分野別セミナー

Abstract: The Euclidean natural gradient method is a widely used tool in statistical optimization. We extend the concept of natural gradient to a Riemannian manifold and develop a computationally efficient method for computing it. The method is fully intrinsic, avoiding reliance on an ambient Euclidean space. We apply the method to the Variational Bayes and Maximum Likelihood Estimation problems, where the parameters lie on a manifold. We establish theoretical convergence guarantees comparable to those of standard stochastic gradient descent, and validate the robustness and efficiency of our approach across a range of learning tasks. Joint work with Dario Draca.