Robust graphs for graph-based methods
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Graph-based two-sample tests and graph-based change-point detection that utilize similarity graphs provide powerful tools for analyzing high-dimensional and non-Euclidean data as these methods do not impose distributional assumptions and have good performance across various scenarios. Current graph-based tests that deliver efficacy across a broad spectrum of alternatives typically reply on the K-nearest neighbor graph or the K-minimum spanning tree. However, these graphs can be vulnerable for high-dimensional data due to the curse of dimensionality. To mitigate this issue, we propose to use a robust graph that is considerably less influenced by the curse of dimensionality. We also establish a theoretical foundation for graph-based methods utilizing this proposed robust graph and demonstrate its consistency under fixed alternatives for both low-dimensional and high-dimensional data.
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