# Locally associated graphical models and mixed convex exponential families

@inproceedings{Lauritzen2020LocallyAG, title={Locally associated graphical models and mixed convex exponential families}, author={Steffen L. Lauritzen and Piotr Zwiernik}, year={2020} }

The notion of multivariate total positivity has proved to be useful in finance and psychology but may be too restrictive in other applications. In this paper we propose a concept of local association, where highly connected components in a graphical model are positively associated and study its properties. Our main motivation comes from gene expression data, where graphical models have become a popular exploratory tool. The models are instances of what we term mixed convex exponential families…

## 2 Citations

Total positivity in multivariate extremes

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An estimator for the parameters of the Hüsler–Reiss distribution under EMTP2 is proposed as the solution of a convex optimization problem with Laplacian constraint and it is proved that this estimator is consistent and typically yields a sparse model with possibly non-decomposable extremal graphical structure.

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This work presents a version of the algorithm which avoids repeated inversion of large matrices, resulting in increased speed, in particular when graphs are sparse, leading to increased speed in Gaussian graphical models.

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