从广义静止随机过程中学习网络

Anirudh Rayas¹, Jiajun Cheng¹, Rajasekhar Anguluri²

¹School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, AZ, USA.

IEEE transactions on signal and information processing over networks

|November 3, 2025

概括

本研究介绍了一种新的方法,用于绘制复杂系统中使用节点数据的网络连接. 该方法可以准确地识别网络结构,即使是在大型,高维的场景中.

科学领域:

网络科学网络科学
统计推理统计推理
系统工程系统工程

背景情况:

具有潜在输入的复杂网络系统在神经科学,金融和工程领域普遍存在.
一个关键的挑战是从观察到的节点潜力推断网络边缘连接.
经常遇到由稳定状态线性保存定律支配的系统.

研究的目的:

从节点潜力开发一种学习边缘连接在复杂的网络系统的方法.
解决网络推理在高维设置中的挑战,网络大小超过样本大小.
为学习网络结构的准确性提供理论保证.

主要方法:

使用一个 $\ell_1$-规范化的 Whittle 的最大概率估计器 (MLE) 在时间相关节点潜在样本上.
假设隐性输入遵循一个具有已知的光谱密度矩阵的广义静止随机过程.
利用拉普拉斯矩阵的稀疏性模式来编码网络结构.

主要成果:

MLE问题被证明是严格凸起的,确保了唯一的解决方案.
在新的相互不一致条件和特定的样本大小约束下,ML估计准确地恢复了网络的稀疏性模式.
对于拉普拉斯矩阵,在元素明智的最大值,弗罗贝尼乌斯和操作员规范中提供了回收保证.

结论:

提出的 $\ell_1$ 规范化的 MLE 方法有效地推断了复杂系统中的网络连接性.
该方法在高维设置中表现出强大的性能,并提供了强大的理论保证.
该方法通过对工程和真实世界的神经网络数据集的模拟来验证.

关键词:

保护法是关于保护的.网络拓推断推断的网络拓学.频谱精度矩阵是一个精确的矩阵.l1 - 规范化的惠特尔的概率估计器.

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