scholarly journals Search Strategies Guided by the Evidence for the Selection of Basis Functions in Regression

2007 ◽  
Author(s):  
Ignacio Barrio ◽  
Enrique Romero ◽  
Lluis Belanche
Keyword(s):  
Search Strategies ◽  
Basis Functions ◽  
Selection Of

On the Problem in Model Selection of Neural Network Regression in Overrealizable Scenario

2002 ◽  
Vol 14 (8) ◽  
pp. 1979-2002 ◽  
Author(s):  
Katsuyuki Hagiwara
Keyword(s):  
Neural Networks ◽  
Lower Bound ◽  
Model Selection ◽  
Radial Basis Functions ◽  
Selection Criterion ◽  
Basis Functions ◽  
Generalization Error ◽  
Radial Basis ◽  
Training Error ◽  
Selection Of

In considering a statistical model selection of neural networks and radial basis functions under an overrealizable case, the problem of unidentifiability emerges. Because the model selection criterion is an unbiased estimator of the generalization error based on the training error, this article analyzes the expected training error and the expected generalization error of neural networks and radial basis functions in overrealizable cases and clarifies the difference from regular models, for which identifiability holds. As a special case of an overrealizable scenario, we assumed a gaussian noise sequence as training data. In the least-squares estimation under this assumption, we first formulated the problem, in which the calculation of the expected errors of unidentifiable networks is reduced to the calculation of the expectation of the supremum of thex2 process. Under this formulation, we gave an upper bound of the expected training error and a lower bound of the expected generalization error, where the generalization is measured at a set of training inputs. Furthermore, we gave stochastic bounds on the training error and the generalization error. The obtained upper bound of the expected training error is smaller than in regular models, and the lower bound of the expected generalization error is larger than in regular models. The result tells us that the degree of overfitting in neural networks and radial basis functions is higher than in regular models. Correspondingly, it also tells us that the generalization capability is worse than in the case of regular models. The article may be enough to show a difference between neural networks and regular models in the context of the least-squares estimation in a simple situation. This is a first step in constructing a model selection criterion in an overrealizable case. Further important problems in this direction are also included in this article.

A Denoising Method Based on EEMD and Interval-Thresholding Strategy

2014 ◽  
Vol 902 ◽  
pp. 336-340 ◽  
Author(s):  
Zhi Zhou ◽  
Xing Man Yang ◽  
Gang Chen
Keyword(s):  
Simulation Experiment ◽  
Adaptive Signal Processing ◽  
Basis Functions ◽  
Signal Denoising ◽  
Wavelet Thresholding ◽  
Denoising Method ◽  
Signal Processing Method ◽  
Adaptive Signal ◽  
Conventional Signal ◽  
Selection Of

As a conventional signal denoising method, wavelet thresholding denoising has problems including selection of basis vectors and poor denoising effect. EMD is an expansion of basis functions that are signal-dependent, but with the problem of mode mixing. In order to solve these problems, a denoising method based on EEMD and interval-thresholding strategy, an adaptive signal processing method is proposed, which can achieve good effects for signal denoising. Firstly, investigated signal is decomposed into IMFs by EEMD adaptively. Then, each IMF is denoising by interval-thresholding method based on sparse code shrinkage. Lastly, the denoised signal is reconstructed by denoised IMFs. Moreover, the presented method is validated by numerical simulation experiment.

scholarly journals Application of Basis Functions for Hull Form Surface Modification

2021 ◽  
Vol 9 (9) ◽  
pp. 1005
Author(s):  
Baiwei Feng ◽  
Chengsheng Zhan ◽  
Zuyuan Liu ◽  
Xide Cheng ◽  
Haichao Chang
Keyword(s):  
Surface Modification ◽  
Resistance Coefficient ◽  
Original Model ◽  
Basis Functions ◽  
Engineering Practice ◽  
Total Resistance ◽  
Hull Form ◽  
Modification Method ◽  
Selection Of

Basis functions are key in constructing interpolation equations in hull surface modification based on radial basis functions (RBF) interpolation. However, few have studied the selection of basis functions in depth. By comparing several typical basis functions through a theoretical analysis and two-dimensional modification examples, the Wendland ψ3,1 (W) function is selected. The advantages of hull form surface modification based on W function interpolation are further validated through a case study. Finally, the modification method is used to optimize a trimaran model. An optimal hull form with fair lines is obtained, and its wave-making resistance coefficient and total resistance are reduced by 8.3% and 3.8%, respectively, compared to those of the original model. These findings not only further illustrate that the W function is relatively suitable for hull form surface modification, but also validate the feasibility and value of the RBF interpolation-based surface modification method in engineering practice.

scholarly journals Literature Monitoring for Pharmacovigilance

2019 ◽  
Vol 7 (1) ◽  
pp. 31-43
Author(s):  
A. G. Khudoshin ◽  
X. Xu ◽  
B. K. Romanov
Keyword(s):  
Good Practice ◽  
Search Strategies ◽  
Reference Database ◽  
High Recall ◽  
Eurasian Economic Union ◽  
Economic Union ◽  
Comparison Of The Results ◽  
Selection Of

Literature monitoring is a complicated aspect of pharmacovigilance. The guidelines on good practice of pharmacovigilance of the Eurasian Economic Union recommend the using of a biomedical reference database containing the maximum number of sources for the monitored drugs, which necessitates the selection of such a database. The aim of the paper is to compare the coverage and functionality of international databases of medical publications recommended for monitoring literature within pharmacovigilance in terms of coverage and functionality. The paper analyzes the coverage and presents the comparison of the results of the search in the databases Embase®, MEDLINE® and eLibrary for 35 drugs. It have been shown that the search in the Embase® database provides the maximum number of sources. In addition, the paper shows the applicability special PV Wizard functionality which facilitate the building of search strategies with high recall, sensitivity and compliance.

Optimal Selection of Basis Functions for Robust Tracking Control of Uncertain Linear Systems - with Application to 3D Printing

2021 ◽  
Author(s):  
Keval Ramani ◽  
Chinedum Okwudire
Keyword(s):  
Linear Systems ◽  
Tracking Control ◽  
Basis Functions ◽  
Frobenius Norm ◽  
Control Input ◽  
Optimal Selection ◽  
Control Methods ◽  
Tracking Accuracy ◽  
Control Effort ◽  
Selection Of

Abstract There is growing interest in the use of the filtered basis functions (FBF) approach to track linear systems, especially nonminimum phase (NMP) plants, because of its distinct advantages compared to other tracking control methods in the literature. The FBF approach expresses the control input to the plant as a linear combination of basis functions with unknown coefficients. The basis functions are forward filtered through the plant dynamics and the coefficients are selected such that tracking error is minimized. Similar to other feedforward control methods, the tracking accuracy of the FBF approach deteriorates in the presence of uncertainties. However, unlike other methods, the FBF approach presents flexibility in terms of the choice of the basis functions, which can be used to improve its accuracy. This paper analyzes the effect of the choice of the basis functions on the tracking accuracy of FBF, in the presence of uncertainties, using the Frobenius norm of the lifted system representation of FBF's error dynamics. Based on the analysis, a methodology for optimal selection of basis functions to maximize robustness is proposed, together with an approach to avoid large control effort when it is applied to NMP systems. The basis functions resulting from this process are called robust basis functions. Applied experimentally to a desktop 3D printer with uncertain NMP dynamics, up to 48% improvement in tracking accuracy is achieved using the proposed robust basis functions compared to B-splines, while utilizing much less control effort.

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