# Nonparanormal Graph Quilting with Applications to Calcium Imaging

arXiv: https://arxiv.org/abs/2305.13491 · HTML: https://mlsanity.com/paper/2305.13491/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 70 references that are in the map.
- First posted on arXiv 22 May 2023.

## Builds on (most cited first, 11 of 11)

- [On Graphical Models via Univariate Exponential Family Distributions](https://mlsanity.com/paper/1301.4183/) (2013)
- [The huge Package for High-dimensional Undirected Graph Estimation in R](https://mlsanity.com/paper/2006.14781/) (2020)
- [Active Learning Algorithms for Graphical Model Selection](https://mlsanity.com/paper/1602.00354/) (2016)
- [On Semiparametric Exponential Family Graphical Models](https://mlsanity.com/paper/1412.8697/) (2014)
- [Low-Rank Covariance Completion for Graph Quilting with Applications to Functional Connectivity](https://mlsanity.com/paper/2209.08273/) (2022)
- [Elliptical graphical modelling](https://mlsanity.com/paper/1506.04321/) (2015)
- [Simple connectome inference from partial correlation statistics in calcium imaging](https://mlsanity.com/paper/1406.7865/) (2014)
- [Neuronal graphs: a graph theory primer for microscopic, functional networks of neurons recorded by Calcium imaging](https://mlsanity.com/paper/2010.09601/) (2020)
- [Subbotin Graphical Models for Extreme Value Dependencies with Applications to Functional Neuronal Connectivity](https://mlsanity.com/paper/2106.11554/) (2021)
- [Hierarchy of neural organization in the embryonic spinal cord: Granger-causality graph analysis of in vivo calcium imaging data](https://mlsanity.com/paper/1407.4380/) (2014)
- [Neuro-PC: Causal Functional Connectivity from Neural Dynamics](https://mlsanity.com/paper/2011.03913/) (2020)

## Built on by (most cited first, 1 of 1)

- [Inpainting the Neural Picture: Inferring Unrecorded Brain Area Dynamics from Multi-Animal Datasets](https://mlsanity.com/paper/2510.11924/) (2025)

## Abstract (arXiv)

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.