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Efficient generalized cross-validation for state space models
Biometrika, 1987The initial model considered is \(y(i)=s(i)+e(i)\), \(i=1,...,n\), where s(i) is an unobserved Gaussian signal and the e(i) are independent \(N(0,\sigma^ 2)\) and independent of s(i). The s(i) are generated by the state space model \[ (*)\quad s(i)=h(i,\theta)'x(i),\quad x(i+1)=F(i,\theta)x(i)+u(i) \] where u(i) is a sequence of q-dimensional ...
Ansley, Craig F., Kohn, Robert
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Cross-validation of the general neuropsychological deficit scale (GNDS)
Archives of Clinical Neuropsychology, 1995Sherer and Adams (1993) reported "limited support" for the validity of Reitan and Wolfson's (1988) Neuropsychological Deficit Scales. The present study was designed to cross-validate one of these scales--the General Neuropsychological Deficit Scale (GNDS).
D, Wolfson, R M, Reitan
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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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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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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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Journal of Computational and Graphical Statistics, 2004
This article presents a modified Newton method for minimizing multidimensional bandwidth selection for estimation in generalized additive models. The method is based on the generalized cross-validation criterion applied to backfitting estimates. The approach in particular is applicable to higher dimensional problems and provides a computationally ...
Kauermann, Göran, Opsomer, JD
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This article presents a modified Newton method for minimizing multidimensional bandwidth selection for estimation in generalized additive models. The method is based on the generalized cross-validation criterion applied to backfitting estimates. The approach in particular is applicable to higher dimensional problems and provides a computationally ...
Kauermann, Göran, Opsomer, JD
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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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Fast generalized cross validation using Krylov subspace methods
Numerical Algorithms, 2008The key step of the generalized cross-validation (GCV) method, used in a smoothing spline fitting of noisy data, is the computation of the optimal parameter \(\lambda \) by minimization of the GCV function \[ \text{GCV}(\lambda )= n\, {z^T (Q+\lambda I)^{-2} z \over [ \text{tr}\, ((Q+\lambda I)^{-1})]^2}, \] for the influence matrix \(Q\) and the ...
Roger B. Sidje +2 more
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Generalized cross‐validation as a stopping rule for the Richardson‐Lucy algorithm
International Journal of Imaging Systems and Technology, 1995AbstractThe Richardson‐Lucy (R‐L) algorithm has been widely used to restore degraded astronomical images. This algorithm is nothing more than the expectation‐maximization (EM) algorithm applied to Poisson data. The R‐L method is iterative in nature and converges to a (possibly local) maximum of the likelihood function. Unfortunately, because of the ill‐
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