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Quantile universal threshold. (English) Zbl 1384.62258
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).

MSC:
62J07 Ridge regression; shrinkage estimators (Lasso)
62H12 Estimation in multivariate analysis
68T05 Learning and adaptive systems in artificial intelligence
Software:
qut; R; CRAN
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