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

2025-04-23

AI Summary

This work addresses covariate-dependent graph structure learning by proposing a deep neural network-based method for modeling non-Gaussian joint distributions, enabling flexible and interpretable estimation of conditional dependency structures that evolve with covariates. The method departs from conventional Gaussian and linear dependence assumptions, and—crucially—introduces the first neural-network framework for covariate-driven graph learning endowed with PAC-style statistical guarantees. It jointly optimizes empirical risk minimization, sparse graph regularization, and nonparametric learning of covariate-to-structure mapping functions. Theoretical analysis establishes convergence rate guarantees under mild regularity conditions. Empirical evaluation on synthetic benchmarks and real-world datasets—from neuroscience and finance—demonstrates substantial improvements over state-of-the-art methods, yielding dynamic graph structures that are both statistically reliable and interpretable.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

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.

Problem

• Estimating covariate-dependent graphical models using neural networks
• Flexible functional dependency without Gaussianity assumption
• Theoretical PAC guarantees under Empirical Risk Minimization

Innovation

• Neural networks estimate covariate-dependent graphical models
• Flexible functional dependency without Gaussianity assumption
• PAC guarantees under Empirical Risk Minimization framework