Smoothing Spline ANOVA Models

Gu, Chong

doi:10.1007/978-1-4757-3683-0

Cited by 402 publications

(285 citation statements)

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“…When the GCV function is almost flat around its minimum, it may lead to very small values of λ (undersmoothing). A lower limit on λ that controls undersmoothing can be achieved by multiplying the trace term in (A.3) by a constant k > 1 (Friedman & Silverman 1989;Gu 2002).…”

Section: Appendix A: Automatic Choice Of the Regularization Parametermentioning

confidence: 99%

Digital deblurring of CMB maps: Performance and efficient implementation

Vio¹,

Nagy

Andreani

et al. 2003

A&A

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Abstract. Digital deblurring of images is an important problem that arises in multifrequency observations of the CosmicMicrowave Background (CMB) where, because of the width of the point spread functions (PSF), maps at different frequencies suffer a different loss of spatial resolution. Deblurring is useful for various reasons: first, it helps to restore high frequency components lost through the smoothing effect of the instrument's PSF; second, emissions at various frequencies observed with different resolutions can be better studied on a comparable resolution; third, some map-based component separation algorithms require maps with similar level of degradation. Because of computational efficiency, deblurring is usually done in the frequency domain. But this approach has some limitations as it requires spatial invariance of the PSF, stationarity of the noise, and is not flexible in the selection of more appropriate boundary conditions. Deblurring in real space is more flexible but usually not used because of its high computational cost. In this paper (the first in a series on the subject) we present new algorithms that allow the use of real space deblurring techniques even for very large images. In particular, we consider the use of Tikhonov deblurring of noisy maps with applications to PLANCK. We provide details for efficient implementations of the algorithms. Their performance is tested on Gaussian and non-Gaussian simulated CMB maps, and PSFs with both circular and elliptical symmetry. Matlab code is made available.

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Section: Appendix A: Automatic Choice Of the Regularization Parametermentioning

confidence: 99%

Digital deblurring of CMB maps: Performance and efficient implementation

Vio¹,

Nagy

Andreani

et al. 2003

A&A

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“…A contribution index, that treats forestry profits as an objective function, based solely on main effects (Gu 2002), was also calculated: (7) where: C i -contribution index of the ratio of short rotation (i = 1) to long rotation (i = 2),…”

Section: Discussionmentioning

confidence: 99%

Visualization of optimized solution space using a simulation system for the development of local forest management planning

2016

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Nakajima T., Kanomata H., Matsumoto M., 2016. Visualization of optimized solution space using a simulation system for the development of local forest management planning. Ann. For. Res. 59(1): 117-128. Abstract.A simulation system, based on pre-existing models, was used to investigate and visualize the solution space for optimizing forest management planning. The simulation system used existing forestry profits estimation models to test the outcomes of different crop rotations by previous studies. The simulation enabled us to predict forestry profits and labor requirements under different forestry management plans, and to examine the consequences for harvesting strategies. A part of the Kyushu region was selected as the study site, because the basic sub-models for predicting timber production, labor requirements and forestry profits were developed in the area. This study has investigated and visualized the solution space optimized for forest economics using various combinations of short and long rotation silvicultural practices implemented at a local scale. Based on the simulations, optimization of the plans was formulated under the forestry scale of compartment and total level. Visualizing the 3-dimensional optimized solution space by using a simulation system is useful for decision-makers involved with local forest management planning. The differences of forestry profits, labor requirements and timber volume depending on the intensity of silvicultural practices were analyzed. The simulation system is also useful for sustainable forest management under the Japanese forestry planning system.

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“…For Tikhonov regularization, it is known [57,95,98] that, with uncorrelated errors, GCV is asymptotically optimal with respect to the prediction risk as the number of data points m → ∞, i.e. the inefficiency goes to 1.…”

Section: Generalized Cross-validationmentioning

confidence: 99%

“…The GCV method has also been extended in other directions, including to non-Gaussian data [57] and to wavelet thresholding [80]. It can also be applied to iterative regularization methods, in particular the conjugate gradient method [67,71], Krylov methods [87], the ART method [126] and the iteratively regularized Gauss-Newton method [59,142].…”

Section: Generalized Cross-validationmentioning

confidence: 99%

Comparingparameter choice methods for regularization of ill-posed problems

Bauer

Lukas

2011

Mathematics and Computers in Simulation

252

111

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In the literature on regularization, many different parameter choice methods have been proposed in both deterministic and stochastic settings. However, based on the available information, it is not always easy to know how well a particular method will perform in a given situation and how it compares to other methods. This paper reviews most of the existing parameter choice methods, and evaluates and compares them in a large simulation study for spectral cut-off and Tikhonov regularization. The test cases cover a wide range of linear inverse problems with both white and colored stochastic noise. The results show some marked differences between the methods, in particular, in their stability with respect to the noise and its type. We conclude with a table of properties of the methods and a summary of the simulation results, from which we identify the best methods.

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Smoothing Spline ANOVA Models

Cited by 402 publications

References 0 publications

Digital deblurring of CMB maps: Performance and efficient implementation

Digital deblurring of CMB maps: Performance and efficient implementation

Visualization of optimized solution space using a simulation system for the development of local forest management planning

Comparingparameter choice methods for regularization of ill-posed problems

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