Multi-task Learning in Vector-valued Reproducing Kernel Banach Spaces with the ℓ¹ Norm

2019/01/04 by Lin, Rongrong, Song, Guohui, Zhang, Haizhang · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1901.01036

Abstract

Targeting at sparse multi-task learning, we consider regularization models with an ℓ¹ 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 ℓ¹ 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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