Bounding sample size with the Vapnik-Chervonenkis dimension
Discrete Applied Mathematics
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Learning in Neural Networks: Theoretical Foundations
Learning in Neural Networks: Theoretical Foundations
Machine Learning
Sparse Greedy Matrix Approximation for Machine Learning
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Generalisation Error Bounds for Sparse Linear Classifiers
COLT '00 Proceedings of the Thirteenth Annual Conference on Computational Learning Theory
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Algorithms for simultaneous sparse approximation: part I: Greedy pursuit
Signal Processing - Sparse approximations in signal and image processing
Recovery of sparse representations by polytope faces pursuit
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
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Polytope Faces Pursuit (PFP) is a greedy algorithm that approximates the sparse solutions recovered by ***1 regularised least-squares (Lasso) [4,10] in a similar vein to (Orthogonal) Matching Pursuit (OMP) [16]. 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) [17]. 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 [7] that takes into account a natural regression loss and experimental results on several benchmark datasets.