PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Learning the Coordinate Gradients
Yiming Ying, Qiang Wu and Colin Campbell
Journal submission 2008.

Abstract

In this paper we study the problem of learning the gradient function with application to variable selection and determining variable covariation. Firstly, we propose a novel unifying framework for coordinate gradient learning from the perspective of multi-task learning. Various variable selection algorithms can be regarded as special instances of this framework. Secondly, we formulate the dual problems of gradient learning with general loss functions. This enables the direct application of standard optimization toolboxes to the case of gradient learning. For instance, gradient learning with SVM loss can be solved by quadratic programming (QP) routines. Thirdly, we propose a novel gradient learning algorithm which can be cast as learning the kernel matrix problem. Its relation with sparse regularization is highlighted. A semi-infinite linear programming (SILP) approach and an iterative optimization approach are proposed to efficiently solve this problem. Finally, we validate our proposed approaches on both synthetic and real datasets.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:5137
Deposited By:Colin Campbell
Deposited On:24 March 2009