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Recovery conditions and sampling strategies for network Lasso

机译：网络套索的恢复条件和采样策略

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The network Lasso is a recently proposed convex optimization method for machine learning from massive network structured datasets, i.e., big data over networks. It is a variant of the well-known least absolute shrinkage and selection operator (Lasso), which is underlying many methods in learning and signal processing involving sparse models. Highly scalable implementations of the network Lasso can be obtained by state-of-the-art proximal methods, e.g., the alternating direction method of multipliers (ADMM). By generalizing the concept of the compatibility condition put forward by van de Geer and Buhlmann as a powerful tool for the analysis of plain Lasso, we derive a sufficient condition, i.e., the network compatibility condition, on the underlying network topology such that network Lasso accurately learns a clustered underlying graph signal. This network compatibility condition relates the location of sampled nodes with the clustering structure of the network. In particular, the NCC informs the choice of which nodes to sample, or in machine learning terms, which data points provide most information if labeled.
机译：网络套索是最近提出的凸优化方法，用于从海量网络结构化数据集（即网络上的大数据）中进行机器学习。它是众所周知的最小绝对收缩和选择算子（Lasso）的变体，它是学习和信号处理中涉及稀疏模型的许多方法的基础。可以通过最新的近端方法，例如乘法器的交替方向方法（ADMM）来获得网络套索的高度可扩展的实现。通过将van de Geer和Buhlmann提出的兼容性条件的概念概括为分析普通Lasso的有力工具，我们得出了基础网络拓扑上的充分条件，即网络兼容性条件，从而使网络Lasso准确学习聚类的基础图信号。该网络兼容性条件将采样节点的位置与网络的群集结构相关联。特别是，NCC会通知选择要采样的节点，或者以机器学习的方式，如果标记，则哪些数据点可提供最多的信息。

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