In many areas such as computational biology, finance or social sciences, knowledge of an underlying graph explaining the interactions between agents is of paramount importance but still challenging. Considering that these interactions may be based on nonlinear relationships adds further complexity to the topology inference problem. Among the latest methods that respond to this need is a topology inference one proposed by the authors, which estimates a possibly directed adjacency matrix in an online manner. Contrasting with previous approaches based on linear models, the considered model is able to explain nonlinear interactions between the agents in a network. The novelty in the considered method is the use of a derivative-reproducing property to enforce network sparsity, while reproducing kernels are used to model the nonlinear interactions. The aim of this paper is to present a thorough convergence analysis of this method. The analysis is proven to be sane both in the mean and mean square sense. In addition, stability conditions are devised to ensure the convergence of the analyzed method.

中文翻译：

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RKHS 中具有导数再现特性的图拓扑推理：算法和收敛性分析


在计算生物学、金融或社会科学等许多领域，解释代理之间相互作用的底层图的知识至关重要，但仍然具有挑战性。考虑到这些相互作用可能基于非线性关系，这进一步增加了拓扑推理问题的复杂性。满足这一需求的最新方法之一是作者提出的拓扑推断，它以在线方式估计可能的有向邻接矩阵。与以前基于线性模型的方法相比，所考虑的模型能够解释网络中代理之间的非线性相互作用。所考虑的方法的新颖之处在于使用导数再现属性来强制网络稀疏性，同时再现核用于对非线性相互作用进行建模。本文的目的是对该方法进行彻底的收敛性分析。该分析在均值和均方意义上被证明是合理的。此外，还设计了稳定性条件以确保分析方法的收敛性。