Auto-regressive moving-average (ARMA) models on real-valued Riemannian manifolds


Simone Fiori

16:00:00 - 17:30:00

R519 , Astronomy and Mathematics Building

A classical learning paradigm is based on criterion optimization over an Euclidean space by a first-order learning algorithm. A more advanced instance of parameter learning is by constrained optimization with smooth equality constraints. In such a context, the constraints on parameters\\\' values reflect the natural constraints presented by the learning problem. In this case, differential geometry is an appropriate mathematical instrument to formulate and to implement a learning theory. The current research aims at introducing a general framework to develop a theory of learning on differentiable manifolds which leads to a second-order learning paradigm. Such a research effort is based on dynamical system theory on manifolds. The formulation of the second-order learning equations on manifolds requires instruments from differential geometry. Likewise, the numerical implementation of second-order learning systems on a computation platform requires instruments from geometric numerical integration. Such a research activity has led to cooperation with the University of Bari (Italy), the Trondheim Technical University (Norway) and the Tokyo University of Agriculture and Technology (Japan).