Gaussian Measure

Gaussian measures, fundamental probability distributions, are central to numerous fields, with current research focusing on efficiently approximating and manipulating them in high dimensions, particularly for applications in machine learning and statistical inference. This involves developing novel quadrature rules, leveraging techniques like normalizing flows and Wasserstein gradient flows to handle non-Gaussian extensions, and employing methods such as spherical harmonics for improved computational efficiency. These advancements are crucial for improving the scalability and accuracy of algorithms in diverse areas, including anomaly detection, Bayesian inference, and generative modeling.