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Generalized Cross-Validation for Large-Scale Problems
Journal of Computational and Graphical Statistics, 1997Abstract Although generalized cross-validation is a popular tool for calculating a regularization parameter, it has been rarely applied to large-scale problems until recently. A major difficulty lies in the evaluation of the cross-validation function that requires the calculation of the trace of an inverse matrix. In the last few years stochastic trace
Gene H. Golub, Urs von Matt
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Least Squares Model Averaging Based on Generalized Cross Validation
Acta Mathematicae Applicatae Sinica, English Series, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Xin-min +3 more
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Generating a Valid Questionnaire Translation for Cross-Cultural Use
American Journal of Occupational Therapy, 2002Occupational therapists who are interested in exporting occupational science concepts or occupational therapy practice principles to different cultural groups often encounter problems surrounding the translation of information from one language to another.
Chia-Ting, Su, L Diane, Parham
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Fast Generalized Cross-Validation Algorithm for Sparse Model Learning
Neural Computation, 2007We propose a fast, incremental algorithm for designing linear regression models. The proposed algorithm generates a sparse model by optimizing multiple smoothing parameters using the generalized cross-validation approach. The performances on synthetic and real-world data sets are compared with other incremental algorithms such as Tipping and Faul's ...
Sundararajan, S +2 more
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General Approximate Cross Validation for Model Selection
Proceedings of the 29th ACM International Conference on Multimedia, 2021Cross-validation (CV) is a ubiquitous model-agnostic tool for assessing the error of machine learning. However, it has high complexity due to the requirement of multiple times of learner training especially in multimedia tasks with huge amounts of data.
Bowei Zhu, Yong Liu 0018
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Generalized Cross Validation stopping rule for Iterated Tikhonov regularization
2021 21st International Conference on Computational Science and Its Applications (ICCSA), 2021Ill-posed inverse problems arise in many fields of science and engineering. These problems are usually very sensitive to the presence of noise in the measured data. Regularization methods aim at reducing this sensitivity. Among these methods Iterated Tikhonov (IT), in both its standard and general form, has been widely investigated due to its ease of ...
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Smoothing Inversion of Fourier Series Using Generalized Cross-Validation
Results in Mathematics, 1996Let \(f\) be a 1-periodic, absolutely continuous function with \(\int_I |f'(t)|^2 dt< \infty\), where \(I=\) \([-1/2, 1/2]\). Instead of the exact Fourier coefficients of \(f\), \(\widehat f_k:= \int_I f(t) e^{- 2\pi ikt} dt\), only a finite sequence of noisy values of \(\widehat f_k\), \(\widehat y_k= \widehat f_k+ \widehat\varepsilon_k\) \((k= 0 ...
Tasche, Manfred, Weyrich, Norman
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On Generalized Cross-Validation for Multivariate Smoothing Spline Functions
SIAM Journal on Scientific and Statistical Computing, 1987The aim of this paper is to contribute to the study of generalized cross- validation showing that it satisfied an asymptotic optimality condition and to prove that under the assumption that the knots have an asymptotic behavior defined by a cumulative distribution function with bounded density. To prove the main theorem (Th.
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Surface approximation by spline smoothing and generalized cross-validation
Mathematics and Computers in Simulation, 1992Abstract A technique is developed to approximate multi-dimensional surfaces based on smoothing splines. The tensor product is used to extend a one-dimensional spline basis to higher dimensions. The method of generalized cross-validation is applied to choose the smoothing parameter which is computed with the aid of the generalized singular value ...
Hongmin Lu, Frank H. Mathis
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Generalized least squares cross‐validation in kernel density estimation
Statistica Neerlandica, 2015The kernel density estimation is a popular method in density estimation. The main issue is bandwidth selection, which is a well‐known topic and is still frustrating statisticians. A robust least squares cross‐validation bandwidth is proposed, which significantly improves the classical least squares cross‐validation bandwidth for its variability and ...
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