Parsimonious Kernel Fisher Discrimination

By applying recent results in optimization transfer, a new algorithm for kernel Fisher Discriminant Analysis is provided that makes use of a non-smooth penalty on the coefficients to provide a parsimonious solution. The algorithm is simple, easily programmed and is shown to perform as well as or better than a number of leading machine learning algorithms on a substantial benchmark. It is then applied to a set of extreme small-sample-size problems in virtual screening where it is found to be less accurate than a currently leading approach but is still comparable in a number of cases

Incremental proximal methods for large scale convex optimization

Laboratory for Information and Decision Systems Report LIDS-P-2847We consider the minimization of a sum∑m [over]i=1 fi (x) consisting of a large number of convex component functions fi . For this problem, incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective. We propose new incremental methods, consisting of proximal iterations applied to single components, as well as combinations of gradient, subgradient, and proximal iterations. We provide a convergence and rate of convergence analysis of a variety of such methods, including some that involve randomization in the selection of components.We also discuss applications in a few contexts, including signal processing and inference/machine learning.United States. Air Force Office of Scientific Research (grant FA9550-10-1-0412

An inexact bundle variant suited to column generation

International audienceWe give a bundle method for constrained convex optimization. Instead of using penalty functions, it shifts iterates towards feasibility, by way of a Slater point, assumed to be known. Besides, the method accepts an oracle delivering function and subgradient values with unknown accuracy. Our approach is motivated by a number of applications in column generation, in which constraints are positively homogeneous--so that zero is a natural Slater point--and an exact oracle may be time consuming. Finally, our convergence analysis employs arguments which have been little used so far in the bundle community. The method is illustrated on a number of cutting-stock problems