Locally associated graphical models and mixed convex exponential families
Year: 2022
Type: article
Abstract: 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 and we show that a mixed dual likelihood estimator has simple exact properties for such families as well as asymptotic properties similar to the maximum likelihood estimator. We further relax the positivity assumption by penalizing negative partial correlations in what we term the positive graphical lasso. Finally, we develop a GOLAZO algorithm based on block-coordinate descent that applies to a number of optimization procedures that arise in the context of graphical models, including the estimation problems described above. We derive results on existence of the optimum for such problems.
Source: The Annals of Statistics
DOI: 10.1214/22-aos2219
Authors: Steffen Lauritzen, Piotr Zwiernik
Institutions: University of Copenhagen, University of Toronto
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3168394712