Abstract
Despite recent advances in regularisation theory, the issue of parameter selection still remains a challenge for most applications. In a recent work the framework of statistical learning was used to approximate the optimal Tikhonov regularisation parameter from noisy data. In this work, we improve their results and extend the analysis to the elastic net regularisation, providing explicit error bounds on the accuracy of the approximated parameter and the corresponding regularisation solution in a simplified case. Furthermore, in the general case we design a data-driven, automated algorithm for the computation of an approximate regularisation parameter. Our analysis combines statistical learning theory with insights from regularisation theory. We compare our approach with state-of-the-art parameter selection criteria and illustrate its superiority in terms of accuracy and computational time on simulated and real data sets.
Abstract (translated)
尽管正则化理论有了新的进展，参数选择问题仍然是大多数应用的挑战。在最近的一项研究中，统计学习框架被用来从噪声数据中近似出最优的Tikhonov正则化参数。在这项工作中，我们改进了它们的结果，并将分析扩展到弹性网络正则化，在简化的情况下，为近似参数的精度和相应的正则化解提供了明确的误差界。此外，在一般情况下，我们设计了一个数据驱动的自动算法来计算一个近似的正则化参数。我们的分析将统计学习理论与正则化理论相结合。我们将我们的方法与最先进的参数选择标准进行了比较，并说明了其在模拟和真实数据集上的准确性和计算时间方面的优势。
URL
https://arxiv.org/abs/1809.08696
