# Nonparametric and high-dimensional functional graphical models

arXiv: https://arxiv.org/abs/2103.10568 · HTML: https://mlsanity.com/paper/2103.10568/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2021.

## Built on by (most cited first, 5 of 5)

- [High-dimensional Functional Graphical Model Structure Learning via Neighborhood Selection Approach](https://mlsanity.com/paper/2105.02487/) (2021)
- [Gaussian Graphical Models as an Ensemble Method for Distributed Gaussian Processes](https://mlsanity.com/paper/2202.03287/) (2022)
- [Entry Dependent Expert Selection in Distributed Gaussian Processes Using Multilabel Classification](https://mlsanity.com/paper/2211.09940/) (2022)
- [Functional-Edged Network Modeling](https://mlsanity.com/paper/2404.00218/) (2024)
- [Learning Functional Graphs with Nonlinear Sufficient Dimension Reduction](https://mlsanity.com/paper/2601.15696/) (2026)

## Abstract (arXiv)

We consider the problem of constructing nonparametric undirected graphical models for high-dimensional functional data. Most existing statistical methods in this context assume either a Gaussian distribution on the vertices or linear conditional means. In this article we provide a more flexible model which relaxes the linearity assumption by replacing it by an arbitrary additive form. The use of functional principal components offers an estimation strategy that uses a group lasso penalty to estimate the relevant edges of the graph. We establish statistical guarantees for the resulting estimators, which can be used to prove consistency if the dimension and the number of functional principal components diverge to infinity with the sample size. We also investigate the empirical performance of our method through simulation studies and a real data application.