关键词: 隐马尔可夫模型, 潜变量模型, 期望最大化（EM）, 向前向后递推

Abstract: Latent variable model plays an important role in characterizing interrelationship among factor variables and constructing relationships between factor and observed variable. However, in real applications, data set often takes on the temporal variability, multimode, skewness, and so on. This paper extends the classic latent variable model to the latent variable model mixed with non-homogenous hidden Markov model. In order to avoid integral about complete data, this paper introduces the expectation-maximization (EM) algorithm to calculate the likelihood function. At the same time, this paper presents the corresponding statistics using the Akaike information criterion and the Bayes information criterion to select appropriate model, which effectively solves the estimation problem in the hidden Markov model. Finally, the experiments are carried out in the mental-health data and the results show that the method is effective.

Key words: hidden Markov model, latent variable model, expectation-maximization (EM), forward-backward recursion