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This paper presents active set support vector regression (ASVR), a new active set strategy to solve a straightforward reformulation of the standard support vector regression problem. This new algorithm is based on the successful ASVM algorithm for classification problems, and consists of solving a finite number of linear equations with a typically large dimensionality equal to the number of points to be approximated. However, by making use of the Sherman-Morrison-Woodbury formula, a much smaller matrix of the order of the original input space is inverted at each step. The algorithm requires no specialized quadratic or linear programming code, but merely a linear equation solver which is publicly available. ASVR is extremely fast, produces comparable generalization error to other popular algorithms, and is available on the web for download.