在线学习有隐藏节点的图结构，实时处理不完整数据。
Online Network Inference from Graph-Stationary Signals with Hidden Nodes
- 基于图平稳信号建模隐藏节点，设计凸优化方法
- 可实时处理流式数据，支持缺失观测下的图学习
- 理论保证在线算法与离线解近似，适合动态场景
图学习旨在从可观测数据中推断未知的图连接关系。传统方法通常假设所有信息可同时获取且所有节点均可见，但在许多真实场景中，数据无法完全知晓，也无法一次性获得。本文提出一种新型在线图估计方法，能够处理隐藏节点的存在。通过假设信号在底层图上是平稳的，构建了对隐藏节点的连接建模。进而将问题转化为一个针对流式、不完整图信号的凸优化问题，并采用高效的近端梯度算法实现实时求解。此外，我们提供了理论条件，说明在线算法在特定情况下与批处理解相近。在合成与真实数据上的实验表明，该方法在存在缺失观测时仍具备良好的在线图学习性能。
原文摘要 · Abstract (English)
Graph learning is the fundamental task of estimating unknown graph connectivity from available data. Typical approaches assume that not only is all information available simultaneously but also that all nodes can be observed. However, in many real-world scenarios, data can neither be known completely nor obtained all at once. We present a novel method for online graph estimation that accounts for the presence of hidden nodes. We consider signals that are stationary on the underlying graph, which provides a model for the unknown connections to hidden nodes. We then formulate a convex optimization problem for graph learning from streaming, incomplete graph signals. We solve the proposed problem through an efficient proximal gradient algorithm that can run in real-time as data arrives sequentially. Additionally, we provide theoretical conditions under which our online algorithm is similar to batch-wise solutions. Through experimental results on synthetic and real-world data, we demonstrate the viability of our approach for online graph learning in the presence of missing observations.
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