5 citations · 8 across the 5 of their papers we have counts for
6 papers
Tropical linear regression and mean payoff games: or, how to measure the distance to equilibria
Marianne Akian, Stéphane Gaubert, Yang Qi +1
We study a tropical linear regression problem consisting in finding the best approximation of a set of points by a tropical hyperplane. We establish a strong duality theorem, showi…
Best k-layer neural network approximations
Lek-Heng Lim, Mateusz Michalek, Yang Qi
We show that the empirical risk minimization (ERM) problem for neural networks has no solution in general. Given a training set with correspondin…
Topology of tensor ranks
Pierre Comon, Lek-Heng Lim, Yang Qi +1
We study path-connectedness and homotopy groups of sets of tensors defined by tensor rank, border rank, multilinear rank, as well as their symmetric counterparts for symmetric tens…
Complex best -term approximations almost always exist in finite dimensions
Yang Qi, Mateusz Michałek, Lek-Heng Lim
We show that in finite-dimensional nonlinear approximations, the best -term approximant of a function almost always exists over but that the same is not true ov…
Semialgebraic Geometry of Nonnegative Tensor Rank
Yang Qi, Pierre Comon, Lek-Heng Lim
We study the semialgebraic structure of , the set of nonnegative tensors of nonnegative rank not more than , and use the results to infer various properties of nonnegative…
Uniqueness of Nonnegative Tensor Approximations
Yang Qi, Pierre Comon, Lek-Heng Lim
We show that for a nonnegative tensor, a best nonnegative rank-r approximation is almost always unique, its best rank-one approximation may always be chosen to be a best nonnegativ…