The proposed methodology for evaluating two-sample tests can be extended to incorporate advanced machine learning (ML)-based approaches by integrating classifiers that leverage deep learning architectures to model complex relationships in high-dimensional data. One potential direction is to utilize generative adversarial networks (GANs) or variational autoencoders (VAEs) to learn the underlying distributions of the data more effectively. These models can be trained to generate synthetic samples that closely resemble the reference distribution, allowing for a more nuanced comparison against alternative hypotheses.
Additionally, the methodology can be enhanced by employing ensemble learning techniques, where multiple ML models are combined to improve robustness and accuracy in detecting distributional differences. For instance, stacking various classifiers that utilize different feature extraction methods or kernel functions can provide a comprehensive view of the data's structure. Furthermore, incorporating unsupervised learning techniques, such as clustering or dimensionality reduction (e.g., t-SNE or UMAP), can help identify latent structures and dependencies that traditional tests may overlook.
To facilitate this integration, the evaluation framework can be adapted to include performance metrics specific to ML models, such as area under the ROC curve (AUC) or F1 scores, alongside traditional statistical measures. This hybrid approach would not only enhance the sensitivity of the tests to complex data patterns but also provide a more interpretable framework for practitioners in fields like particle physics, biology, and finance.