems and Control Applications |
| url | https://arxiv.org/abs/2504.01759 |