Distributions of pattern statistics in sparse Markov models
Distributions of pattern statistics in sparse Markov models
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DOI：
10.1007/s10463-019-00714-6
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发表时间：
2020-08-01
影响因子：
1
通讯作者：
Martin, Donald E. K.
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文献类型：
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作者：
Martin, Donald E. K.
马尔可夫模型很好地逼近了与许多分类时间序列相关的概率，因此得到了广泛的应用。然而，与它们相关的一个主要缺点是模型参数的数量按模型的阶数指数增长，因此在应用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提供的选择相对较少。稀疏马尔可夫模型是具有条件历史的马尔可夫模型，这些条件历史被分组到类中，使得每个类的成员的条件概率分布是恒定的。该模型更好地处理了因模型参数太少而产生的偏差和因模型参数太多而产生的差异之间的权衡。本文将通过状态空间极小的马尔可夫链有效计算模式分布的方法推广到稀疏马尔可夫框架。
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.