Probability Measure

Probability measures are mathematical objects quantifying uncertainty and are central to numerous fields. Current research focuses on efficiently computing and manipulating probability measures, particularly in high-dimensional spaces, using techniques like Wasserstein gradient flows, Sobolev transport, and deep learning-based approximations. These advancements are crucial for improving algorithms in machine learning, uncertainty quantification, and optimal transport problems, leading to more robust and efficient solutions in various applications. The development of novel methods for handling incomplete or ambiguous probabilistic information is also a significant area of ongoing investigation.