Nguyen Hien D, McLachlan Geoffrey J, Orban Pierre, Bellec Pierre, Janke Andrew L
Department of Mathematics and Statistics, La Trobe University, Victoria, Bundoora 3086, Australia
School of Mathematics and Physics, University of Queensland, St. Lucia 4072, Australia
Neural Comput. 2017 Apr;29(4):990-1020. doi: 10.1162/NECO_a_00938. Epub 2017 Jan 17.
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 evaluating 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 with 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.
自回归混合（MoAR）模型提供了一种基于模型的时间序列数据聚类方法。MoAR模型的最大似然（ML）估计需要评估大量正态随机变量密度的乘积。在实际场景中，随着时间序列长度的增加，这些乘积会收敛到零，因此如果不使用数值技巧，MoAR模型的ML估计就变得不可行。我们提出一种最大伪似然（MPL）估计方法作为使用数值技巧的替代方法。MPL估计器被证明是一致的，并且可以通过期望最大化（EM）算法进行计算。在能够计算ML估计器的情况下，通过模拟来评估MPL估计器相对于ML估计器的性能。作为该方法的一个示例，给出了一个应用于静息态功能磁共振成像（fMRI）实验产生的时间序列数据聚类的例子。
