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Multivariate goodness-of-fit and two-sample tests are important components ofmany nuclear and particle physics analyses. While a variety of powerful methodsare available if the dimensionality of the feature space is small, such testsrapidly lose power as the dimensionality increases and the data inevitablybecome sparse. Machine learning classifiers are powerful tools capable ofreducing highly multivariate problems into univariate ones, on which commonlyused tests such as $\chi^2$ or Kolmogorov-Smirnov may be applied. We exploreapplying both traditional and machine-learning-based tests to several exampleproblems, and study how the power of each approach depends on thedimensionality. A pedagogical discussion is provided on which types of problemsare best suited to using traditional versus machine-learning-based tests, andon the how to properly employ the machine-learning-based approach.

Machine learning and multivariate goodness of fit