Divergences and Statistical Manifolds in Machine Learning

Description

Statistical manifolds offer a powerful geometric framework for analyzing the structure of complex data, probabilistic models, and stochastic learning machines. This talk introduces key concepts from information geometry and illustrates how applying geometric principles to machine learning problems can deepen theoretical insight and support the development of more effective algorithms and data structures. In particular, we describe the Hilbert-Birkhoff geometry of the simplex for dimensionality reduction and clustering tasks and of the SPD bicone of positive-definite matrices. Second, we present some recent extensions and generalizations of Bregman divergences (BDs) with applications: duo Bregman pseudo-divergences and curved Bregman divergences. Finally, we conclude this talk with the concept of maximal invariants which provides a valuable perspective for analyzing and understanding the structural forms of
statistical divergences.