Unifying Framework for Fast Learning Rate of Non-Sparse Multiple Kernel Learning
Unifying Framework for Fast Learning Rate of Non-Sparse Multiple Kernel Learning
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发表时间：
2011-12
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通讯作者：
Taiji Suzuki
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作者：
Taiji Suzuki
本文针对一般正则化，给出了多核学习（MKL）的一个新的推广误差界。本文的主要目标是稠密型正则化，包括lp-MKL，它采用lp-混合范数正则化而不是l1-混合范数正则化。根据最近的数值实验，稀疏正则化并不一定表现出良好的性能相比，密集型正则化。基于这一事实，本文给出了一个通用的理论工具，以获得快速的学习率，适用于任意混合范数型正则化的统一方式。作为我们一般结果的副产品，我们展示了lp-MKL的快速学习率，这是现有界限中最紧的。我们还表明，我们的一般学习率达到了极大极小下界。最后，我们表明，当候选再生核希尔伯特空间的复杂性是不均匀的，密集型正则化显示出更好的学习率相比，稀疏l1正则化。
In this paper, we give a new generalization error bound of Multiple Kernel Learning (MKL) for a general class of regularizations. Our main target in this paper is dense type regularizations including lp-MKL that imposes lp-mixed-norm regularization instead of l1-mixed-norm regularization. According to the recent numerical experiments, the sparse regularization does not necessarily show a good performance compared with dense type regularizations. Motivated by this fact, this paper gives a general theoretical tool to derive fast learning rates that is applicable to arbitrary mixed-norm-type regularizations in a unifying manner. As a by-product of our general result, we show a fast learning rate of lp-MKL that is tightest among existing bounds. We also show that our general learning rate achieves the minimax lower bound. Finally, we show that, when the complexities of candidate reproducing kernel Hilbert spaces are inhomogeneous, dense type regularization shows better learning rate compared with sparse l1 regularization.