We explore the problem of inferring the graph Laplacian of a weighted, undirected network from snapshots of a single or multiple discrete-time consensus dynamics, subject to parameter uncertainty, taking place on the network. Specifically, we consider three problems in which we assume different levels of knowledge about the diffusion rates, observation times, and the input signal power of the dynamics. To solve these underdetermined problems, we propose a set of algorithms that leverage the spectral properties of the observed data and tools from convex optimization. Furthermore, we provide theoretical performance guarantees associated with these algorithms. We complement our theoretical work with numerical experiments, that demonstrate how our proposed methods outperform current state-of-the-art algorithms and showcase their effectiveness in recovering both synthetic and real-world networks.

中文翻译：

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来自未知参数的共识动力学的网络推断

我们探讨了根据参数不确定性在网络上发生的单个或多个离散时间共识动力学的快照来推断加权无向网络的图拉普拉斯算子的问题。具体来说，我们考虑三个问题，在这些问题中，我们假设对扩散速率，观察时间和动力学输入信号功率的了解程度不同。为了解决这些不确定的问题，我们提出了一组算法，这些算法可以利用观测数据的频谱特性和凸优化工具。此外，我们提供了与这些算法相关的理论性能保证。我们通过数值实验来补充理论工作，