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Graph-based tests are a class of non-parametric two-sample tests useful foranalyzing high-dimensional data. The framework offers both flexibility andpower in a wide-range of testing scenarios. The test statistics are constructedfrom similarity graphs (such as $K$-nearest neighbor graphs) and consequently,their performance is sensitive to the structure of the graph. When the graphhas problematic structures, as is common for high-dimensional data, this canresult in poor or unstable performance among existing graph-based tests. Weaddress this challenge and develop graph-based test statistics that are robustto problematic structures of the graph. The limiting null distribution of therobust test statistics is derived. We illustrate the new tests via simulationstudies and a real-world application on Chicago taxi trip-data.

A Robust Framework for Graph-based Two-Sample Tests Using Weights