Multi-task Learning in vector-valued reproducing kernel Banach spaces with the ℓ1 norm
Multi-task Learning in vector-valued reproducing kernel Banach spaces with the ℓ1 norm
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DOI：
10.1016/j.jco.2020.101514
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发表时间：
2019-01
期刊：
影响因子：
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通讯作者：
Rongrong Lin;Guohui Song;Haizhang Zhang
中科院分区：
文献类型：
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作者：
Rongrong Lin;Guohui Song;Haizhang Zhang
针对稀疏多任务学习，我们考虑了核函数系数上具有101惩罚的正则化模型。为了给这一模型提供一种核方法，我们构造了一类赋范数的向量值再生核Banach空间.提出了多任务容许核的概念，使得构造的空间具有理想的性质，包括关键的线性表示定理。这样的内核相关的有界Lebesgue常数的内核插值问题。我们研究了多任务内核的勒贝格常数，并提供了容许内核的例子。此外，我们提出了数值实验的合成数据和真实世界的基准数据，以证明所提出的建设和正则化模型的优点。
Targeting at sparse multi-task learning, we consider regularization models with an ℓ 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 ℓ 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.