无限隐Markov模型理论及仿真研究

Theory and Simulation Research of the Infinite Hidden Markov Model

论述了传统隐Markov模型的理论及其存在的不足,并在此基础之上,阐明了无限隐Markov模型的理论及算法。在i HMM中,首先,从Dirichlet过程进行状态间转移概率的计算推导。然后,使用分层Dirichlet过程进行隐状态状态机制和生成机制的推理。其次,对模型超越参数的推理、优化和似然估计。还通过仿真实例对i HMM推理算法进行了验证,仿真结果表明i HMM具有很好的状态数目发掘能力,能够准确反映状态序列的结构特征。

This paper discussed the theory and the shortage of traditional hidden Markov models,and based on this,the theory and algorithms of the infinite Hidden Markov Model were also illuminated in detail. In i HMM,firstly,the inference of state transition probability was calculated in Dirichlet process. Secondly,a hierarchical Dirichlet process was used to infer hidden state mechanism and the emission mechanism. Lastly,the model hyperparameter optimization and likelihood estimation were discussed. The good performance of the inference algorithm of i HMM is tested and verified through the simulation examples,and the results show that i HMM is equipped with a good ability to explore the number of states,and reflect the state of the sequence of structural features accurately.