# Latent Multimodal Functional Graphical Model Estimation

arXiv: https://arxiv.org/abs/2210.17237 · HTML: https://mlsanity.com/paper/2210.17237/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 48 references that are in the map.
- First posted on arXiv 31 Oct 2022.

## Builds on (most cited first, 7 of 7)

- [Integrative Factor Regression and Its Inference for Multimodal Data Analysis](https://mlsanity.com/paper/1911.04056/) (2019)
- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [Joint Estimation of Multiple Graphical Models from High Dimensional Time Series](https://mlsanity.com/paper/1311.0219/) (2013)
- [High-dimensional Functional Graphical Model Structure Learning via Neighborhood Selection Approach](https://mlsanity.com/paper/2105.02487/) (2021)
- [Partial Separability and Functional Graphical Models for Multivariate Gaussian Processes](https://mlsanity.com/paper/1910.03134/) (2019)
- [Integrative Multi-View Reduced-Rank Regression: Bridging Group-Sparse and Low-Rank Models](https://mlsanity.com/paper/1807.10375/) (2018)
- [Joint Functional Gaussian Graphical Models](https://mlsanity.com/paper/2110.06653/) (2021)

## Built on by (most cited first, 3 of 3)

- [Trans-Glasso: A Transfer Learning Approach to Precision Matrix Estimation](https://mlsanity.com/paper/2411.15624/) (2024)
- [Functional-Edged Network Modeling](https://mlsanity.com/paper/2404.00218/) (2024)
- [Sparse Bayesian Deep Functional Learning with Structured Region Selection](https://mlsanity.com/paper/2602.20651/) (2026)

## Abstract (arXiv)

Joint multimodal functional data acquisition, where functional data from multiple modes are measured simultaneously from the same subject, has emerged as an exciting modern approach enabled by recent engineering breakthroughs in the neurological and biological sciences. One prominent motivation to acquire such data is to enable new discoveries of the underlying connectivity by combining multimodal signals. Despite the scientific interest, there remains a gap in principled statistical methods for estimating the graph underlying multimodal functional data. To this end, we propose a new integrative framework that models the data generation process and identifies operators mapping from the observation space to the latent space. We then develop an estimator that simultaneously estimates the transformation operators and the latent graph. This estimator is based on the partial correlation operator, which we rigorously extend from the multivariate to the functional setting. Our procedure is provably efficient, with the estimator converging to a stationary point with quantifiable statistical error. Furthermore, we show recovery of the latent graph under mild conditions. Our work is applied to analyze simultaneously acquired multimodal brain imaging data where the graph indicates functional connectivity of the brain. We present simulation and empirical results that support the benefits of joint estimation.