Nuclear charge radius predictions by kernel ridge regression with odd-even effects

The extended kernel ridge regression(EKRR)method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models.These are:(i)the isospin-dependent A^(1∕3) formula,(ii)relativistic continuum Hartree-Bogoliubov(RCHB)theory,(iii)Hartree-Fock-Bogoliubov(HFB)model HFB25,(iv)the Weizsacker-Skyrme(WS)model WS*,and(v)HFB25*model.In the last two models,the charge radii were calculated using a five-parameter formula with the nuclear shell corrections and deformations obtained from the WS and HFB25 models,respectively.For each model,the resultant root-mean-square deviation for the 1014 nuclei with proton number Z≥8 can be significantly reduced to 0.009-0.013 fm after considering the modification with the EKRR method.The best among them was the RCHB model,with a root-mean-square deviation of 0.0092 fm.The extrapolation abilities of the KRR and EKRR methods for the neutron-rich region were examined,and it was found that after considering the odd-even effects,the extrapolation power was improved compared with that of the original KRR method.The strong odd-even staggering of nuclear charge radii of Ca and Cu isotopes and the abrupt kinks across the neutron N=126 and 82 shell closures were also calculated and could be reproduced quite well by calculations using the EKRR method.

Revisiting Akaike’s Final Prediction Error and the Generalized Cross Validation Criteria in Regression from the Same Perspective: From Least Squares to Ridge Regression and Smoothing Splines

In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.

Ridge regression energy levels calculation of neutral ytterbium(Z=70)

In view of the difficulty in calculating the atomic structure parameters of high-Z elements,the Hartree–Fock with relativistic corrections(HFR)theory in combination with the ridge regression(RR)algorithm rather than the Cowan code’s least squares fitting(LSF)method is proposed and applied.By analyzing the energy level structure parameters of the HFR theory and using the fitting experimental energy level extrapolation method,some excited state energy levels of the Yb I(Z=70)atom including the 4f open shell are calculated.The advantages of the ridge regression algorithm are demonstrated by comparing it with Cowan code’s LSF results.In addition,the results obtained by the new method are compared with the experimental results and other theoretical results to demonstrate the reliability and accuracy of our approach.

Novel Pilot-aided Ridge Regression Channel Estimation for SC-FDE System on Time-varying Frequency Selective Fading Channel

A novel pilot-aided ridge regression (RR) channel estimation for SC-FDE system on time-varying frequency selective fading channel is derived. Previous least square (LS) channel estimation, which does not consider and utilize the influence of noise, has poor performance when the observed signal is corrupted abnormally by noise. In order to overcome the inherent disadvantage of LS estimation, the proposed RR estimation uses the influence of noise to get better performance. The performance of this new estimator is examined. The numerical results are presented to show that the new estimation improves the accuracy of estimation especially in low channel signal-to-noise ratio (CSNR) level and outperforms LS estimation. In addition, the proposed RR estimation can get the gains of about 1dB compared with LS estimation.

A feature selection method combined with ridge regression and recursive feature elimination in quantitative analysis of laser induced breakdown spectroscopy

In the spectral analysis of laser-induced breakdown spectroscopy,abundant characteristic spectral lines and severe interference information exist simultaneously in the original spectral data.Here,a feature selection method called recursive feature elimination based on ridge regression(Ridge-RFE)for the original spectral data is recommended to make full use of the valid information of spectra.In the Ridge-RFE method,the absolute value of the ridge regression coefficient was used as a criterion to screen spectral characteristic,the feature with the absolute value of minimum weight in the input subset features was removed by recursive feature elimination(RFE),and the selected features were used as inputs of the partial least squares regression(PLS)model.The Ridge-RFE method based PLS model was used to measure the Fe,Si,Mg,Cu,Zn and Mn for 51 aluminum alloy samples,and the results showed that the root mean square error of prediction decreased greatly compared to the PLS model with full spectrum as input.The overall results demonstrate that the Ridge-RFE method is more efficient to extract the redundant features,make PLS model for better quantitative analysis results and improve model generalization ability.

The Simultaneous Determination of Five Components Including Acetaminophen by Ridge Regression Spectrophotometry

Ridge regression spectrophotometry(LHG)is used for thesimultaneous determination of five components(acetaminophen,p-aminophenol, caffeine, chlorphenamine maleate and guaifenesin)incough syr- up. The computer program of LHG is based on VB language.The difficulties in overlapping of absorption spectrums of fivecompounds are overcome by this procedure. The experimental resultsshow that the recovery of each component is in the range from97.9/100 to 103.3/100 and each component obtains satisfactory resultswithout any pre-separation.

Identifying Unusual Observations in Ridge Regression Linear Model Using Box-Cox Power Transformation Technique

The use of [1] Box-Cox power transformation in regression analysis is now common;in the last two decades there has been emphasis on diagnostics methods for Box-Cox power transformation, much of which has involved deletion of influential data cases. The pioneer work of [2] studied local influence on constant variance perturbation in the Box-Cox unbiased regression linear mode. Tsai and Wu [3] analyzed local influence method of [2] to assess the effect of the case-weights perturbation on the transformation-power estimator in the Box-Cox unbiased regression linear model. Many authors noted that the influential observations on the biased estimators are different from the unbiased estimators. In this paper I describe a diagnostic method for assessing the local influence on the constant variance perturbation on the transformation in the Box-Cox biased ridge regression linear model. Two real macroeconomic data sets are used to illustrate the methodologies.

The Application of Ridge Regression in Dynamic Balancing of Flexible Rotors Based on Influence Coefficient Method

Based on the model structure of the influence coefficient method analyzed in depth by matrix theory ,it is explained the reason why the unreasonable and instable correction masses with bigger MSE are obtained by LS influence coefficient method when there are correlation planes in the dynamic balancing. It also presencd the new ridge regression method for solving correction masses according to the Tikhonov regularization theory, and described the reason why the ridge regression can eliminate the disadvantage of the LS method. Applying this new method to dynamic balancing of gas turbine, it is found that this method is superior to the LS method when influence coefficient matrix is ill-conditioned,the minimal correction masses and residual vibration are obtained in the dynamic balancing of rotors.

Diabetes Prediction Algorithm Using Recursive Ridge Regression L2

At present,the prevalence of diabetes is increasing because the human body cannot metabolize the glucose level.Accurate prediction of diabetes patients is an important research area.Many researchers have proposed techniques to predict this disease through data mining and machine learning methods.In prediction,feature selection is a key concept in preprocessing.Thus,the features that are relevant to the disease are used for prediction.This condition improves the prediction accuracy.Selecting the right features in the whole feature set is a complicated process,and many researchers are concentrating on it to produce a predictive model with high accuracy.In this work,a wrapper-based feature selection method called recursive feature elimination is combined with ridge regression(L2)to form a hybrid L2 regulated feature selection algorithm for overcoming the overfitting problem of data set.Overfitting is a major problem in feature selection,where the new data are unfit to the model because the training data are small.Ridge regression is mainly used to overcome the overfitting problem.The features are selected by using the proposed feature selection method,and random forest classifier is used to classify the data on the basis of the selected features.This work uses the Pima Indians Diabetes data set,and the evaluated results are compared with the existing algorithms to prove the accuracy of the proposed algorithm.The accuracy of the proposed algorithm in predicting diabetes is 100%,and its area under the curve is 97%.The proposed algorithm outperforms existing algorithms.

Aeromagnetic compensation method based on ridge regression algorithm

With the development of UAV technology,UAV aerial magnetic survey plays an important role in the airborne geophysical prospecting.In the aeromagnetic survey,the magnetic field interferences generated by the magnetic components on the aircraft greatly affect the accuracy of the survey results.Therefore,it is necessary to use aeromagnetic compensation technology to eliminate the interfering magnetic field.So far,the aeromagnetic compensation methods used are mainly linear regression compensation methods based on the T-L equation.The least square is one of the most commonly used methods to solve multiple linear regressions.However,considering that the correlation between data may lead to instability of the algorithm,we use the ridge regression algorithm to solve the multicollinearity problem in the T-L equation.Subsequently this method is applied to the aeromagnetic survey data,and the standard deviation is selected as the index to evaluate the compensation effect to verify the effectiveness of the method.

Ridge回归模型下金融支持对安徽农村产业融合的影响

农村一二三产业融合发展是农业农村转型发展的根本选择,对实施乡村振兴战略、全面建设社会主义现代化国家具有重大意义。本文以安徽省为切入点,构建农村产业融合评价体系,通过熵值法测度安徽农村产业融合发展水平;运用Ridge回归模型分析金融支持对安徽农村产业融合的影响。实证研究结果表明,政府财政支持、金融机构支农力度、金融业发展水平对促进安徽省农村产业融合发展有着正向作用。本文在此基础上提出了相关政策建议。

一种基于核ridge回归的解耦控制系统

提出了一种新的基于核ridge回归的解耦方法.该方法具有传统径向基(RBF)神经网络解耦方法对被控对象数学模型依赖性小的特点,同时又能有效地克服RBF神经网络解耦方法对训练样本要求高、噪声敏感和解耦速度慢的缺点,经核ridge解耦器补偿后的控制系统具有被调节量和调节量之间耦合作用小、动态特性好、稳定性强的优点.补偿后的控制系统具有很强的校正能力,对外界各种干扰也有较强的解耦效果和控制质量.仿真试验表明,采用核ridge解耦器的多变量控制系统能够有效地解除系统各变量之间的耦合作用,且结构简单、易于实现,大大增强了解耦控制系统的实用性能.

基于EWT-GRU-RR的配电网短期电力负荷预测模型

随着间歇分布式电源的大规模并入,电力负荷的波动性和非线性特征日益明显,现有单一预测模型较难实现精准预测。本研究提出一种经验小波变换(EWT)、门控循环单元(GRU)和岭回归(RR)相结合的短期电力负荷预测模型EWT-GRU-RR。首先,应用灰色关联度选取与负荷高相关性的气象耦合因素,作为相似日的分类指标;然后,采用皮尔逊系数法对类别内的负荷进行最佳相似日选取以减小计算规模;接着,采用EWT将相似日负荷数据分解得到不同频率的负荷模态序列;最后,采用GRU与RR分别对不同频率模态序列进行多步预测,并将预测分量叠加得到最终负荷预测结果。实验结果表明,本研究所提模型的预测误差较单一预测模型GRU减少了77%以上,较支持向量机回归(SVR)减少了75%以上,较先采用经验模态分解(EMD)进行分解再采用径向基函数神经网络(RBF)和RR组合预测模型EMD-RBF-RR减少了75%以上,较先采用EMD进行分解再采用GRU和RR组合预测模型EMD-GRU-RR减少了76%以上,有效提高了负荷预测精度。

Examination of machine learning for assessing physical effects:Learning the relativistic continuum mass table with kernel ridge regression

The kernel ridge regression(KRR)method and its extension with odd-even effects(KRRoe)are used to learn the nuclear mass table obtained by the relativistic continuum Hartree-Bogoliubov theory.With respect to the binding energies of 9035 nuclei,the KRR method achieves a root-mean-square deviation of 0.96 MeV,and the KRRoe method remarkably reduces the deviation to 0.17 MeV.By investigating the shell effects,one-nucleon and twonucleon separation energies,odd-even mass differences,and empirical proton-neutron interactions extracted from the learned binding energies,the ability of the machine learning tool to grasp the known physics is discussed.It is found that the shell effects,evolutions of nucleon separation energies,and empirical proton-neutron interactions are well reproduced by both the KRR and KRRoe methods,although the odd-even mass differences can only be reproduced by the KRRoe method.

A New Test for Large Dimensional Regression Coefficients

In the article, hypothesis test for coefficients in high dimensional regression models is considered. I develop simultaneous test statistic for the hypothesis test in both linear and partial linear models. The derived test is designed for growing p and fixed n where the conventional F-test is no longer appropriate. The asymptotic distribution of the proposed test statistic under the null hypothesis is obtained.

On Diagnostics in Stochastic Restricted Linear Regression Models

The aim of this paper is to propose some diagnostic methods in stochastic restricted linear regression models. A review of stochastic restricted linear regression models is given. For the model, this paper studies the method and application of the diagnostic mostly. Firstly, review the estimators of this model. Secondly, show that the case deletion model is equivalent to the mean shift outlier model for diagnostic purpose. Then, some diagnostic statistics are given. At last, example is given to illustrate our results.

Modified Cp Criterion for Optimizing Ridge and Smooth Parameters in the MGR Estimator for the Nonparametric GMANOVA Model

Longitudinal trends of observations can be estimated using the generalized multivariate analysis of variance (GMANOVA) model proposed by [10]. In the present paper, we consider estimating the trends nonparametrically using known basis functions. Then, as in nonparametric regression, an overfitting problem occurs. [13] showed that the GMANOVA model is equivalent to the varying coefficient model with non-longitudinal covariates. Hence, as in the case of the ordinary linear regression model, when the number of covariates becomes large, the estimator of the varying coefficient becomes unstable. In the present paper, we avoid the overfitting problem and the instability problem by applying the concept behind penalized smoothing spline regression and multivariate generalized ridge regression. In addition, we propose two criteria to optimize hyper parameters, namely, a smoothing parameter and ridge parameters. Finally, we compare the ordinary least square estimator and the new estimator.

中国碳排放影响因素分解及峰值预测研究

随着我国对2030年前达到碳排放峰值意愿的逐渐增强,首先,利用对数平均迪氏分解(Logarithmic Mean Divisia Index, LMDI)模型对我国2011—2019年人均碳排放量变化的影响因素进行分解,以明确各影响因素的贡献量、贡献率,并得出2011—2019年我国人均碳排放累积增长约为1.09 t。其中,经济发展起主要促进作用,累积贡献值约为5.61 t;能源结构优化和能源强度降低起抑制作用,累积贡献值分别约为-0.66 t和-3.86 t。其次,依据相关政策公布的经济社会发展预定目标,设定3种模拟情景下的指标变动量,并预测2022—2030年的CO_(2)排放量。结果显示:基准情景下CO_(2)排放量在2027年达到峰值,约为110.87亿t,人均CO_(2)排放量为7.69 t;低减排情景下CO_(2)排放量在2029年达到峰值,约为112.04亿t,人均CO_(2)排放量为7.75 t;高减排情景下CO_(2)排放量峰值出现在2023年,约为110.00亿t,人均CO_(2)排放量为7.74 t。

基于贝叶斯岭回归的长江航运服务业集聚动力机制研究

以江苏省13地市2 249家航运服务企业为研究对象,构建涵盖港口运营、经济发展和社会环境三方面的指标体系,为消除多重共线性确保拟合效果,利用贝叶斯岭回归模型研究不同类型的航运服务业集聚动力机制,结果表明:江苏省航运服务企业仍以运输仓储类低端航运服务企业为主,在沿海、沿江区域集聚效应明显;低端、中端航运服务企业的空间集聚的动力机制相近,受港口运营情况影响最为显著;高端航运服务企业对社会环境、经济发展等指标更加敏感,集装箱吞吐量之外的其他港口运营指标对其影响不显著;各地应因地制宜找准航运服务业发展着力点,制定差异化支持政策推动港航业转型升级。

安徽制造业绿色发展回归模型构建与对策研究

制造业绿色发展是经济绿色高质量发展的关键。为研究安徽省制造业绿色发展状况,收集安徽省2012-2021年十年统计年鉴数据,运用岭回归、变量自回归(VAR)模型,计算化石能源消耗、工业三废排放的回归系数,并计算综合回归系数,探索制造业与化石能源消耗、工业三废排放之间的互动关系。结果表明,化石能源消耗对制造业发展显著正向影响,且影响程度最大。工业废水、工业二氧化硫排放对制造业发展呈负向影响。工业固废产量对制造业发展呈现正向影响。基于模型分析结果,提出安徽省制造业低碳发展建议。