Fitting Sparse Markov Models to Categorical Time Series Using Convex Clustering
提出一种基于凸聚类和正则化的方法拟合稀疏马尔可夫模型，解决高阶马尔可夫链参数过多的问题，并通过模拟和疾病亚型分类数据验证其有效性。
Higher-order Markov chains are frequently used to model categorical time series. However, a major problem with fitting such models is the exponentially growing number of parameters in the model order. A popular approach to parsimonious modeling is to use a Variable Length Markov Chain (VLMC), which determines relevant contexts (recent pasts) of variable orders and forms a context tree. A more general parsimonious modeling approach is given by Sparse Markov Models (SMMs), where the possible histories of order m are partitioned such that transition probability vectors are identical for histories belonging to the same group. In this paper, we develop an elegant method of fitting SMMs based on convex clustering and regularization. The regularization parameter is selected using the BIC criterion. Theoretical results establish model selection consistency for large sample sizes. Extensive simulation results under different set-ups are presented to study finite sample performance of the method. Real data analysis on modelling and classifying disease sub-types demonstrates the applicability of our method.