The Potts-Ising model for discrete multivariate data
The Potts-Ising model for discrete multivariate data
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发表时间：
2020
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通讯作者：
Zahra S. Razaee;A. Amini
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作者：
Zahra S. Razaee;A. Amini
多元离散数据中的依赖关系建模是一个具有挑战性的问题，特别是在高维数据中。波茨模型是一种通用的此类模型，适合每个坐标都是分类变量的情况。然而，当类别数量很大时，完整的Potts模型有太多的参数无法准确拟合。我们介绍了一个变化的波茨模型，允许一般的分类边际和伊辛型多变量依赖。这将完全Potts模型中的参数数量从k（d 2 K 2）减少到O（d 2 + Kd），其中K是类别的数量，d是数据的维度。我们证明了拟合这个新的Potts-Ising模型的复杂性与Ising模型的复杂性相同。特别是，采用邻域回归框架，该模型可以通过求解d个单独的逻辑回归来拟合。通过与现有方法的比较，我们证明了该模型在真实的数据中捕获多变量依赖关系的能力。
Modeling dependencies in multivariate discrete data is a challenging problem, especially in high dimensions. The Potts model is a versatile such model, suitable when each coordinate is a categorical variable. However, the full Potts model has too many parameters to be accurately fit when the number of categories is large. We introduce a variation on the Potts model that allows for general categorical marginals and Ising-type multivariate dependence. This reduces the number of parameters from Ω( d 2 K 2 ) in the full Potts model to O ( d 2 + Kd ) , where K is the number of categories and d is the dimension of the data. We show that the complexity of fitting this new Potts-Ising model is the same as that of an Ising model. In particular, adopting the neighborhood regression framework, the model can be fit by solving d separate logistic regressions. We demonstrate the ability of the model to capture multivariate dependencies in real data by comparing with existing approaches.