Conventional artificial neural networks used to solve electrical resistivity imaging (ERI) inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian ne...Conventional artificial neural networks used to solve electrical resistivity imaging (ERI) inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network (PBNN) nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter αk, which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and field data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.展开更多
On the basis of artificial neural network (ANN) model, this paper presents an algorithm for inversing snow depth with use of AMSR-E (Advanced Microwave Scanning Radiometer-Earth Observing System (EOS)) dataset, i.e., ...On the basis of artificial neural network (ANN) model, this paper presents an algorithm for inversing snow depth with use of AMSR-E (Advanced Microwave Scanning Radiometer-Earth Observing System (EOS)) dataset, i.e., brightness temperature at 18.7 and 36.5GHz in Qinghai-Tibet Plateau during the snow season of 2002-2003. In order to overcome the overfitting problem in ANN modeling, this methodology adopts a Bayesian regularization approach. The experiments are performed to compare the results obtained from the ANN-based algorithm with those obtained from other existing algorithms, i.e., Chang algorithm, spectral polarization difference (SPD) algorithm, and temperature gradient (TG) algorithm. The experimental results show that the presented algorithm has the highest accuracy in estimating snow depth. In addition, the effects of the noises in datasets on model fitting can be decreased due to adopting the Bayesian regularization approach.展开更多
Before-after study with the empirical Bayes(EB)method is the state-of-the-art approach for estimating crash modification factors(CMFs).The EB method not only addresses the regression-to-the-mean bias,but also improves...Before-after study with the empirical Bayes(EB)method is the state-of-the-art approach for estimating crash modification factors(CMFs).The EB method not only addresses the regression-to-the-mean bias,but also improves accuracy.However,the performance of the CMFs derived from the EB method has never been fully investigated.This study aims to examine the accuracy of CMFs estimated with the EB method.Artificial realistic data(ARD)and real crash data are used to evaluate the CMFs.The results indicate that:1)The CMFs derived from the EB before-after method are nearly the same as the true values.2)The estimated CMF standard errors do not reflect the true values.The estimation remains at the same level regardless of the pre-assumed CMF standard error.The EB before-after study is not sensitive to the variation of CMF among sites.3)The analyses with real-world traffic and crash data with a dummy treatment indicate that the EB method tends to underestimate the standard error of the CMF.Safety researchers should recognize that the CMF variance may be biased when evaluating safety effectiveness by the EB method.It is necessary to revisit the algorithm for estimating CMF variance with the EB method.展开更多
Firstly,general regression neural network(GRNN) was used for variable selection of key influencing factors of residential load(RL) forecasting.Secondly,the key influencing factors chosen by GRNN were used as the input...Firstly,general regression neural network(GRNN) was used for variable selection of key influencing factors of residential load(RL) forecasting.Secondly,the key influencing factors chosen by GRNN were used as the input and output terminals of urban and rural RL for simulating and learning.In addition,the suitable parameters of final model were obtained through applying the evidence theory to combine the optimization results which were calculated with the PSO method and the Bayes theory.Then,the model of PSO-Bayes least squares support vector machine(PSO-Bayes-LS-SVM) was established.A case study was then provided for the learning and testing.The empirical analysis results show that the mean square errors of urban and rural RL forecast are 0.02% and 0.04%,respectively.At last,taking a specific province RL in China as an example,the forecast results of RL from 2011 to 2015 were obtained.展开更多
Under square loss, this paper constructs the empirical Bayes(EB) estimation for the parameter of normal distribution which has both asymptotic optimality and admissibility. Moreover, the convergence rate of the EB e...Under square loss, this paper constructs the empirical Bayes(EB) estimation for the parameter of normal distribution which has both asymptotic optimality and admissibility. Moreover, the convergence rate of the EB estimation obtained is proved to be O(n^-1).展开更多
The application of support vector machines to forecasting problems is becoming popular, lately. Several comparisons between neural networks trained with error backpropagation and support vector machines have shown adv...The application of support vector machines to forecasting problems is becoming popular, lately. Several comparisons between neural networks trained with error backpropagation and support vector machines have shown advantage for the latter in different domains of application. However, some difficulties still deteriorate the performance of the support vector machines. The main one is related to the setting of the hyperparameters involved in their training. Techniques based on meta-heuristics have been employed to determine appropriate values for those hyperparameters. However, because of the high noneonvexity of this estimation problem, which makes the search for a good solution very hard, an approach based on Bayesian inference, called relevance vector machine, has been proposed more recently. The present paper aims at investigating the suitability of this new approach to the short-term load forecasting problem.展开更多
The interaction of nanoparticles with proteins is extremely complex, important for understanding the biological properties of nanomaterials, but is very poorly understood. We have employed a combinatorial library of s...The interaction of nanoparticles with proteins is extremely complex, important for understanding the biological properties of nanomaterials, but is very poorly understood. We have employed a combinatorial library of surface modified gold nanoparticles to interrogate the relationships between the nanoparticle surface chemistry and the specific and nonspecific binding to a common, important, and representative enzyme, acetylcholinesterase (ACHE). We also used Bayesian neural networks to generate robust quantitative structure-property relationship (QSPR) models relating the nanoparticle surface to the AChE binding that also provided significant understanding into the molecular basis for these interactions. The results illustrate the insights that result from a synergistic blending of experimental combinatorial synthesis and biological testing of nanoparticles with quantitative computational methods and molecular modeling.展开更多
In this paper, the Bayes estimator and the parametric empirical Bayes estimator(PEBE) of mean vector in multivariate normal distribution are obtained. The superiority of the PEBE over the minimum variance unbiased est...In this paper, the Bayes estimator and the parametric empirical Bayes estimator(PEBE) of mean vector in multivariate normal distribution are obtained. The superiority of the PEBE over the minimum variance unbiased estimator(MVUE) and a revised James-Stein estimators(RJSE) are investigated respectively under mean square error(MSE) criterion. Extensive simulations are conducted to show that performance of the PEBE is optimal among these three estimators under the MSE criterion.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.41374118)the Research Fund for the Higher Education Doctoral Program of China(Grant No.20120162110015)+3 种基金the China Postdoctoral Science Foundation(Grant No.2015M580700)the Hunan Provincial Natural Science Foundation,the China(Grant No.2016JJ3086)the Hunan Provincial Science and Technology Program,China(Grant No.2015JC3067)the Scientific Research Fund of Hunan Provincial Education Department,China(Grant No.15B138)
文摘Conventional artificial neural networks used to solve electrical resistivity imaging (ERI) inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network (PBNN) nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter αk, which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and field data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.
基金Under the auspices of Special Basic Research Fund for Central Public Scientific Research Institutes (No. 2007-03)
文摘On the basis of artificial neural network (ANN) model, this paper presents an algorithm for inversing snow depth with use of AMSR-E (Advanced Microwave Scanning Radiometer-Earth Observing System (EOS)) dataset, i.e., brightness temperature at 18.7 and 36.5GHz in Qinghai-Tibet Plateau during the snow season of 2002-2003. In order to overcome the overfitting problem in ANN modeling, this methodology adopts a Bayesian regularization approach. The experiments are performed to compare the results obtained from the ANN-based algorithm with those obtained from other existing algorithms, i.e., Chang algorithm, spectral polarization difference (SPD) algorithm, and temperature gradient (TG) algorithm. The experimental results show that the presented algorithm has the highest accuracy in estimating snow depth. In addition, the effects of the noises in datasets on model fitting can be decreased due to adopting the Bayesian regularization approach.
基金Project(51978082)supported by the National Natural Science Foundation of ChinaProject(19B022)supported by the Outstanding Youth Foundation of Hunan Education Department,ChinaProject(2019QJCZ056)supported by the Young Teacher Development Foundation of Changsha University of Science&Technology,China。
文摘Before-after study with the empirical Bayes(EB)method is the state-of-the-art approach for estimating crash modification factors(CMFs).The EB method not only addresses the regression-to-the-mean bias,but also improves accuracy.However,the performance of the CMFs derived from the EB method has never been fully investigated.This study aims to examine the accuracy of CMFs estimated with the EB method.Artificial realistic data(ARD)and real crash data are used to evaluate the CMFs.The results indicate that:1)The CMFs derived from the EB before-after method are nearly the same as the true values.2)The estimated CMF standard errors do not reflect the true values.The estimation remains at the same level regardless of the pre-assumed CMF standard error.The EB before-after study is not sensitive to the variation of CMF among sites.3)The analyses with real-world traffic and crash data with a dummy treatment indicate that the EB method tends to underestimate the standard error of the CMF.Safety researchers should recognize that the CMF variance may be biased when evaluating safety effectiveness by the EB method.It is necessary to revisit the algorithm for estimating CMF variance with the EB method.
基金Project(07JA790092) supported by the Research Grants from Humanities and Social Science Program of Ministry of Education of ChinaProject(10MR44) supported by the Fundamental Research Funds for the Central Universities in China
文摘Firstly,general regression neural network(GRNN) was used for variable selection of key influencing factors of residential load(RL) forecasting.Secondly,the key influencing factors chosen by GRNN were used as the input and output terminals of urban and rural RL for simulating and learning.In addition,the suitable parameters of final model were obtained through applying the evidence theory to combine the optimization results which were calculated with the PSO method and the Bayes theory.Then,the model of PSO-Bayes least squares support vector machine(PSO-Bayes-LS-SVM) was established.A case study was then provided for the learning and testing.The empirical analysis results show that the mean square errors of urban and rural RL forecast are 0.02% and 0.04%,respectively.At last,taking a specific province RL in China as an example,the forecast results of RL from 2011 to 2015 were obtained.
基金Supported by the Natural Science Foundation of China(70471057)Supported by the Natural Science Foundation of Education Department of Shaanxi Province(03JK065)
文摘Under square loss, this paper constructs the empirical Bayes(EB) estimation for the parameter of normal distribution which has both asymptotic optimality and admissibility. Moreover, the convergence rate of the EB estimation obtained is proved to be O(n^-1).
文摘The application of support vector machines to forecasting problems is becoming popular, lately. Several comparisons between neural networks trained with error backpropagation and support vector machines have shown advantage for the latter in different domains of application. However, some difficulties still deteriorate the performance of the support vector machines. The main one is related to the setting of the hyperparameters involved in their training. Techniques based on meta-heuristics have been employed to determine appropriate values for those hyperparameters. However, because of the high noneonvexity of this estimation problem, which makes the search for a good solution very hard, an approach based on Bayesian inference, called relevance vector machine, has been proposed more recently. The present paper aims at investigating the suitability of this new approach to the short-term load forecasting problem.
文摘The interaction of nanoparticles with proteins is extremely complex, important for understanding the biological properties of nanomaterials, but is very poorly understood. We have employed a combinatorial library of surface modified gold nanoparticles to interrogate the relationships between the nanoparticle surface chemistry and the specific and nonspecific binding to a common, important, and representative enzyme, acetylcholinesterase (ACHE). We also used Bayesian neural networks to generate robust quantitative structure-property relationship (QSPR) models relating the nanoparticle surface to the AChE binding that also provided significant understanding into the molecular basis for these interactions. The results illustrate the insights that result from a synergistic blending of experimental combinatorial synthesis and biological testing of nanoparticles with quantitative computational methods and molecular modeling.
基金supported by National Natural Science Foundation of China(Grant Nos.11201452 and 11271346)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20123402120017)the Fundamental Research Funds for the Central Universities(Grant No.WK0010000052)
文摘In this paper, the Bayes estimator and the parametric empirical Bayes estimator(PEBE) of mean vector in multivariate normal distribution are obtained. The superiority of the PEBE over the minimum variance unbiased estimator(MVUE) and a revised James-Stein estimators(RJSE) are investigated respectively under mean square error(MSE) criterion. Extensive simulations are conducted to show that performance of the PEBE is optimal among these three estimators under the MSE criterion.