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With modern calcium imaging technology, activities of thousands of neuronscan be recorded in vivo. These experiments can potentially provide new insightsinto intrinsic functional neuronal connectivity, defined as contemporaneouscorrelations between neuronal activities. As a common tool for estimatingconditional dependencies in high-dimensional settings, graphical models are anatural choice for estimating functional connectivity networks. However, rawneuronal activity data presents a unique challenge: the relevant information inthe data lies in rare extreme value observations that indicate neuronal firing,rather than in the observations near the mean. Existing graphical modelingtechniques for extreme values rely on binning or thresholding observations,which may not be appropriate for calcium imaging data. In this paper, wedevelop a novel class of graphical models, called the Subbotin graphical model,which finds sparse conditional dependency structures with respect to theextreme value observations without requiring data pre-processing. We firstderive the form of the Subbotin graphical model and show the conditions underwhich it is normalizable. We then study the empirical performance of theSubbotin graphical model and compare it to existing extreme value graphicalmodeling techniques and functional connectivity models from neurosciencethrough several simulation studies as well as a real-world calcium imaging dataexample.

Subbotin Graphical Models for Extreme Value Dependencies with Applications to Functional Neuronal Connectivity