论文标题
概括保证稀疏内核近似具有熵最佳特征
Generalization Guarantees for Sparse Kernel Approximation with Entropic Optimal Features
论文作者
论文摘要
尽管它们取得了成功，但内核方法在实践中遭受了巨大的计算成本。在本文中，代替了$ n $输入的常用内核扩展，我们开发了一种新颖的最佳设计，从而最大程度地提高了内核特征之间的熵。此过程导致有关熵最佳特征（EOF）的内核扩展，由于特征差异而大大改善了数据表示。在温和的技术假设下，我们的概括性结合表明，只有$ o（n^{\ frac {1} {4}}}）$特征（忽略对数因素），我们可以实现最佳的统计准确性（即$ o（1/\ sqrt {n}）$）。我们设计的显着特征是它的稀疏性大大降低了时间和空间成本。我们在基准数据集上进行的数值实验验证了EOF优于核近似中最新的优势。
Despite their success, kernel methods suffer from a massive computational cost in practice. In this paper, in lieu of commonly used kernel expansion with respect to $N$ inputs, we develop a novel optimal design maximizing the entropy among kernel features. This procedure results in a kernel expansion with respect to entropic optimal features (EOF), improving the data representation dramatically due to features dissimilarity. Under mild technical assumptions, our generalization bound shows that with only $O(N^{\frac{1}{4}})$ features (disregarding logarithmic factors), we can achieve the optimal statistical accuracy (i.e., $O(1/\sqrt{N})$). The salient feature of our design is its sparsity that significantly reduces the time and space cost. Our numerical experiments on benchmark datasets verify the superiority of EOF over the state-of-the-art in kernel approximation.
