Refereeing the Referees: Evaluating Two-Sample Tests for Validating Generators in Precision Sciences
This provides an efficient, standardized tool for model comparison in precision sciences like particle physics, though it is incremental as it builds on existing methods.
The paper tackles the problem of evaluating non-parametric two-sample tests for high-dimensional generative models in scientific applications, showing that one-dimensional-based tests achieve sensitivity comparable to multivariate metrics with significantly lower computational cost.
We propose a robust methodology to evaluate the performance and computational efficiency of non-parametric two-sample tests, specifically designed for high-dimensional generative models in scientific applications such as in particle physics. The study focuses on tests built from univariate integral probability measures: the sliced Wasserstein distance and the mean of the Kolmogorov-Smirnov statistics, already discussed in the literature, and the novel sliced Kolmogorov-Smirnov statistic. These metrics can be evaluated in parallel, allowing for fast and reliable estimates of their distribution under the null hypothesis. We also compare these metrics with the recently proposed unbiased Fréchet Gaussian Distance and the unbiased quadratic Maximum Mean Discrepancy, computed with a quartic polynomial kernel. We evaluate the proposed tests on various distributions, focusing on their sensitivity to deformations parameterized by a single parameter $ε$. Our experiments include correlated Gaussians and mixtures of Gaussians in 5, 20, and 100 dimensions, and a particle physics dataset of gluon jets from the JetNet dataset, considering both jet- and particle-level features. Our results demonstrate that one-dimensional-based tests provide a level of sensitivity comparable to other multivariate metrics, but with significantly lower computational cost, making them ideal for evaluating generative models in high-dimensional settings. This methodology offers an efficient, standardized tool for model comparison and can serve as a benchmark for more advanced tests, including machine-learning-based approaches.