Locally associated graphical models and mixed convex exponential families
提出局部关联概念，用于图模型中高度连接组件的正关联分析；引入混合凸指数族和正图套索方法，并开发GOLAZO算法求解相关优化问题，适用于基因表达数据等场景。
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.