Markov models provide a good approximation to probabilities associated with many categorical time series, and thus they are applied extensively. However, a major drawback associated with them is that the number of model parameters grows exponentially in the order of the model, and thus only very low-order models are considered in applications. Another drawback is lack of flexibility, in that Markov models give relatively few choices for the number of model parameters. Sparse Markov models are Markov models with conditioning histories that are grouped into classes such that the conditional probability distribution for members of each class is constant. The model gives a better handling of the trade-off between bias associated with having too few model parameters and variance from having too many. In this paper, methodology for efficient computation of pattern distributions through Markov chains with minimal state spaces is extended to the sparse Markov framework.

中文翻译：

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稀疏马尔可夫模型中模式统计的分布

马尔可夫模型提供了与许多分类时间序列相关的概率的良好近似，因此它们被广泛应用。然而，与它们相关的一个主要缺点是模型参数的数量以模型的顺序呈指数增长，因此在应用程序中只考虑非常低阶的模型。另一个缺点是缺乏灵活性，因为马尔可夫模型对模型参数的数量给出的选择相对较少。稀疏马尔可夫模型是具有条件历史的马尔可夫模型，这些历史被分组到类中，使得每个类成员的条件概率分布是恒定的。该模型可以更好地处理与模型参数过少相关的偏差与模型参数过多引起的方差之间的权衡。在本文中，