Probabilistic graphical models have become an important unsupervised learning tool for detecting network structures for a variety of problems, including the estimation of functional neuronal connectivity from two-photon calcium imaging data. However, in the context of calcium imaging, technological limitations only allow for partially overlapping layers of neurons in a brain region of interest to be jointly recorded. In this case, graph estimation for the full data requires inference for edge selection when many pairs of neurons have no simultaneous observations. This leads to the Graph Quilting problem, which seeks to estimate a graph in the presence of block-missingness in the empirical covariance matrix. Solutions for the Graph Quilting problem have previously been studied for Gaussian graphical models; however, neural activity data from calcium imaging are often non-Gaussian, thereby requiring a more flexible modeling approach. Thus, in our work, we study two approaches for nonparanormal Graph Quilting based on the Gaussian copula graphical model, namely a maximum likelihood procedure and a low-rank based framework. We provide theoretical guarantees on edge recovery for the former approach under similar conditions to those previously developed for the Gaussian setting, and we investigate the empirical performance of both methods using simulations as well as real data calcium imaging data. Our approaches yield more scientifically meaningful functional connectivity estimates compared to existing Gaussian graph quilting methods for this calcium imaging data set.

翻译：概率图模型已成为多种问题中检测网络结构的重要无监督学习工具，包括从双光子钙成像数据估计功能性神经连接。然而，在钙成像背景下，技术限制仅允许联合记录感兴趣脑区域中部分重叠的神经元层。此时，当许多神经元对缺乏同步观测时，完整数据的图估计需要针对边选择进行推断。这引出了"图拼接"问题，即当经验协方差矩阵出现分块缺失时，试图估计图结构。图拼接问题的解决方案此前已在高斯图模型中得到研究；然而，钙成像的神经活动数据往往非高斯，因此需要更灵活的建模方法。为此，我们在工作中研究了基于高斯连接函数图模型的两种非参数正态图拼接方法——最大似然方法和低秩框架。我们为前一种方法在类似先前高斯设定的条件下提供了边恢复的理论保证，并通过模拟实验和真实钙成像数据探究了两种方法的实证性能。与现有基于高斯的图拼接方法相比，我们的方法在该钙成像数据集上生成了更具科学意义的功能连接估计。