Kernel Polytope Faces Pursuit.
In: Buntine, W and Grobelnik, M and Mladenic, D and ShaweTaylor, J, (eds.)
MACHINE LEARNING AND KNOWLEDGE DISCOVERY IN DATABASES, PT I.
(pp. 290 - 301).
Polytope Faces Pursuit (PFP) is a greedy algorithm that approximates the sparse solutions recovered by l(1) regularised least-squares (Lasso) [4,10] in a similar vein to (Orthogonal) Matching Pursuit (OMP) . The algorithm is based on the geometry of the polar polytope where at each step a basis function is chosen by finding the maximal vertex using a. path-following method. The algorithmic complexity is of a similar order to OMP whilst being able to solve problems known to be hard for (O)MP. Matching Pursuit was extended to build kernel-based solutions to machine learning problems, resulting in the sparse regression algorithm, Kernel Matching, Pursuit (KMP) . We develop a new algorithm to build sparse kernel-based solutions using PFP, which we call Kernel Polytope Faces Pursuit (KPFP). We show the usefulness of this algorithm by providing a generalisation error bound  that takes into account a natural regression loss and experimental results on several benchmark datasets.
|Title:||Kernel Polytope Faces Pursuit|
|Event:||Joint European Conference on Machine Learning (ECML)/European Conference on Principles and Practice of Knowledge Discovery in Databases (PKDD)|
|Dates:||2009-09-07 - 2009-09-11|
|Keywords:||Polytope Faces Pursuit, Orthogonal Matching Pursuit, Pseudo-dimension, Sample Compression Bounds, Regression, Kernel methods, VAPNIK-CHERVONENKIS DIMENSION|
|UCL classification:||UCL > School of BEAMS > Faculty of Engineering Science > Computer Science
UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science
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