Nonparanormal graph quilting with applications to calcium imaging
Nonparanormal graph quilting with applications to calcium imaging
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DOI：
10.1002/sta4.623
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发表时间：
2023-01-01
期刊：
影响因子：
1.7
通讯作者：
Allen，Genevera I.
中科院分区：
文献类型：
--
作者：
Chang，Andersen;Zheng，Lili;Allen，Genevera I.
概率图模型已经成为一种重要的无监督学习工具，用于检测各种问题的网络结构，包括从双光子钙成像数据中估计功能神经元连接。然而，在钙成像的背景下，技术限制仅允许共同记录感兴趣的大脑区域中的部分重叠的神经元层。在这种情况下，当许多对神经元没有同时观测时，对完整数据的图估计需要对边缘选择进行推断。这导致了图绗缝问题，该问题试图在经验协方差矩阵中存在块缺失的情况下估计图。之前已经针对高斯图形模型研究了图形绗缝问题的解决方案;然而，来自钙成像的神经活动数据通常是非高斯的，因此需要更灵活的建模方法。因此，在我们的工作中，我们研究了两种基于高斯copula图模型的非超自然图绗缝方法，即最大似然过程和基于低秩的框架。我们提供了理论上的保证，在类似的条件下，以前开发的高斯设置的边缘恢复的方法，我们调查的经验表现，这两种方法使用模拟以及真实的数据钙成像数据。我们的方法产生更有科学意义的功能连接估计相比，现有的高斯图绗缝方法，钙成像数据集。
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 modelling 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.