使用部分可观测数据识别静止马尔科夫链的发生器矩阵
Xuyan Xiang1,2, Jieming Zhou2, Yingchun Deng2
1School of Mathematics and Physics Science, Hunan University of Arts and Science, Changde 415000, China.
Chaos (Woodbury, N.Y.)
|February 22, 2024
概括
从有限的数据中识别静止马尔科夫链的发生器矩阵至关重要. 这项研究将撞击时间分布概括为解码生成器矩阵,使用系统状态的最小观测.
科学领域:
- 数学 数学 是一个数学.
- 可能性理论概率理论.
- 计算统计学 计算统计学
背景情况:
- 现实世界的系统往往具有不可访问的状态,使静止马尔科夫链的分析复杂化.
- 识别发电机矩阵对于理解系统动态至关重要,但对部分观测具有挑战性.
研究的目的:
- 开发使用最小观测方法识别静止马尔科夫链的发生器矩阵的方法.
- 对于不可逆转的静止马尔科夫链的撞击时间分布的概念进行概括.
主要方法:
- 从可逆到不可逆的静止马尔科夫链的撞击时间分布的概括.
- 使用禁忌速率和特定状态 (叶子和相邻状态) 的观察来解码发生器矩阵.
- 开发和验证用于准确计算发电机矩阵的算法.
主要成果:
- 可逆和特定不可逆的静止马尔科夫链的发生器矩阵可以在温和条件下使用有限的观测来确定.
- 拟议的算法在数值示例中展示了准确性和效率.
- 该研究证实,部分可观测的数据足以识别发电机矩阵.
结论:
- 这项研究提供了一种新的方法来解决静态马尔科夫链与不可访问的状态的反向问题.
- 这些发现具有实际意义,正如神经生理学中的应用所证明的那样.
- 这些方法可以从不完整的观测数据中重建系统动态.
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