时间序列数据基于模型聚类的最大伪距估计
Maximum Pseudolikelihood Estimation for Model-Based Clustering of Time Series Data
摘要：
混合自回归模型（MoAR）为时间序列数据的聚类提供了一种基于模型的方法。MoAR模型的极大似然（ML）估计需要估计正态随机变量的大量密度的乘积。在实际情况下，这些产品收敛到零的长度的时间序列的增加，因此ML估计的MoAR模型变得不可行，而不使用数值技巧。我们提出了一个最大的伪像（MPL）估计方法作为替代使用的数值技巧。MPL估计被证明是一致的，可以通过EM（期望-最大化）算法计算。模拟被用来评估性能的MPL估计对ML估计的情况下，后者能够计算。聚类的时间序列数据所产生的休息状态功能磁共振成像实验的应用程序作为演示的方法。
英文摘要：
Mixture of autoregressions (MoAR) models provide a model-based approach to the clustering of time series data. The maximum likelihood (ML) estimation of MoAR models requires the evaluation of products of large numbers of densities of normal random variables. In practical scenarios, these products converge to zero as the length of the time series increases, and thus the ML estimation of MoAR models becomes infeasible without the use of numerical tricks. We propose a maximum pseudolikelihood (MPL) estimation approach as an alternative to the use of numerical tricks. The MPL estimator is proved to be consistent and can be computed via an EM (expectation--maximization) algorithm. Simulations are used to assess the performance of the MPL estimator against that of the ML estimator in cases where the latter was able to be calculated. An application to the clustering of time series data arising from a resting-state fMRI experiment is presented as a demonstration of the methodology.
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