Neuroimaging is the growing area of neuroscience devoted to produce data with the goal of capturing processes and dynamics of the human brain. We consider the problem of inferring the brain connectivity network from time-dependent functional magnetic resonance imaging (fMRI) scans. To this aim we propose the symmetric graphical lasso, a penalized likelihood method with a fused type penalty function that takes into explicit account the natural symmetrical structure of the brain. Symmetric graphical lasso allows one to learn simultaneously both the network structure and a set of symmetries across the two hemispheres. We implement an alternating directions method of multipliers algorithm to solve the corresponding convex optimization problem. Furthermore, we apply our methods to estimate the brain networks of two subjects, one healthy and one affected by mental disorder, and to compare them with respect to their symmetric structure. The method applies once the temporal dependence characterizing fMRI data have been accounted for and we compare the impact on the analysis of different detrending techniques on the estimated brain networks. Although we focus on brain networks, symmetric graphical lasso is a tool which can be more generally applied to learn multiple networks in a context of dependent samples.

中文翻译：

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具有对称性的大脑网络的融合图形套索

神经影像学是神经科学不断发展的领域，致力于产生数据，目标是捕捉人脑的过程和动态。我们考虑从依赖于时间的功能磁共振成像 (fMRI) 扫描推断大脑连接网络的问题。为此，我们提出了对称图形套索，这是一种具有融合型惩罚函数的惩罚似然方法，该方法明确考虑了大脑的自然对称结构。对称图形套索允许同时学习网络结构和跨越两个半球的一组对称性。我们实现了乘法器算法的交替方向方法来解决相应的凸优化问题。此外，我们应用我们的方法来估计两个受试者的大脑网络，一个健康的和一个受精神障碍影响的，并比较它们的对称结构。该方法适用于表征 fMRI 数据的时间依赖性，我们比较了不同去趋势技术对估计大脑网络的分析的影响。尽管我们专注于大脑网络，对称图形套索是一种工具，可以更广泛地应用于在依赖样本的上下文中学习多个网络。