"Learning sums of ridge functions from minimal samples"

Sep 4

Friday, September 4, 2015

11:45 am - 12:45 pm
Gross Hall 330


MASSIMO FORNASIER, Technical University of Munich

Lunch begins at 11:45am, seminar at 12noon Abstract. We address the uniform approximation of sums of ridge functions Pm i=1 gi(ai x) on Rd from a small number of query sam- ples, under mild smoothness assumptions on the functions gi's and near-orthogonality of the ridge directions ai's. The sample points are randomly generated and are universal, in the sense that the sampled queries on those points will allow the proposed recovery algorithms to perform a uniform approximation of any sum of ridge function with high-probability. Our general approximation strategy is developed as a sequence of algorithms to perform individual sub-tasks. We rst approx- imate the span of the ridge directions. Then we use a straightforward substitution, which reduces the dimensionality of the problem from d to m. The core of the algorithm is the approximation of ridge directions expressed in terms of rank 1 matrices ai ai, realized by formulating their individual identication as a suitable nonlinear program, maximiz- ing the spectral norm of certain competitors constrained over the unit Frobenius sphere. The nal step is then to approximate the functions g1; : : : ; gm by ^g1; : : : ; ^gm. Prof. Massimo Fornasier holds the Chair in Applied Numerical Analysis at the Technische Universitat Munchen. http://www-m15.ma.tum.de/Allgemeines/MassimoFornasier if you would like ot meet with him during his stay contact mauro@math.duke.edu