# Low-Rank Covariance Completion for Graph Quilting with Applications to Functional Connectivity

arXiv: https://arxiv.org/abs/2209.08273 · HTML: https://mlsanity.com/paper/2209.08273/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 60 references that are in the map.
- First posted on arXiv 17 Sep 2022.

## Builds on (most cited first, 6 of 6)

- [Noisy Matrix Completion: Understanding Statistical Guarantees for Convex Relaxation via Nonconvex Optimization](https://mlsanity.com/paper/1902.07698/) (2019)
- [On Graphical Models via Univariate Exponential Family Distributions](https://mlsanity.com/paper/1301.4183/) (2013)
- [Structured Matrix Completion with Applications to Genomic Data Integration](https://mlsanity.com/paper/1504.01823/) (2015)
- [Multi-source Learning via Completion of Block-wise Overlapping Noisy Matrices](https://mlsanity.com/paper/2105.10360/) (2021)
- [Large-Scale Sparse Inverse Covariance Estimation via Thresholding and Max-Det Matrix Completion](https://mlsanity.com/paper/1802.04911/) (2018)
- [Asymptotically Normal and Efficient Estimation of Covariate-Adjusted Gaussian Graphical Model](https://mlsanity.com/paper/1309.5923/) (2013)

## Built on by (most cited first, 4 of 4)

- [Inpainting the Neural Picture: Inferring Unrecorded Brain Area Dynamics from Multi-Animal Datasets](https://mlsanity.com/paper/2510.11924/) (2025)
- [Nonparanormal Graph Quilting with Applications to Calcium Imaging](https://mlsanity.com/paper/2305.13491/) (2023)
- [Cluster Quilting: Spectral Clustering for Patchwork Learning](https://mlsanity.com/paper/2406.13833/) (2024)
- [Group-Aware Matrix Estimation and Latent Subspace Recovery](https://mlsanity.com/paper/2605.20559/) (2026)

## Abstract (arXiv)

As a tool for estimating networks in high dimensions, graphical models are commonly applied to calcium imaging data to estimate functional neuronal connectivity, i.e. relationships between the activities of neurons. However, in many calcium imaging data sets, the full population of neurons is not recorded simultaneously, but instead in partially overlapping blocks. This leads to the Graph Quilting problem, as first introduced by (Vinci et.al. 2019), in which the goal is to infer the structure of the full graph when only subsets of features are jointly observed. In this paper, we study a novel two-step approach to Graph Quilting, which first imputes the complete covariance matrix using low-rank covariance completion techniques before estimating the graph structure. We introduce three approaches to solve this problem: block singular value decomposition, nuclear norm penalization, and non-convex low-rank factorization. While prior works have studied low-rank matrix completion, we address the challenges brought by the block-wise missingness and are the first to investigate the problem in the context of graph learning. We discuss theoretical properties of the two-step procedure, showing graph selection consistency of one proposed approach by proving novel L infinity-norm error bounds for matrix completion with block-missingness. We then investigate the empirical performance of the proposed methods on simulations and on real-world data examples, through which we show the efficacy of these methods for estimating functional connectivity from calcium imaging data.