Multi-task Learning in Vector-valued Reproducing Kernel Banach Spaces with the $\ell^1$ Norm

Rongrong Lin; Guohui Song; Haizhang Zhang

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arXiv · 1901.01036

Multi-task Learning in Vector-valued Reproducing Kernel Banach Spaces with the $\ell^1$ Norm

Rongrong Lin·Guohui Song·Haizhang Zhang

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Abstract

Targeting at sparse multi-task learning, we consider regularization models with an $\ell^1$ penalty on the coefficients of kernel functions. In order to provide a kernel method for this model, we construct a class of vector-valued reproducing kernel Banach spaces with the $\ell^1$ norm. The notion of multi-task admissible kernels is proposed so that the constructed spaces could have desirable properties including the crucial linear representer theorem. Such kernels are related to bounded Lebesgue constants of a kernel interpolation question. We study the Lebesgue constant of multi-task kernels and provide examples of admissible kernels. Furthermore, we present numerical experiments for both synthetic data and real-world benchmark data to demonstrate the advantages of the proposed construction and regularization models.

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BibTeX RIS

Rongrong Lin, Guohui Song, Haizhang Zhang. 2019-01-04. Multi-task Learning in Vector-valued Reproducing Kernel Banach Spaces with the $\ell^1$ Norm. https://arxiv.org/abs/1901.01036

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