Traditional hidden Markov models have been a useful tool to understand and model stochastic dynamic data; in the case of non-Gaussian data, models such as mixture of Gaussian hidden Markov models can be used. However, these suffer from the computation of precision matrices and have a lot of unnecessary parameters. As a consequence, such models often perform better when it is assumed that all variables are independent, a hypothesis that may be unrealistic. Hidden Markov models based on kernel density estimation are also capable of modeling non-Gaussian data, but they assume independence between variables. In this article, we introduce a new hidden Markov model based on kernel density estimation, which is capable of capturing kernel dependencies using context-specific Bayesian networks. The proposed model is described, together with a learning algorithm based on the expectation-maximization algorithm. Additionally, the model is compared to related HMMs on synthetic and real data. From the results, the benefits in likelihood and classification accuracy from the proposed model are quantified and analyzed.

翻译：传统隐马尔可夫模型是理解和建模随机动态数据的有用工具；对于非高斯数据，可以使用诸如高斯混合隐马尔可夫模型等模型。然而，这类模型在计算精度矩阵时存在困难，并包含大量不必要的参数。因此，当假设所有变量独立时（该假设可能不切实际），这些模型往往表现更好。基于核密度估计的隐马尔可夫模型也能对非高斯数据进行建模，但同样假设变量之间相互独立。本文提出一种基于核密度估计的新型隐马尔可夫模型，该模型能通过基于上下文的贝叶斯网络捕捉核依赖关系。我们详细描述了所提出的模型及其基于期望最大化算法的学习算法。此外，将所提模型与现有的相关隐马尔可夫模型在合成数据和真实数据上进行了比较。通过结果，我们量化并分析了所提模型在似然度和分类准确率方面的优势。