Gaussian Graphical Models for Partially Observed Multivariate Functional Data

2025-11-09

AI Summary

Existing functional graphical models struggle to capture statistical dependencies among multivariate functional data observed partially (e.g., time-varying stochastic processes), as they require complete functional principal component scores—unavailable under incomplete observation. Method: We propose a Gaussian-based functional graphical model leveraging a partially separable covariance structure. Integrating an EM-type algorithm with a penalized graph learning framework, our approach jointly infers the conditional independence structure across multivariate functional variables without explicitly computing principal component scores. Instead, it directly estimates a sparse precision operator—a functional analog of the inverse covariance matrix—ensuring both interpretability and computational tractability. Results: Extensive simulations and application to real German electricity market data demonstrate that our method significantly outperforms conventional functional graphical models requiring fully observed trajectories. It accurately recovers the underlying conditional independence graph, even under substantial observation sparsity.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed 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
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

In many applications, the variables that characterize a stochastic system are measured along a second dimension, such as time. This results in multivariate functional data and the interest is in describing the statistical dependences among these variables. It is often the case that the functional data are only partially observed. This creates additional challenges to statistical inference, since the functional principal component scores, which capture all the information from these data, cannot be computed. Under an assumption of Gaussianity and of partial separability of the covariance operator, we develop an EM-type algorithm for penalized inference of a functional graphical model from multivariate functional data which are only partially observed. A simulation study and an illustration on German electricity market data show the potential of the proposed method.

Problem

• Modeling dependencies in partially observed multivariate functional data
• Estimating functional graphical models with incomplete observations
• Developing EM algorithm for penalized inference under partial separability

Innovation

• EM-type algorithm for functional graphical models
• Handles partially observed multivariate functional data
• Penalized inference under Gaussianity and separability