三阶隐马氏模型算法及其与一阶隐马氏模型的关系

Algorithms of Third-Order Hidden Markov Model and Its Relationship with First-Order Hidden Markov Model

为了考虑更多的统计特征,提出了一类三阶隐马氏模型,其中状态转移和输出观测同时取决于当前状态和前面两个状态.研究和推导了这类三阶隐马氏模型中估值问题的向前—向后算法、解码问题的Viterbi算法和学习问题的Baum-Welch算法.对此类三阶隐马氏模型,构造了一个与之等价的一阶隐马氏模型,提出并证明了它们的等价性定理.研究结果丰富了隐马氏模型的算法理论,可为一些实际应用提供更好的方法.

In order to consider more statistical characteristics, a class of third-order hidden Markov model is proposed. In this model, both state transition and output observation depend on the current state and on the two preceding states as well. Three algorithms of the third-order hidden Markov model are studied and derived, including the forward-backward algorithm for observation sequence evaluation, the Viterbi algorithm for determining the optimal state sequence, and the Baum-Welch algorithm for training the third-order hidden Markov model. A first-order hidden Markov model equivalent to the third-order hidden Markov model is constructed. A theorem of their equivalence is proposed and proved. This study contributes to the algorithmic theory of the hidden Markov model, and provides a better method to practical applications.