二阶隐马尔可夫模型的学习算法及其与一阶隐马尔可夫模型的关系

The Learning Algorithm of the Second Order HMM and Its Relationship with the First Order HMM

研究和推导了二阶隐马尔可夫模型 (HMM2 )的学习算法 ,其中包括前向、后向变量的定义与计算 ,Viter-bi算法 ,以及 Baum - Welch算法 .同时还研究了 HMM2与一阶隐马尔可夫模型 (HMM1)之间的关系 ,发现对任给的 HMM2 ,总存在一个 HMM1与之等价 ,提出了 HMM2与 HMM1的等价性定理 。

In this paper, we investigate the learning algorithm of the second order HMM (HMM2), which includes the forward variable algorithm, backward variable algorithm, Viterbi algorithm and Baum Welch algorithm. Meanwhile, we study the relationship between the HMM2 and the first order HMM (HMM1), and find that for any HMM2 there always exists a HMM1 which is equal to the HMM2. We propose and prove the equivalent theorem of the HMM2 and HMM1.