In recent days, a combination of finite mixture model (FMM) and hidden Markov model (HMM) is becoming popular for partitioning heterogeneous temporal data into homogeneous groups (clusters) with homogeneous time points (regimes). The regression mixtures commonly considered in this approach can also accommodate for covariates present in data. The classical fixed covariate approach, however, may not always serve as a reasonable assumption as it is incapable of accounting for the contribution of covariates in cluster formation. This paper introduces a novel approach for detecting clusters and regimes in time series data in the presence of random covariates. The computational challenges related to the proposed model has been discussed, and several simulation studies are performed. An application to United States COVID-19 data yields meaningful clusters and regimes.

中文翻译：

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具有协变量依赖的隐马尔可夫回归的有限混合模型

最近，有限混合模型 (FMM) 和隐马尔可夫模型 (HMM) 的组合越来越流行，用于将异构时间数据划分为具有同质时间点（区域）的同质组（集群）。这种方法中通常考虑的回归混合也可以适应数据中存在的协变量。然而，经典的固定协变量方法可能并不总是作为一个合理的假设，因为它无法解释协变量在集群形成中的贡献。本文介绍了一种在存在随机协变量的情况下检测时间序列数据中的聚类和状态的新方法。已经讨论了与所提出的模型相关的计算挑战，并进行了一些模拟研究。