Learning Functional Graphs with Nonlinear Sufficient Dimension Reduction

2026-01-22

AI Summary

Existing functional graphical models are often constrained by Gaussian or copula-Gaussian assumptions or rely on non-probabilistic conditional independence criteria, limiting their flexibility and estimation accuracy. This work proposes a novel functional graph modeling approach based on nonparametric functional sufficient dimension reduction, which mitigates the curse of dimensionality through nonlinear dimension reduction while preserving a probabilistic conditional independence framework to enhance structural learning accuracy. By uniquely integrating nonlinear sufficient dimension reduction with probabilistic conditional independence testing, the method overcomes the limitations of conventional distributional assumptions and achieves both theoretical rigor and computational efficiency. Extensive simulations and real f-MRI data analyses demonstrate that the proposed method significantly outperforms existing approaches in edge identification accuracy and computational stability.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Computer Vision: Other Foundations of Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• 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

Abstract

Functional graphical models have undergone extensive development during the recent years, leading to a variety models such as the functional Gaussian graphical model, the functional copula Gaussian graphical model, the functional Bayesian graphical model, the nonparametric functional additive graphical model, and the conditional functional graphical model. These models rely either on some parametric form of distributions on random functions, or on additive conditional independence, a criterion that is different from probabilistic conditional independence. In this paper we introduce a nonparametric functional graphical model based on functional sufficient dimension reduction. Our method not only relaxes the Gaussian or copula Gaussian assumptions, but also enhances estimation accuracy by avoiding the ``curse of dimensionality''. Moreover, it retains the probabilistic conditional independence as the criterion to determine the absence of edges. By doing simulation study and analysis of the f-MRI dataset, we demonstrate the advantages of our method.

Problem

• functional graphical models
• nonparametric
• sufficient dimension reduction
• conditional independence
• curse of dimensionality

Innovation

• functional graphical model
• sufficient dimension reduction
• nonparametric
• conditional independence
• curse of dimensionality