A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Science
It addresses the need for researchers in scientific fields to understand and apply statistical distances for evaluating generative models, but it is incremental as it synthesizes existing methods without introducing new ones.
This work tackles the problem of evaluating generative models in science by providing an accessible guide to sample-based statistical distances, demonstrating their application on models from decision-making and medical imaging domains and showing that different distances can yield varying results on similar data.
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.