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- Title
Sparse additive support vector machines in bounded variation space.
- Authors
Wang, Yue; Lian, Heng
- Abstract
We propose the t otal v ariation penalized s parse a dditive support vector m achine (TVSAM) for performing classification in the high-dimensional settings, using a mixed |$l_{1}$| -type functional regularization scheme to induce sparsity and smoothness simultaneously. We establish a representer theorem for TVSAM, which turns the infinite-dimensional problem into a finite-dimensional one, thereby providing computational feasibility. Even for the least squares loss, our result fills a gap in the literature when compared with the existing representer theorem. Theoretically, we derive some risk bounds for TVSAM under both exact sparsity and near sparsity, and with arbitrarily specified internal knots. In this process, we develop an important interpolation inequality for the space of functions of bounded variation, relying on analytic techniques such as mollification and partition of unity. An efficient implementation based on the alternating direction method of multipliers is employed.
- Subjects
FUNCTIONS of bounded variation; SUPPORT vector machines; INTERPOLATION spaces; FUNCTION spaces; LEAST squares; ADDITIVES
- Publication
Information & Inference: A Journal of the IMA, 2024, Vol 13, Issue 1, p1
- ISSN
2049-8764
- Publication type
Article
- DOI
10.1093/imaiai/iaae003