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

摘要： 潜变量模型在刻画因子之间的相互关系以及因子与观测变量之间的关联性时具有重要作用。在实际应用中，观测数据往往呈现出时序变异、多峰、偏态等特性，因此将经典的潜变量模型延伸到非齐次隐马尔可夫潜变量模型，并且为避免对完全数据的积分计算，将期望最大化（expectation-maximization，EM）算法引入到似然函数的计算上；采用Akaike信息准则和Bayes信息准则选择合适的模型，提出了相应的统计计算和检验方法，有效解决了隐马尔可夫模型中的最大估算似然函数问题；最后选择心理-健康数据进行了实验，实验结果表明该方法是有效的。

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