Session A1 - Approximation Theory
July 10, 17:40 ~ 18:15
Rescaled Pure Greedy Algorithm for Hilbert and Banach spaces and beyond
Texas A&M University, USA - firstname.lastname@example.org
We show that a very simple modication of the Pure Greedy Algorithm for approximating functions by sparse sums from a dictionary in a Hilbert or more generally a Banach space has optimal convergence rates. Moreover, this greedy strategy can be applied to convex optimization in Banach spaces. We prove its convergent rates under a suitable behavior of the modulus of uniform smoothness of the objective function and test our algorithm on several data sets involving the log-likelihood function for logistic regression.
Joint work with Zheming Gao (University of North Carolina).