局部相伴图模型与混合凸指数族
Locally associated graphical models and mixed convex exponential families
摘要：
多元总正性的概念已被证明在金融和心理学中是有用的，但在其他应用中可能过于局限。在本文中，我们提出了一个概念的局部关联，其中高度连接的组件在一个图形模型是积极的关联，并研究其性质。我们的主要动机来自基因表达数据，其中图形模型已成为一种流行的探索工具。该模型的实例，我们称之为混合凸指数家庭，我们表明，混合双似然估计具有简单的确切性质，这样的家庭以及渐近性质类似的极大似然估计。我们进一步放宽了积极性假设，惩罚负的偏相关性，我们称之为积极的图形套索。最后，我们开发了一个基于块坐标下降的GOLAZO算法，该算法适用于图形模型中出现的一些优化过程，包括上述估计问题。我们得到的结果存在的最佳这类问题。
英文摘要：
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.
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