Kolmogorov Smirnov

The Kolmogorov-Smirnov (KS) test is a non-parametric statistical method used to compare the cumulative distribution functions of two samples, assessing whether they originate from the same underlying distribution. Current research focuses on extending the KS test's capabilities to higher dimensions and more complex data types, including multivariate time series and high-dimensional data from generative models, often employing techniques like sliced KS statistics or integrating it within Generative Adversarial Networks (GANs) frameworks. These advancements improve the efficiency and robustness of the test, particularly in applications like evaluating generative models in fields such as particle physics and robust statistics, where traditional methods may struggle. The resulting improvements in model validation and robust estimation have significant implications for various scientific disciplines.