# Covariate-dependent Graphical Model Estimation via Neural Networks with Statistical Guarantees

arXiv: https://arxiv.org/abs/2504.16356 · HTML: https://mlsanity.com/paper/2504.16356/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 60 references that are in the map.
- First posted on arXiv 23 Apr 2025.

## Builds on (most cited first, 17 of 17)

- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [Interpretable Models for Granger Causality Using Self-explaining Neural Networks](https://mlsanity.com/paper/2101.07600/) (2021)
- [Stability and Deviation Optimal Risk Bounds with Convergence Rate O(1/n)](https://mlsanity.com/paper/2103.12024/) (2021)
- [On the representation and learning of monotone triangular transport maps](https://mlsanity.com/paper/2009.10303/) (2020)
- [On Graphical Models via Univariate Exponential Family Distributions](https://mlsanity.com/paper/1301.4183/) (2013)
- [Contextual Explanation Networks](https://mlsanity.com/paper/1705.10301/) (2017)
- [Learning non-Gaussian graphical models via Hessian scores and triangular transport](https://mlsanity.com/paper/2101.03093/) (2021)
- [Causal Discovery with Heterogeneous Observational Data](https://mlsanity.com/paper/2201.12392/) (2022)
- [The huge Package for High-dimensional Undirected Graph Estimation in R](https://mlsanity.com/paper/2006.14781/) (2020)
- [Generalized Precision Matrix for Scalable Estimation of Nonparametric Markov Networks](https://mlsanity.com/paper/2305.11379/) (2023)
- [High Dimensional Gaussian Graphical Regression Models with Covariates](https://mlsanity.com/paper/2011.05245/) (2020)
- [Contextual Directed Acyclic Graphs](https://mlsanity.com/paper/2310.15627/) (2023)
- [Bayesian Covariate-Dependent Graph Learning with a Dual Group Spike-and-Slab Prior](https://mlsanity.com/paper/2409.17404/) (2024)
- [Covariate-Assisted Bayesian Graph Learning for Heterogeneous Data](https://mlsanity.com/paper/2308.07806/) (2023)

## Abstract (arXiv)

Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and investigate a deep neural network-based approach to estimate it. The method allows for flexible functional dependency on the covariate, and fits the data reasonably well in the absence of a Gaussianity assumption. Theoretical results with PAC guarantees are established for the method, under assumptions commonly used in an Empirical Risk Minimization framework. The performance of the proposed method is evaluated on several synthetic data settings and benchmarked against existing approaches. The method is further illustrated on real datasets involving data from neuroscience and finance, respectively, and produces interpretable results.