论文标题
理性的近似及其用于改善深度学习分类器的应用
Rational approximation and its application to improving deep learning classifiers
论文作者
论文摘要
按多项式函数比率的理性近似是多项式近似的灵活替代方法。特别是，有理功能表现出对多项式近似值不有效的非平滑和非Lipschitz函数的准确估计。我们证明，出现在最佳统一有理近似中的优化问题是准胶盒，并展示了如何在快速有效的方法中使用此事实来计算最佳近似值。本文介绍了对出现的优化问题的理论研究，并提供了几个数值实验的结果。在我们的所有计算中，算法终止于最佳解决方案。我们将近似值作为预处理步骤应用于深度学习分类器，并证明与原始信号的分类相比，分类精度显着提高。
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial approximations are not efficient. We prove that the optimisation problems appearing in the best uniform rational approximation are quasiconvex, and show how to use this fact for calculating the best approximation in a fast and efficient method. The paper presents a theoretical study of the arising optimisation problems and provides results of several numerical experiments. In all our computations, the algorithms terminated at optimal solutions. We apply our approximation as a preprocess step to deep learning classifiers and demonstrate that the classification accuracy is significantly improved compared to the classification of the raw signals.
