利用迭代比例拟合从边际推断动态网络
Inferring Dynamic Networks from Marginals with Iterative Proportional Fitting
AI总结：
本文建立了一个生成性网络模型，证明迭代比例拟合（IPF）能恢复其最大似然估计，并提出了保证IPF在稀疏数据上收敛的算法，通过实验验证了其有效性。
摘要：
一个常见的网络推断问题，源于现实世界的数据约束，是如何从时间聚合的邻接矩阵和时变边际（即行和与列和）推断动态网络。先前解决此问题的方法重新利用了经典的迭代比例拟合（IPF）过程，也称为Sinkhorn算法，并取得了有前景的经验结果。然而，使用IPF的统计基础尚未被充分理解：在何种设置下，IPF能从其边际提供对动态网络的原则性估计，以及它对网络的估计效果如何？在本工作中，我们通过识别一个生成性网络模型来建立这样的设置，该模型的最大似然估计可由IPF恢复。我们的模型既揭示了在此类设置中使用IPF的隐含假设，也支持新的分析，例如IPF参数估计的依赖于结构的误差界。当IPF在稀疏网络数据上无法收敛时，我们引入了一种原则性算法，该算法保证IPF在网络结构的最小变化下收敛。最后，我们使用合成数据和真实数据进行了实验，这些实验证明了我们理论和算法贡献的实用价值。
英文摘要：
A common network inference problem, arising from real-world data constraints, is how to infer a dynamic network from its time-aggregated adjacency matrix and time-varying marginals (i.e., row and column sums). Prior approaches to this problem have repurposed the classic iterative proportional fitting (IPF) procedure, also known as Sinkhorn's algorithm, with promising empirical results. However, the statistical foundation for using IPF has not been well understood: under what settings does IPF provide principled estimation of a dynamic network from its marginals, and how well does it estimate the network? In this work, we establish such a setting, by identifying a generative network model whose maximum likelihood estimates are recovered by IPF. Our model both reveals implicit assumptions on the use of IPF in such settings and enables new analyses, such as structure-dependent error bounds on IPF's parameter estimates. When IPF fails to converge on sparse network data, we introduce a principled algorithm that guarantees IPF converges under minimal changes to the network structure. Finally, we conduct experiments with synthetic and real-world data, which demonstrate the practical value of our theoretical and algorithmic contributions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
