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Abstract:
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Understanding and discovering dependence between multiple properties or measurements of our world is a fundamental task not just in science, but also policy, commerce, and other domains. We propose a novel dependence test statistic called ``Multiscale Graph Correlation'' (MGC), having the following properties: (1) Theoretical consistency such that the testing power converges to 1 under any dependency structure. (2) Strong empirical performance on a wide variety of low- and high-dimensional simulation settings. (3) Provides insight into the optimal local scale in which dependency is strongest. (4) On real data, detects dependence when it exists, and does not inflate the false positive rate in the absence of dependency. Briefly, we combine the ideas of distance correlation testing with nearest-neighbor testing to develop MGC, and demonstrate its properties and advantages by extensive theory, simulations, and real data examples. We can therefore use this test in a variety of settings in which previous tests failed to detect signal or provide insight.
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