Fast exact leave-one-out cross-validation of sparse least-squares support vector machines

Cawley, Gavin C.; Talbot, Nicola L. C.

doi:10.1016/j.neunet.2004.07.002

Cited by 282 publications

(202 citation statements)

References 23 publications

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“…The process is repeated for all the singletons in the training set. We use Allen's PRESS (predicted residual sum of squares) statistic for this process, P RESS = T i e 2 (i) [9], where e (i) = y i −ŷ (i) is the residual for the ith example with the ith example excluded from the training process andŷ (i) is the predicted response for the ith example based on the training process. Fortunately, we have e (i) = ei 1−hii where e i = y i −ŷ i is the residual for the ith example in the training process which includes all examples andŷ i is the fitted response based on this training.…”

Section: Kernel Ridge Regression As a Learning Methodsmentioning

confidence: 99%

Non-invasive Activation Times Estimation Using 3D Echocardiography

Prakosa

Sermesant

Delingette

et al. 2010

Statistical Atlases and Computational Models of the Heart

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Abstract. Despite advances in both medical image analysis and intracardiac electrophysiological mapping technology, the understanding of cardiac mechano-electrical coupling is still incomplete. This knowledge is of high interest since it would help estimating the cardiac electrophysiology function from the analysis of widely available cardiac images, such as 3D echocardiography. This is important, for example, in the evaluation of the cardiac resynchronization therapy (CRT) where the placement and tuning of the pacemaker leads plays a crucial role in the outcome of the therapy. This paper proposes a method to estimate activation times of myocardium using a cardiac electromechanical model. We use Kernel Ridge Regression to find the relationship between the kinematic descriptors (strain and displacement) and the contraction force caused by the action potential propagation. This regression model is then applied to two 3D echocardiographic sequences from a patient, one in sinus rhythm and the other one with left ventricle pacing, for which strains and displacements have been estimated using incompressible diffeomorphic demons for non-rigid registration.

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Section: Kernel Ridge Regression As a Learning Methodsmentioning

confidence: 99%

Non-invasive Activation Times Estimation Using 3D Echocardiography

Prakosa

Sermesant

Delingette

et al. 2010

Statistical Atlases and Computational Models of the Heart

View full text Add to dashboard Cite

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“…K-fold cross-validation is used because it makes good use of the available data both as training and test data (Cawley & Talbot, 2004).…”

Section: Model Validationmentioning

confidence: 99%

Calibration of Timetable Parameters for Rail-Guided Systems

Zhao¹,

Martin²,

Cui³

et al. 2016

International Journal of Railway

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In order to achieve a comprehensive utilization of railway networks, it is necessary to accurately assess the timetable indicators that effect the train operation. This paper describes the parameter calibration for two timetable indicators: scheduled running time and scheduled dwell time. For the scheduled running time, an existing model is employed and the single timetable parameter (percentage of minimum running time) in that model is optimized. For the scheduled dwell time, two intrinsic characteristics: the significance of stations and the average headway at each station are proposed firstly to form a new model, and the corresponding timetable parameters (the weight of the significance and the weight of the average headway) are calibrated subsequently. The Floyd Algorithm is used to obtain the connectivity among stations, which represents the significance of the stations. A case study is conducted in a light rail transportation system with 17 underground stations. The results of this research show that the optimal value of the scheduled running time parameter can be automatically determined, and the proposed model for the scheduled dwell time works well with a high coefficient of determination and low relative root mean square error through the leave-one-out validation.

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“…To test the computational speed of the proposed CV method in practice, we make an experimental speed comparison between that and the fastest previously proposed CV approach for sparse RLS, the O(mn 2 ) time LOOCV algorithm proposed by Cawley and Talbot (2004). We only test LOOCV without removing the basis vectors, because the baseline method is defined only for that setting.…”

Section: Speed Comparisonsmentioning

confidence: 99%

“…Recently, Cawley and Talbot (2004) proposed this type of LOOCV algorithm. Its computational complexity of only O(mn 2 ) makes it much more practical than the LOOCV algorithm of standard RLS used together with the above mentioned modified kernel function, because it is as expensive as the training process of sparse RLS.…”

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confidence: 99%

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Efficient cross-validation for kernelized least-squares regression with sparse basis expansions

2012

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We propose an efficient algorithm for calculating hold-out and cross-validation (CV) type of estimates for sparse regularized least-squares predictors. Holding out H data points with our method requires O(min(H 2 n, H n 2 )) time provided that a predictor with n basis vectors is already trained. In addition to holding out training examples, also some of the basis vectors used to train the sparse regularized least-squares predictor with the whole training set can be removed from the basis vector set used in the hold-out computation.In our experiments, we demonstrate the speed improvements provided by our algorithm in practice, and we empirically show the benefits of removing some of the basis vectors during the CV rounds.

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Fast exact leave-one-out cross-validation of sparse least-squares support vector machines

Cited by 282 publications

References 23 publications

Non-invasive Activation Times Estimation Using 3D Echocardiography

Non-invasive Activation Times Estimation Using 3D Echocardiography

Calibration of Timetable Parameters for Rail-Guided Systems

Efficient cross-validation for kernelized least-squares regression with sparse basis expansions

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