# On Sufficient Graphical Models

arXiv: https://arxiv.org/abs/2307.04353 · HTML: https://mlsanity.com/paper/2307.04353/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 52 references that are in the map.
- First posted on arXiv 10 Jul 2023.

## Builds on (most cited first, 2 of 2)

- [Bayesian Graphical Models for Multivariate Functional Data](https://mlsanity.com/paper/1411.4158/) (2014)
- [Graph estimation with joint additive models](https://mlsanity.com/paper/1304.4654/) (2013)

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

- [Belted and Ensembled Neural Network for Linear and Nonlinear Sufficient Dimension Reduction](https://mlsanity.com/paper/2412.08961/) (2024)
- [Learning Functional Graphs with Nonlinear Sufficient Dimension Reduction](https://mlsanity.com/paper/2601.15696/) (2026)

## Abstract (arXiv)

We introduce a sufficient graphical model by applying the recently developed nonlinear sufficient dimension reduction techniques to the evaluation of conditional independence. The graphical model is nonparametric in nature, as it does not make distributional assumptions such as the Gaussian or copula Gaussian assumptions. However, unlike a fully nonparametric graphical model, which relies on the high-dimensional kernel to characterize conditional independence, our graphical model is based on conditional independence given a set of sufficient predictors with a substantially reduced dimension. In this way we avoid the curse of dimensionality that comes with a high-dimensional kernel. We develop the population-level properties, convergence rate, and variable selection consistency of our estimate. By simulation comparisons and an analysis of the DREAM 4 Challenge data set, we demonstrate that our method outperforms the existing methods when the Gaussian or copula Gaussian assumptions are violated, and its performance remains excellent in the high-dimensional setting.