Hidden Markov models (HMMs) and their extensions have proven to be powerful tools for classification of observations that stem from systems with temporal dependence as they take into account that observations close in time are likely generated from the same state (i.e., class). When information on the classes of the observations is available in advanced, supervised methods can be applied. In this paper, we provide details for the implementation of four models for classification in a supervised learning context: HMMs, hidden semi-Markov models (HSMMs), autoregressive-HMMs, and autoregressive-HSMMs. Using simulations, we study the classification performance under various degrees of model misspecification to characterize when it would be important to extend a basic HMM to an HSMM. As an application of these techniques we use the models to classify accelerometer data from Merino sheep to distinguish between four different behaviors of interest. In particular in the field of movement ecology, collection of fine-scale animal movement data over time to identify behavioral states has become ubiquitous, necessitating models that can account for the dependence structure in the data. We demonstrate that when the aim is to conduct classification, various degrees of model misspecification of the proposed model may not impede good classification performance unless there is high overlap between the state-dependent distributions, that is, unless the observation distributions of the different states are difficult to differentiate. Supplementary materials accompanying this paper appear on-line.

隐马尔可夫模型 (HMM) 及其扩展已被证明是用于对源自具有时间依赖性的系统的观察进行分类的强大工具，因为它们考虑到接近时间的观察可能是从同一状态（即类）生成的。当有关观察类别的信息在高级可用时，可以应用监督方法。在本文中，我们提供了在监督学习上下文中实现四种分类模型的详细信息：HMM、隐藏半马尔可夫模型 (HSMM)、自回归 HMM 和自回归 HSMM。使用模拟，我们研究了不同程度的模型错误指定下的分类性能，以表征何时将基本 HMM 扩展到 HSMM 很重要。作为这些技术的应用，我们使用模型对来自美利奴羊的加速度计数据进行分类，以区分四种不同的感兴趣行为。特别是在运动生态学领域，随着时间的推移收集精细的动物运动数据以识别行为状态已经变得无处不在，需要模型来解释数据中的依赖结构。我们证明，当目标是进行分类时，所提出模型的不同程度的模型错误指定可能不会妨碍良好的分类性能，除非状态相关分布之间存在高度重叠，也就是说，除非不同状态的观察分布是难以区分。本文随附的补充材料出现在网上。