Functional Factor Modeling of Brain Connectivity
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脑连接的函数型因子建模
- 研究问题
- 面对离散观测的多维函数型脑成像数据，如何将长距离和短距离统计依赖分离，并获得可解释、可识别的功能连接结构？
- 方法与思路
- 作者将函数观测分解为不相关的全局与局部分量，在全局协方差光滑有限秩、局部协方差带状的条件下采用秩约束矩阵补全。
- 材料陈述的贡献
- 摘要称上述结构下分解可识别，并可构造一致的载荷估计量；模拟及静息态脑成像应用展示估计和后处理结果的解释性。
- 阅读关注点
- 应核对光滑性、有限秩及带状协方差条件如何保证识别，并检查离散观测下矩阵补全、载荷一致性和后处理解释的依据。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或获期刊接收；摘要未给出条件的完整技术形式，也未证明连接具有因果意义。
原文摘要
Many fMRI analyses examine functional connectivity, or statistical dependencies among remote brain regions. Yet popular methods for studying whole-brain functional connectivity often yield results that are difficult to interpret. Factor analysis offers a natural framework in which to study such dependencies, particularly given its emphasis on interpretability. However, multivariate factor models break down when applied to functional and spatiotemporal data, like fMRI. We present a factor model for discretely-observed multidimensional functional data that is well-suited to the study of functional connectivity. Unlike classical factor models which decompose a multivariate observation into a "common" term that captures covariance between observed variables and an uncorrelated "idiosyncratic" term that captures variance unique to each observed variable, our model decomposes a functional observation into two uncorrelated components: a "global" term that captures long-range dependencies and a "local" term that captures short-range dependencies. We show that if the global covariance is smooth with finite rank and the local covariance is banded with potentially infinite rank, then this decomposition is identifiable. Under these conditions, recovery of the global covariance amounts to rank-constrained matrix completion, which we exploit to formulate consistent loading estimators. We study these estimators, and their more interpretable post-processed counterparts, through simulations, then use our approach to uncover a rich covariance structure in a collection of resting-state fMRI scans.