"Learning sums of ridge functions from minimal samples"

Lunch begins at 11:45am, seminar at 12noonAbstract. We address the uniform approximation of sums of ridgefunctionsPmi=1 gi(ai x) on Rd from a small number of query sam-ples, under mild smoothness assumptions on the functions gi's andnear-orthogonality of the ridge directions ai's. The sample points arerandomly generated and are universal, in the sense that the sampledqueries on those points will allow the proposed recovery algorithms toperform a uniform approximation of any sum of ridge function withhigh-probability. Our general approximation strategy is developed as asequence of algorithms to perform individual sub-tasks. We rst approx-imate the span of the ridge directions. Then we use a straightforwardsubstitution, which reduces the dimensionality of the problem from d tom. The core of the algorithm is the approximation of ridge directionsexpressed in terms of rank 1 matrices ai ai, realized by formulatingtheir individual identication as a suitable nonlinear program, maximiz-ing the spectral norm of certain competitors constrained over the unitFrobenius sphere. The nal step is then to approximate the functionsg1; : : : ; gm by ^g1; : : : ; ^gm.Prof. Massimo Fornasier holds the Chair in Applied Numerical Analysis atthe Technische Universitat Munchen.http://www-m15.ma.tum.de/Allgemeines/MassimoFornasierif you would like ot meet with him during his stay contact mauro@math.duke.edu