# The Functional Graphical Lasso

arXiv: https://arxiv.org/abs/2306.02347 · HTML: https://mlsanity.com/paper/2306.02347/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2023.

## Built on by (most cited first, 2 of 2)

- [Kernel Embeddings and the Separation of Measure Phenomenon](https://mlsanity.com/paper/2505.04613/) (2025)
- [Likelihood Ratio Tests by Kernel Gaussian Embedding](https://mlsanity.com/paper/2508.07982/) (2025)

## Abstract (arXiv)

We consider the problem of recovering conditional independence relationships between p jointly distributed Hilbertian random elements given n realizations thereof. We operate in the sparse high-dimensional regime, where n ll p and no element is related to more than d ll p other elements. In this context, we propose an infinite-dimensional generalization of the graphical lasso. We prove model selection consistency under natural assumptions and extend many classical results to infinite dimensions. In particular, we do not require finite truncation or additional structural restrictions. The plug-in nature of our method makes it applicable to any observational regime, whether sparse or dense, and indifferent to serial dependence. Importantly, our method can be understood as naturally arising from a coherent maximum likelihood philosophy.