发表机构
Delft University of Technology; King Juan Carlos University（代尔夫特理工大学; 胡安·卡洛斯国王大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出联合精度神经网络（PNN-Joint），通过交替优化联合估计稀疏精度矩阵与图神经网络权重，实现任务感知图推断，在低数据下鲁棒且性能领先。
AI 中文摘要
从数据中挖掘有意义的潜在结构以解决下游任务，是信号处理和机器学习中的一个基本挑战。虽然主成分分析（PCA）和协方差神经网络（VNNs）成功地利用协方差矩阵来处理数据，但它们本质上同时捕获了直接和间接的相关性。精度矩阵（逆协方差）通过显式编码条件独立性来克服这一局限，使其在图套索和图拓扑识别中被广泛研究。然而，有限样本下的精度估计以不稳定著称，且正则化估计器仍与任务无关。在本工作中，我们的主要贡献是解决任务感知图推断这一具有挑战性的问题。我们提出了联合精度神经网络（PNN-Joint），这是一种通过交替优化方案联合估计稀疏、统计上可靠的精度矩阵以及图神经网络权重的框架。作为支撑这一工作的基础框架，我们引入了精度神经网络（PNNs），这是一类在精度估计器上运行的更广泛的图卷积网络，并建立了它们与PCA和VNNs的谱联系，以及它们对有限样本误差的稳定性。在合成数据以及真实世界的神经影像和运动传感器数据集上的广泛实证评估表明，PNN-Joint能够生成高度可解释的任务感知图，在低数据环境下表现出显著的鲁棒性，并在真实世界任务中始终达到最佳或次佳的性能。
英文摘要
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.
