The prediction accuracy and generalization of fermentation process modeling on exopolysaccharide (EPS) production from Lactobacillus are often deteriorated by noise existing in the corresponding experimental data. In ...The prediction accuracy and generalization of fermentation process modeling on exopolysaccharide (EPS) production from Lactobacillus are often deteriorated by noise existing in the corresponding experimental data. In order to circumvent this problem, a novel entropy-based criterion is proposed as the objective function of several commonly used modeling methods, i.e. Multi-Layer Perceptron (MLP) network, Radial Basis Function (RBF) neural network, Takagi-Sugeno-Kang (TSK) fuzzy system, for fermentation process model in this study. Quite different from the traditional Mean Square Error (MSE) based criterion, the novel entropy-based criterion can be used to train the parameters of the adopted modeling methods from the whole distribution structure of the training data set, which results in the fact that the adopted modeling methods can have global approximation capability. Compared with the MSE- criterion, the advantage of this novel criterion exists in that the parameter learning can effectively avoid the over-fitting phenomenon, therefore the proposed criterion based modeling methods have much better generalization ability and robustness. Our experimental results confirm the above virtues of the proposed entropy-criterion based modeling methods.展开更多
In this paper, the estimators of the scale parameter of the exponential distribution obtained by applying four methods, using complete data, are critically examined and compared. These methods are the Maximum Likeliho...In this paper, the estimators of the scale parameter of the exponential distribution obtained by applying four methods, using complete data, are critically examined and compared. These methods are the Maximum Likelihood Estimator (MLE), the Square-Error Loss Function (BSE), the Entropy Loss Function (BEN) and the Composite LINEX Loss Function (BCL). The performance of these four methods was compared based on three criteria: the Mean Square Error (MSE), the Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC). Using Monte Carlo simulation based on relevant samples, the comparisons in this study suggest that the Bayesian method is better than the maximum likelihood estimator with respect to the estimation of the parameter that offers the smallest values of MSE, AIC, and BIC. Confidence intervals were then assessed to test the performance of the methods by comparing the 95% CI and average lengths (AL) for all estimation methods, showing that the Bayesian methods still offer the best performance in terms of generating the smallest ALs.展开更多
文摘The prediction accuracy and generalization of fermentation process modeling on exopolysaccharide (EPS) production from Lactobacillus are often deteriorated by noise existing in the corresponding experimental data. In order to circumvent this problem, a novel entropy-based criterion is proposed as the objective function of several commonly used modeling methods, i.e. Multi-Layer Perceptron (MLP) network, Radial Basis Function (RBF) neural network, Takagi-Sugeno-Kang (TSK) fuzzy system, for fermentation process model in this study. Quite different from the traditional Mean Square Error (MSE) based criterion, the novel entropy-based criterion can be used to train the parameters of the adopted modeling methods from the whole distribution structure of the training data set, which results in the fact that the adopted modeling methods can have global approximation capability. Compared with the MSE- criterion, the advantage of this novel criterion exists in that the parameter learning can effectively avoid the over-fitting phenomenon, therefore the proposed criterion based modeling methods have much better generalization ability and robustness. Our experimental results confirm the above virtues of the proposed entropy-criterion based modeling methods.
文摘In this paper, the estimators of the scale parameter of the exponential distribution obtained by applying four methods, using complete data, are critically examined and compared. These methods are the Maximum Likelihood Estimator (MLE), the Square-Error Loss Function (BSE), the Entropy Loss Function (BEN) and the Composite LINEX Loss Function (BCL). The performance of these four methods was compared based on three criteria: the Mean Square Error (MSE), the Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC). Using Monte Carlo simulation based on relevant samples, the comparisons in this study suggest that the Bayesian method is better than the maximum likelihood estimator with respect to the estimation of the parameter that offers the smallest values of MSE, AIC, and BIC. Confidence intervals were then assessed to test the performance of the methods by comparing the 95% CI and average lengths (AL) for all estimation methods, showing that the Bayesian methods still offer the best performance in terms of generating the smallest ALs.
