主题间分析：用密集的内部图推断稀疏的交互
Inter-Subject Analysis: Inferring Sparse Interactions with Dense Intra-Graphs
摘要：
我们开发了一个新的建模框架，跨学科分析（ISA）。ISA的目标是探索不同主体之间的依存结构，主体内依存是讨厌的。研究自然刺激下脑区之间的功能连接在神经科学中有重要的应用。我们的框架是基于高斯图模型，ISA可以转换为问题的估计和推理的主题间精度矩阵。主要的统计挑战是，我们不对整个精度矩阵施加稀疏性约束，我们只假设受试者间部分是稀疏的。对于估计，我们建议估计一个替代参数，以绕过非稀疏问题，它可以实现渐近一致性，即使内部主题依赖是密集的。对于推理，我们提出了一个“解开和和弦”的过程来消除我们的估计。在不对对数似然函数的逆Hessian函数作稀疏性假设的情况下，该方法也是有效的。这种推论方法具有普遍性，并可应用于其它许多统计问题，因而具有独立的理论价值。仿真和脑成像数据的数值实验验证了我们的方法和理论。
英文摘要：
We develop a new modeling framework for Inter-Subject Analysis (ISA). The goal of ISA is to explore the dependency structure between different subjects with the intra-subject dependency as nuisance. It has important applications in neuroscience to explore the functional connectivity between brain regions under natural stimuli. Our framework is based on the Gaussian graphical models, under which ISA can be converted to the problem of estimation and inference of the inter-subject precision matrix. The main statistical challenge is that we do not impose sparsity constraint on the whole precision matrix and we only assume the inter-subject part is sparse. For estimation, we propose to estimate an alternative parameter to get around the non-sparse issue and it can achieve asymptotic consistency even if the intra-subject dependency is dense. For inference, we propose an "untangle and chord" procedure to de-bias our estimator. It is valid without the sparsity assumption on the inverse Hessian of the log-likelihood function. This inferential method is general and can be applied to many other statistical problems, thus it is of independent theoretical interest. Numerical experiments on both simulated and brain imaging data validate our methods and theory.
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