More on the Ridge Parameter Estimators for the Gamma Ridge Regression Model: Simulation and Applications

Yasin, Ahad; Amin, Muhammad; Qasim, Muhammad; Muse, Abdisalam Hassan; Mastor, Adam Braima

doi:10.1155/2022/6769421

Cited by 4 publications

(4 citation statements)

References 31 publications

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“…As a result, the variances of the estimated weight coefficients are very large when using the ordinary least-squares method. Ridge regression is designed to address this problem by imposing a penalty on the size of the coefficients. , Then, the solution of the original normal equations is w ( α ) = false( X T X + ξ I false) − 1 X T y where ξ is the ridge coefficient, also known as the penalty coefficient. From another perspective, the optimal solution of eq can be obtained by minimizing the following loss function L = min w ( || italicXw − y || 2 2 + ξ || w || 2 2 ) As shown, the linear least-squares function and regularization are given by the l2-norm in Ridge regression.…”

Section: Multiple-output Machine Learning Modelsmentioning

confidence: 99%

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Customized Software Package for the Simultaneous Prediction of Multiple Fluidization Characteristic Parameters in Liquid–Solid Fluidized Beds

He,

Lei,

Xie

2024

Ind. Eng. Chem. Res.

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In liquid−solid fluidized beds, there are many parameters that need to be determined for their optimization design. This study develops four machine learning models for the simultaneous prediction of the bed expansion ratio, voidage, and drag coefficient in liquid−solid fluidized beds. The Ridge regression model, K-nearest neighbor model, support vector regression, and XGBoost model are trained and tested based on the liquid−solid fluidization experimental data set. The methods of grid-search and nested cross-validation are employed for hyperparameter tuning. It is found that the XGBoost model is the best-performing model. The results of 5-fold cross-validation and Leave-One-Out confirm that there is no overfitting problem. The voidage, drag coefficient, and bed expansion ratio are all accurately predicted, and the average R 2 is 0.992, 0.976, and 0.974, respectively. Furthermore, the method of principal component analysis is employed to analyze the high-dimensional fluidization data, and the feature importance of each principal component is obtained. For convenience in use, a customized software package is developed by Python language. The software has a good graphical interface function and supports user-defined models, which can be trained using users' own data set and customized model parameters. The software is expected to benefit the preliminary design of fluidized beds.

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Section: Multiple-output Machine Learning Modelsmentioning

confidence: 99%

“…Ridge regression is designed to address this problem by imposing a penalty on the size of the coefficients. 41,42 Then, the solution of the original normal equations is w X X I X y ( ) ( )…”

Section: Ridge Regression Modelmentioning

confidence: 99%

Customized Software Package for the Simultaneous Prediction of Multiple Fluidization Characteristic Parameters in Liquid–Solid Fluidized Beds

He,

Lei,

Xie

2024

Ind. Eng. Chem. Res.

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“…As λ increases, the intensity of regularization increases and the complexity of the model decreases. Through cross-validation, we can find the best λ value that minimizes the cross-validation error [23][24][25][26]. In this paper, we use five-fold cross-validation to get the best λ value under different datasets, as shown in Table 8.…”

Section: Modelingmentioning

confidence: 99%

Small Sample Sound Quality Prediction Method of Hy-Vo Chain Transmission System Based on Fuzzy Generation

Li,

An,

Cheng

et al. 2024

Applied Sciences

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To improve the noise comfort of the whole machine, it is necessary to establish the sound quality prediction model of the Hy-Vo chain transmission system. Compared with the silent chain transmission system, the Hy-Vo chain transmission system normally operates at a lower speed and cannot have too much load at the limit speed. It is difficult to obtain a sufficient quantity of high-quality noise samples because there are few different working conditions. For small sample sound quality prediction, we use a sample enhancement method called fuzzy generation based on fuzzy mathematics. Firstly, audio samples of the Hy-Vo chain transmission system are collected through noise tests. Secondly, the processed samples are evaluated objectively and subjectively. After a correlation test of the subjective evaluation results, correct subjective evaluation scores of each noise sample are obtained. With the help of fuzzy generation, we can obtain a sufficient number of new samples. By mixing the original samples with the generated samples, a new dataset is created. Through using a general regression neural network (GRNN), support vector regression (SVR) model, and ridge regression (RR) method, the sound quality of the Hy-Vo chain transmission system can be predicted. Different from prediction results under the original dataset, using the fuzzy generation method can not only significantly reduce the prediction error of the model but also improve stability.

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“…e ridge, Liu, Liu-type, and other estimators given by several authors are alternatives to MLE to overcome the multicollinearity in the linear regression model [18,19]. ese estimators have been extended to the GLMs [20][21][22][23][24][25][26][27][28][29]. Also, robust estimators have been proposed to handle the problem of multicollinearity and outlier values together (See [30]- [31]).…”

Section: Introductionmentioning

confidence: 99%

Performance of the Ridge and Liu Estimators in the zero‐inflated Bell Regression Model

Algamal

Lukman

Abonazel

et al. 2022

Journal of Mathematics

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The Poisson regression model is popularly used to model count data. However, the model suffers drawbacks when there is overdispersion—when the mean of the Poisson distribution is not the same as the variance. In this situation, the Bell regression model fits well to the data. Also, there is a high tendency of excess zeros in the count data. In this case, the zero-inflated Bell regression model is an alternative to the Bell regression model. The parameters of the zero-inflated Bell regression model are mostly estimated using the method of maximum likelihood. Linear dependency is a threat in a real-life application when modeling the relationship between the response variable and two or more explanatory variables in a generalized linear model such as the zero-inflated Bell regression model. It reduced the efficiency of the maximum likelihood estimator. Therefore, we developed the ridge and Liu estimators for the zero-inflated Bell regression model to deal with this issue. The simulation and application results support the dominance of the proposed methods over the conventional maximum likelihood estimator.

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More on the Ridge Parameter Estimators for the Gamma Ridge Regression Model: Simulation and Applications

Cited by 4 publications

References 31 publications

Customized Software Package for the Simultaneous Prediction of Multiple Fluidization Characteristic Parameters in Liquid–Solid Fluidized Beds

Customized Software Package for the Simultaneous Prediction of Multiple Fluidization Characteristic Parameters in Liquid–Solid Fluidized Beds

Small Sample Sound Quality Prediction Method of Hy-Vo Chain Transmission System Based on Fuzzy Generation

Performance of the Ridge and Liu Estimators in the zero‐inflated Bell Regression Model

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