论文标题
本地相关的图形模型和混合凸指数家族
Locally associated graphical models and mixed convex exponential families
论文作者
论文摘要
事实证明，多元总阳性的概念在金融和心理学中很有用，但在其他应用中可能过于限制。在本文中，我们提出了一个本地关联的概念，其中图形模型中高度连接的组件正相关并研究其特性。我们的主要动机来自基因表达数据，其中图形模型已成为流行的探索性工具。这些模型是我们称之为混合凸指数家族的实例，我们表明，混合的双重可能性估计量具有与最大似然估计器相似的此类家族的简单精确特性。我们通过对正面图形套索中的负面部分相关性进行惩罚，进一步放松了阳性假设。最后，我们基于块坐标下降开发了一种golazo算法，该算法适用于在图形模型的上下文中出现的许多优化过程，包括上述估计问题。我们得出了有关此类问题最佳的结果。
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.
