PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Kernel Polytope Face Pursuit
Tom Diethe and Zakria Hussain
In: ECML PKDD 2009, 7-11 September 2009, Bled, Slovenia.

Abstract

Polytope Faces Pursuit (PFP) is a greedy algorithm that approximates the sparse solutions recovered by ℓ1 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.

EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:6613
Deposited By:Zakria Hussain
Deposited On:08 March 2010