论文标题
通过线性编程基于可能性的指数随机图模型的推断
Likelihood-based Inference for Exponential-Family Random Graph Models via Linear Programming
论文作者
论文摘要
本文讨论了确定给定点还是一组点的问题，是$ d $ dimensions中另一组点的凸船体内。当使用特定的loglikelihood函数近似值的指数族模型时，此问题自然而然地在统计环境中出现。特别是，我们在此处讨论网络模型的应用程序。虽然可以通过简单的线性程序来解决凸船体问题，但在统计文献中，这种方法并不众所周知。此外，本文详细介绍了当前在用于网络建模的广泛使用的“ ERGM”软件包中实现的凸船体测试算法的几个重大改进。
This article discusses the problem of determining whether a given point, or set of points, lies within the convex hull of another set of points in $d$ dimensions. This problem arises naturally in a statistical context when using a particular approximation to the loglikelihood function for an exponential family model; in particular, we discuss the application to network models here. While the convex hull question may be solved via a simple linear program, this approach is not well known in the statistical literature. Furthermore, this article details several substantial improvements to the convex hull-testing algorithm currently implemented in the widely used 'ergm' package for network modeling.
