Giacobino, Caroline; Sardy, Sylvain; Diaz-Rodriguez, Jairo; Hengartner, Nick Quantile universal threshold. (English) Zbl 1384.62258 Electron. J. Stat. 11, No. 2, 4701-4722 (2017). The well known “bias-variance trade-off dilemma” appearing in machine learning theory is addressed. It is know that this dilemma can be handled by various regularization techniques starting from classical [A. N. Tikhonov, Sov. Math., Dokl. 5, 1035–1038 (1963; Zbl 0141.11001); translation from Dokl. Akad. Nauk SSSR 151, 501–504 (1963); A. N. Tikhonov and V. Y. Arsenin, Solutions of ill-posed problems. New York etc.: John Wiley & Sons; Washington, D.C.: V. H. Winston & Sons (1977; Zbl 0354.65028)], followed by their Bayesian interpretation and many others. In this paper, the authors propose their approach using the novel concept of a zero-thresholding function and a null-thresholding statistic, that can be explicitly derived for a large class of estimators. The efficiency of the approach, called the quantile universal threshold, is demonstrated on synthetic and real data and implemented as R package qut which is available from the Comprehensive R Archive Network (CRAN). Reviewer: Denis Sidorov (Irkutsk) Cited in 1 ReviewCited in 8 Documents MSC: 62J07 Ridge regression; shrinkage estimators (Lasso) 62H12 Estimation in multivariate analysis 68T05 Learning and adaptive systems in artificial intelligence Keywords:convex optimization; high-dimensionality; sparsity; regularization; thresholding Citations:Zbl 0141.11001; Zbl 0354.65028 Software:qut; R; CRAN PDFBibTeX XMLCite \textit{C. Giacobino} et al., Electron. J. Stat. 11, No. 2, 4701--4722 (2017; Zbl 1384.62258) Full Text: DOI arXiv Euclid