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Abstract:
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Deciphering potential associations between network structures and the corresponding nodal attributes of interest is a core problem in network science. As the network topology is structured and often high-dimensional, many nonparametric statistical tests are not directly applicable, whereas model-based approaches are dominant in network inference. In this paper, we propose a model-free approach to test independence between network topology and nodal attributes, via diffusion maps and distance-based correlations. We prove in theory that the diffusion maps based on the adjacency matrix from an infinitely exchangeable graph can provide a set of conditionally independent coordinates for each node in graph, which yields a consistent test statistic for network dependence testing with distance-based correlations combined. The new approach excels in capturing nonlinear and high-dimensional network dependencies, and is robust against parameter choices and noise, as demonstrated by superior testing powers throughout various popular network models. An application on brain data is provided to illustrate its advantage and utility.
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