Statistical Manifold

Statistical manifolds are spaces of probability distributions viewed through a geometric lens, enabling the application of differential geometry to statistical problems. Current research focuses on developing and applying manifold-based models and algorithms in diverse areas, including machine learning (e.g., generative models, density estimation, federated learning), motion planning, and analysis of complex data like natural language and biological systems. This approach offers advantages in handling high-dimensional data, improving model robustness and generalization, and providing theoretically grounded methods for tasks where traditional Euclidean approaches are insufficient. The resulting advancements have significant implications for various scientific fields and practical applications requiring efficient and robust data analysis and modeling.