Explaining the Generalized Cross-Validation on Linear Models

Chaves, Lucas Monteiro; Carvalho, Laerte Dias de; Reis, Carlos José dos; Souza, Devanil Jaques de

doi:10.3844/jmssp.2019.298.307

Cited by 2 publications

(1 citation statement)

References 9 publications

(12 reference statements)

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“…For example, in prior work for optical topography, 11 different methods for choosing the hyperparameter were reviewed [18] with the conclusion that the classical L-curve was the best. For medical imaging, the BestRes method [17], to which our approach is conceptually similar, was favorably compared to five other methods including generalized cross-validation (GCV) [35,36], another frequently used technique (although under the conditions in [17], GCV resulted in severely underregularized solutions and was found to be unreliable). Therefore, here we compare the hyperparameter at the onset of artefacts to hyperparameters selected using BestRes, the L-curve, and GCV.…”

Section: Comparison Of Hyperparameters Obtained From L-curve Gcv and ...mentioning

confidence: 99%

EIT for tactile sensing: considering artefacts in hyperparameter selection

Smela

2022

Eng. Res. Express

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Electrical impedance tomography (EIT) is employed in tactile sensing to create an image of impedance changes within a continuous sensor using electrodes placed only at the perimeter. Noise destabilizes EIT images, and the onset of instability is associated with the appearance of artefacts, which are spurious image features that are not associated with sensor responses to contacts. Artefacts are detrimental because the essential features of contacts, or targets, must be correctly represented, including how many there are and their approximate shapes and locations, yet their presence has not previously been used as a performance measure. Regularization, the extent of which is determined by the hyperparameter λ, is used to manage the destabilization, but it results in spatially non-uniform defocusing of image features. We therefore introduce an efficient criterion for evaluating tactile sensor image quality based on the onset of artefacts. Using simulated data and the one-step Gauss-Newton reconstruction algorithm with the Laplace prior, the noise level at which artefacts first appear at a given hyperparameter, or noise threshold Nth(λ), is found. How the relationship depends on target characteristics and other factors is shown, and Nth can vary by orders of magnitude. The conceptually similar BestRes method and the classical L-curve and generalized cross-validation (GCV) methods for determining an optimal hyperparameter are evaluated using the criterion of artefact-free images. The L-curve generates hyperparameters that are well matched to the onset of artefacts, except at high noise; the other two result in artefacts. For high dynamic range tactile inputs, setting the threshold at a fixed value using a method such as Nth is not advisable, and automatic regularization tailored to the input may be needed using a method such as the L-curve or GCV, provided that the computational overhead is tolerable.

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