Entropic Barycenter

Entropic barycenters provide a robust method for averaging probability distributions, offering a geometrically meaningful representation of central tendency that overcomes limitations of traditional averaging techniques. Current research focuses on developing efficient algorithms, such as those based on damped Sinkhorn iterations and energy-based models, to compute these barycenters, particularly for continuous distributions and high-dimensional data, often incorporating double regularization to improve stability and accuracy. These advancements are impacting fields like image analysis and generative modeling, enabling improved techniques for data representation and synthesis. The development of efficient and unbiased algorithms for computing entropic barycenters is driving progress in various applications.