Integral Probability Metric

Integral probability metrics (IPMs) are a class of distances between probability distributions, offering a flexible framework for comparing data distributions in various applications. Current research focuses on improving the efficiency of IPM estimation, particularly in high-dimensional spaces and under data invariances, often leveraging neural networks for approximation. This work is significant because IPMs provide a unifying perspective on various divergence measures, bridging the gap between established methods like KL-divergence and newer approaches, and enabling advancements in areas such as domain generalization and two-sample testing. Improved IPM estimation methods lead to more accurate and efficient statistical inference and machine learning algorithms.