Joint Precision Neural Networks: Task-Aware Dependency and Predictive Learning

2026-10-05

AI Summary

This study addresses the instability of precision matrix estimation and the lack of task relevance under limited sample conditions by proposing the PNN-Joint framework. This framework introduces a novel task-aware graph reasoning mechanism that establishes a joint learning paradigm coupling sparse precision matrices with graph neural network weights, optimized synergistically via an alternating optimization strategy. The primary contributions of this work lie in overcoming the limitations of conventional decoupled two-stage modeling approaches, thereby demonstrating superior robustness in low-data regimes. Furthermore, it generates interpretable graph structures that significantly enhance predictive performance across multiple downstream tasks.

Abstract

Exploiting meaningful latent structures from data to solve downstream tasks is a fundamental challenge in signal processing and machine learning. While Principal Component Analysis (PCA) and coVariance Neural Networks (VNNs) successfully leverage the covariance matrix to process data, they inherently capture both direct and indirect correlations. The precision matrix (inverse covariance) overcomes this by explicitly encoding conditional independencies, making it largely studied in graphical lasso and graph topology identification. However, finite-sample precision estimates are notoriously unstable, and regularized estimators remain task-agnostic. In this work, our principal contribution is tackling the challenging problem of task-aware graph inference. We propose Precision Neural Networks-Joint (PNN-Joint), a framework that jointly estimates a sparse, statistically grounded precision matrix alongside graph neural network weights via an alternating optimization scheme. As a foundational framework to support this, we introduce Precision Neural Networks (PNNs), a broader class of graph convolutional networks operating on precision estimators, and establish their spectral connections to PCA and VNNs alongside their stability to finite-sample errors. Extensive empirical evaluations on synthetic data, as well as real-world neuroimaging and motion sensor datasets, demonstrate that PNN-Joint yields highly interpretable task-aware graphs, exhibits remarkable robustness in low-data regimes, and consistently achieves the best or second-best performance among competitors on real-world tasks.

Problem

• Task-aware graph inference
• Precision matrix estimation
• Finite-sample instability
• Latent structure discovery

Innovation

• Precision Neural Networks
• Task-Aware Graph Inference
• Alternating Optimization
• Precision Matrix Estimation
• Graph Convolutional Networks