Abstract for the talk on 17.10.2018 (11:00 h)Seminar on Nonlinear Algebra
Max Pfeffer (MPI MIS, Leipzig)
Learning paths from signature tensors
17.10.2018, 11:00 h, MPI für Mathematik in den Naturwissenschaften Leipzig, E1 05 (Leibniz-Saal)
Matrix congruence extends naturally to the setting of tensors. We apply methods from tensor decomposition, algebraic geometry and numerical optimization to this group action. Given a tensor in the orbit of another tensor, we compute a matrix which transforms one to the other. Our primary application is an inverse problem from stochastic analysis: the recovery of paths from their signature tensors of order three. We establish identifiability results and recovery algorithms for piecewise linear paths, polynomial paths, and generic dictionaries. A detailed analysis of the relevant condition numbers is presented. We also compute the shortest path with a given signature tensor.