Deligianni Fani, Varoquaux Gael, Thirion Bertrand, Robinson Emma, Sharp David J, Edwards A David, Rueckert Daniel
Department of Computing, Imperial College London, UK.
Inf Process Med Imaging. 2011;22:296-307. doi: 10.1007/978-3-642-22092-0_25.
We present a novel probabilistic framework to learn across several subjects a mapping from brain anatomical connectivity to functional connectivity, i.e. the covariance structure of brain activity. This prediction problem must be formulated as a structured-output learning task, as the predicted parameters are strongly correlated. We introduce a model selection framework based on cross-validation with a parametrization-independent loss function suitable to the manifold of covariance matrices. Our model is based on constraining the conditional independence structure of functional activity by the anatomical connectivity. Subsequently, we learn a linear predictor of a stationary multivariate autoregressive model. This natural parameterization of functional connectivity also enforces the positive-definiteness of the predicted covariance and thus matches the structure of the output space. Our results show that functional connectivity can be explained by anatomical connectivity on a rigorous statistical basis, and that a proper model of functional connectivity is essential to assess this link.
我们提出了一种新颖的概率框架，用于跨多个受试者学习从脑解剖连接性到功能连接性的映射，即脑活动的协方差结构。由于预测参数高度相关，此预测问题必须被表述为结构化输出学习任务。我们引入了一个基于交叉验证的模型选择框架，该框架具有适用于协方差矩阵流形的与参数化无关的损失函数。我们的模型基于通过解剖连接性来约束功能活动的条件独立性结构。随后，我们学习一个平稳多元自回归模型的线性预测器。这种功能连接性的自然参数化还强制预测协方差的正定，从而与输出空间的结构相匹配。我们的结果表明，功能连接性可以在严格的统计基础上由解剖连接性来解释，并且适当的功能连接性模型对于评估这种联系至关重要。
