A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Science

Sebastian Bischoff, Alana Darcher, Michael Deistler, Richard Gao, Franziska Gerken, Manuel Gloeckler, Lisa Haxel, Jaivardhan Kapoor, Janne K Lappalainen, Jakob H. Macke, Guy Moss, Matthijs Pals, Felix C Pei, Rachel Rapp, A Erdem Sağtekin, Cornelius Schröder, Auguste Schulz, Zinovia Stefanidi, Shoji Toyota, Linda Ulmer et al. (1 additional authors not shown)

Abstract: Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the samples these models generate? This work aims to provide an accessible entry point to understanding popular sample-based statistical distances, requiring only foundational knowledge in mathematics and statistics. We focus on four commonly used notions of statistical distances representing different methodologies: Using low-dimensional projections (Sliced-Wasserstein; SW), obtaining a distance using classifiers (Classifier Two-Sample Tests; C2ST), using embeddings through kernels (Maximum Mean Discrepancy; MMD), or neural networks (Fréchet Inception Distance; FID). We highlight the intuition behind each distance and explain their merits, scalability, complexity, and pitfalls. To demonstrate how these distances are used in practice, we evaluate generative models from different scientific domains, namely a model of decision-making and a model generating medical images. We showcase that distinct distances can give different results on similar data. Through this guide, we aim to help researchers to use, interpret, and evaluate statistical distances for generative models in science.

Submission Length: Long submission (more than 12 pages of main content)

Changes Since Last Submission: We would like to thank the action editor and reviewers for all their work in the discussion period. We proofread and corrected the paper and improved the natural flow, especially by restructuring section 3. Additionally, we added an explicit "Limitations" section for SWD.

Code: https://github.com/mackelab/labproject

Assigned Action Editor: ~Serguei_Barannikov1

Submission Number: 2392