Conference abstracts

Session A1 - Approximation Theory

July 10, 17:40 ~ 18:15

Rescaled Pure Greedy Algorithm for Hilbert and Banach spaces and beyond

Guergana Petrova

Texas A&M University, USA   -

We show that a very simple modi cation 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).

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FoCM 2017, based on a nodethirtythree design.