Qiu Huitong, Han Fang, Liu Han, Caffo Brian
Johns Hopkins University, Baltimore, USA.
Princeton University, Princeton, USA.
J R Stat Soc Series B Stat Methodol. 2016 Mar 1;78(2):487-504. doi: 10.1111/rssb.12123. Epub 2015 Jul 6.
In this manuscript we consider the problem of jointly estimating multiple graphical models in high dimensions. We assume that the data are collected from subjects, each of which consists of possibly dependent observations. The graphical models of subjects vary, but are assumed to change smoothly corresponding to a measure of closeness between subjects. We propose a kernel based method for jointly estimating all graphical models. Theoretically, under a double asymptotic framework, where both (, ) and the dimension can increase, we provide the explicit rate of convergence in parameter estimation. It characterizes the strength one can borrow across different individuals and the impact of data dependence on parameter estimation. Empirically, experiments on both synthetic and real resting state functional magnetic resonance imaging (rs-fMRI) data illustrate the effectiveness of the proposed method.
在本手稿中，我们考虑高维情况下联合估计多个图形模型的问题。我们假设数据是从多个主体收集的，每个主体由可能相关的观测值组成。各主体的图形模型各不相同，但假定会根据主体之间的接近程度度量而平滑变化。我们提出一种基于核的方法来联合估计所有图形模型。从理论上讲，在一个双渐近框架下，其中（，）和维度都可以增加，我们给出了参数估计中的明确收敛速率。它刻画了可以在不同个体间借用的强度以及数据相关性对参数估计的影响。从实证角度看，对合成数据和真实静息态功能磁共振成像（rs - fMRI）数据的实验都说明了所提方法的有效性。
