The Potts-Ising model for discrete multivariate data

Code

• github.com/aaamini/pois_comparisons
  OfficialIn papernone★ 1

Abstract

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 (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 by comparing with existing approaches.

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