Incorporating empirical knowledge into data-driven variable selection for quantitative analysis of coal ash content by laser-induced breakdown spectroscopy

Laser-induced breakdown spectroscopy(LIBS)has become a widely used atomic spectroscopic technique for rapid coal analysis.However,the vast amount of spectral information in LIBS contains signal uncertainty,which can affect its quantification performance.In this work,we propose a hybrid variable selection method to improve the performance of LIBS quantification.Important variables are first identified using Pearson's correlation coefficient,mutual information,least absolute shrinkage and selection operator(LASSO)and random forest,and then filtered and combined with empirical variables related to fingerprint elements of coal ash content.Subsequently,these variables are fed into a partial least squares regression(PLSR).Additionally,in some models,certain variables unrelated to ash content are removed manually to study the impact of variable deselection on model performance.The proposed hybrid strategy was tested on three LIBS datasets for quantitative analysis of coal ash content and compared with the corresponding data-driven baseline method.It is significantly better than the variable selection only method based on empirical knowledge and in most cases outperforms the baseline method.The results showed that on all three datasets the hybrid strategy for variable selection combining empirical knowledge and data-driven algorithms achieved the lowest root mean square error of prediction(RMSEP)values of 1.605,3.478 and 1.647,respectively,which were significantly lower than those obtained from multiple linear regression using only 12 empirical variables,which are 1.959,3.718 and 2.181,respectively.The LASSO-PLSR model with empirical support and 20 selected variables exhibited a significantly improved performance after variable deselection,with RMSEP values dropping from 1.635,3.962 and 1.647 to 1.483,3.086 and 1.567,respectively.Such results demonstrate that using empirical knowledge as a support for datadriven variable selection can be a viable approach to improve the accuracy and reliability of LIBS quantification.

Sufficient variable selection of high dimensional nonparametric nonlinear systems based on Fourier spectrum of density-weighted derivative

The variable selection of high dimensional nonparametric nonlinear systems aims to select the contributing variables or to eliminate the redundant variables.For a high dimensional nonparametric nonlinear system,however,identifying whether a variable contributes or not is not easy.Therefore,based on the Fourier spectrum of densityweighted derivative,one novel variable selection approach is developed,which does not suffer from the dimensionality curse and improves the identification accuracy.Furthermore,a necessary and sufficient condition for testing a variable whether it contributes or not is provided.The proposed approach does not require strong assumptions on the distribution,such as elliptical distribution.The simulation study verifies the effectiveness of the novel variable selection algorithm.

Quantitative analysis of the content of nitrogen and sulfur in coal based on laserinduced breakdown spectroscopy: effects of variable selection

Coal is a crucial fossil energy in today’s society,and the detection of sulfir(S) and nitrogen(N)in coal is essential for the evaluation of coal quality.Therefore,an efficient method is needed to quantitatively analyze N and S content in coal,to achieve the purpose of clean utilization of coal.This study applied laser-induced breakdown spectroscopy(LIBS) to test coal quality,and combined two variable selection algorithms,competitive adaptive reweighted sampling(CARS) and the successive projections algorithm(SPA),to establish the corresponding partial least square(PLS) model.The results of the experiment were as follows.The PLS modeled with the full spectrum of 27,620 variables has poor accuracy,the coefficient of determination of the test set(R^2 P) and root mean square error of the test set(RMSEP) of nitrogen were 0.5172 and 0.2263,respectively,and those of sulfur were0.5784 and 0.5811,respectively.The CARS-PLS screened 37 and 25 variables respectively in the detection of N and S elements,but the prediction ability of the model did not improve significantly.SPA-PLS finally screened 14 and 11 variables respectively through successive projections,and obtained the best prediction effect among the three methods.The R^2 P and RMSEP of nitrogen were0.9873 and 0.0208,respectively,and those of sulfur were 0.9451 and 0.2082,respectively.In general,the predictive results of the two elements increased by about 90% for RMSEP and 60% for R2 P compared with PLS.The results show that LIBS combined with SPA-PLS has good potential for detecting N and S content in coal,and is a very promising technology for industrial application.

Variable Selection of Partially Linear Single-index Models

In this article, we study the variable selection of partially linear single-index model(PLSIM). Based on the minimized average variance estimation, the variable selection of PLSIM is done by minimizing average variance with adaptive l1 penalty. Implementation algorithm is given. Under some regular conditions, we demonstrate the oracle properties of aLASSO procedure for PLSIM. Simulations are used to investigate the effectiveness of the proposed method for variable selection of PLSIM.

Variable selection-based SPC procedures for high-dimensional multistage processes

Monitoring high-dimensional multistage processes becomes crucial to ensure the quality of the final product in modern industry environments. Few statistical process monitoring(SPC) approaches for monitoring and controlling quality in highdimensional multistage processes are studied. We propose a deviance residual-based multivariate exponentially weighted moving average(MEWMA) control chart with a variable selection procedure. We demonstrate that it outperforms the existing multivariate SPC charts in terms of out-of-control average run length(ARL) for the detection of process mean shift.

Cross-Validation, Shrinkage and Variable Selection in Linear Regression Revisited

In deriving a regression model analysts often have to use variable selection, despite of problems introduced by data- dependent model building. Resampling approaches are proposed to handle some of the critical issues. In order to assess and compare several strategies, we will conduct a simulation study with 15 predictors and a complex correlation structure in the linear regression model. Using sample sizes of 100 and 400 and estimates of the residual variance corresponding to R2 of 0.50 and 0.71, we consider 4 scenarios with varying amount of information. We also consider two examples with 24 and 13 predictors, respectively. We will discuss the value of cross-validation, shrinkage and backward elimination (BE) with varying significance level. We will assess whether 2-step approaches using global or parameterwise shrinkage (PWSF) can improve selected models and will compare results to models derived with the LASSO procedure. Beside of MSE we will use model sparsity and further criteria for model assessment. The amount of information in the data has an influence on the selected models and the comparison of the procedures. None of the approaches was best in all scenarios. The performance of backward elimination with a suitably chosen significance level was not worse compared to the LASSO and BE models selected were much sparser, an important advantage for interpretation and transportability. Compared to global shrinkage, PWSF had better performance. Provided that the amount of information is not too small, we conclude that BE followed by PWSF is a suitable approach when variable selection is a key part of data analysis.

Spectroscopic Multicomponent Analysis Using Multi-objective Optimization for Variable Selection

The multiple determination tasks of chemical properties are a classical problem in analytical chemistry. The major problem is concerned in to find the best subset of variables that better represents the compounds. These variables are obtained by a spectrophotometer device. This device measures hundreds of correlated variables related with physicocbemical properties and that can be used to estimate the component of interest. The problem is the selection of a subset of informative and uncorrelated variables that help the minimization of prediction error. Classical algorithms select a subset of variables for each compound considered. In this work we propose the use of the SPEA-II （strength Pareto evolutionary algorithm II）. We would like to show that the variable selection algorithm can selected just one subset used for multiple determinations using multiple linear regressions. For the case study is used wheat data obtained by NIR （near-infrared spectroscopy） spectrometry where the objective is the determination of a variable subgroup with information about E protein content （%）, test weight （Kg/HI）, WKT （wheat kernel texture） （%） and farinograph water absorption （%）. The results of traditional techniques of multivariate calibration as the SPA （successive projections algorithm）, PLS （partial least square） and mono-objective genetic algorithm are presents for comparisons. For NIR spectral analysis of protein concentration on wheat, the number of variables selected from 775 spectral variables was reduced for just 10 in the SPEA-II algorithm. The prediction error decreased from 0.2 in the classical methods to 0.09 in proposed approach, a reduction of 37%. The model using variables selected by SPEA-II had better prediction performance than classical algorithms and full-spectrum partial least-squares.

Logistic and SVM Credit Score Models Based on Lasso Variable Selection

There are many factors influencing personal credit. We introduce Lasso technique to personal credit evaluation, and establish Lasso-logistic, Lasso-SVM and Group lasso-logistic models respectively. Variable selection and parameter estimation are also conducted simultaneously. Based on the personal credit data set from a certain lending platform, it can be concluded through experiments that compared with the full-variable Logistic model and the stepwise Logistic model, the variable selection ability of Group lasso-logistic model was the strongest, followed by Lasso-logistic and Lasso-SVM respectively. All three models based on Lasso variable selection have better filtering capability than stepwise selection. In the meantime, the Group lasso-logistic model can eliminate or retain relevant virtual variables as a group to facilitate model interpretation. In terms of prediction accuracy, Lasso-SVM had the highest prediction accuracy for default users in the training set, while in the test set, Group lasso-logistic had the best classification accuracy for default users. Whether in the training set or in the test set, the Lasso-logistic model has the best classification accuracy for non-default users. The model based on Lasso variable selection can also better screen out the key factors influencing personal credit risk.

Joint Variable Selection of Mean-Covariance Model for Longitudinal Data

In this paper we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving moving average coefficients and a diagonal matrix involving innovation variances, which are modeled as linear functions of covariates. Then, we propose a penalized maximum likelihood method for variable selection in joint mean and covariance models based on this decomposition. Under certain regularity conditions, we establish the consistency and asymptotic normality of the penalized maximum likelihood estimators of parameters in the models. Simulation studies are undertaken to assess the finite sample performance of the proposed variable selection procedure.

Automatic Variable Selection for High-Dimensional Linear Models with Longitudinal Data

High-dimensional longitudinal data arise frequently in biomedical and genomic research. It is important to select relevant covariates when the dimension of the parameters diverges as the sample size increases. We consider the problem of variable selection in high-dimensional linear models with longitudinal data. A new variable selection procedure is proposed using the smooth-threshold generalized estimating equation and quadratic inference functions (SGEE-QIF) to incorporate correlation information. The proposed procedure automatically eliminates inactive predictors by setting the corresponding parameters to be zero, and simultaneously estimates the nonzero regression coefficients by solving the SGEE-QIF. The proposed procedure avoids the convex optimization problem and is flexible and easy to implement. We establish the asymptotic properties in a high-dimensional framework where the number of covariates increases as the number of cluster increases. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedure.

Fast Variable Selection by Block Addition and Block Deletion

We propose the threshold updating method for terminating variable selection and two variable selection methods. In the threshold updating method, we update the threshold value when the approximation error smaller than the current threshold value is obtained. The first variable selection method is the combination of forward selection by block addi-tion and backward selection by block deletion. In this method, starting from the empty set of the input variables, we add several input variables at a time until the approximation error is below the threshold value. Then we search deletable variables by block deletion. The second method is the combination of the first method and variable selection by Linear Programming Support Vector Regressors (LPSVRs). By training an LPSVR with linear kernels, we evaluate the weights of the decision function and delete the input variables whose associated absolute weights are zero. Then we carry out block addition and block deletion. By computer experiments using benchmark data sets, we show that the proposed methods can perform faster variable selection than the method only using block deletion, and that by the threshold updating method, the approximation error is lower than that by the fixed threshold method. We also compare our method with an imbedded method, which determines the optimal variables during training, and show that our method gives comparable or better variable selection performance.

Spatial Prediction of Soil Salinity in a Semiarid Oasis: Environmental Sensitive Variable Selection and Model Comparison

Timely monitoring and early warning of soil salinity are crucial for saline soil management. Environmental variables are commonly used to build soil salinity prediction model. However, few researches have been done to summarize the environmental sensitive variables for soil electrical conductivity(EC) estimation systematically. Additionally, the performance of Multiple Linear Regression(MLR), Geographically Weighted Regression(GWR), and Random Forest regression(RFR) model, the representative of current main methods for soil EC prediction, has not been explored. Taking the north of Yinchuan plain irrigation oasis as the study area, the feasibility and potential of 64 environmental variables, extracted from the Landsat 8 remote sensed images in dry season and wet season, the digital elevation model, and other data, were assessed through the correlation analysis and the performance of MLR, GWR, and RFR model on soil salinity estimation was compared. The results showed that: 1) 10 of 15 imagery texture and spectral band reflectivity environmental variables extracted from Landsat 8 image in dry season were significantly correlated with soil EC, while only 3 of these indices extracted from Landsat 8 image in wet season have significant correlation with soil EC. Channel network base level, one of the terrain attributes, had the largest absolute correlation coefficient of 0.47 and all spatial location factors had significant correlation with soil EC. 2) Prediction accuracy of RFR model was slightly higher than that of the GWR model, while MLR model produced the largest error. 3) In general, the soil salinization level in the study area gradually increased from south to north. In conclusion, the remote sensed imagery scanned in dry season was more suitable for soil EC estimation, and topographic factors and spatial location also play a key role. This study can contribute to the research on model construction and variables selection for soil salinity estimation in arid and semiarid regions.

Variable Selection in Randomized Block Design Experiment

In the experimental field, researchers need very often to select the best subset model as well as reach the best model estimation simultaneously. Selecting the best subset of variables will improve the prediction accuracy as noninformative variables will be removed. Having a model with high prediction accuracy allows the researchers to use the model for future forecasting. In this paper, we investigate the differences between various variable selection methods. The aim is to compare the analysis of the frequentist methodology (the backward elimination), penalised shrinkage method (the Adaptive LASSO) and the Least Angle Regression (LARS) for selecting the active variables for data produced by the blocked design experiment. The result of the comparative study supports the utilization of the LARS method for statistical analysis of data from blocked experiments.

Bayesian Variable Selection for Mixture Process Variable Design Experiment

This paper discussed Bayesian variable selection methods for models from split-plot mixture designs using samples from Metropolis-Hastings within the Gibbs sampling algorithm. Bayesian variable selection is easy to implement due to the improvement in computing via MCMC sampling. We described the Bayesian methodology by introducing the Bayesian framework, and explaining Markov Chain Monte Carlo (MCMC) sampling. The Metropolis-Hastings within Gibbs sampling was used to draw dependent samples from the full conditional distributions which were explained. In mixture experiments with process variables, the response depends not only on the proportions of the mixture components but also on the effects of the process variables. In many such mixture-process variable experiments, constraints such as time or cost prohibit the selection of treatments completely at random. In these situations, restrictions on the randomisation force the level combinations of one group of factors to be fixed and the combinations of the other group of factors are run. Then a new level of the first-factor group is set and combinations of the other factors are run. We discussed the computational algorithm for the Stochastic Search Variable Selection (SSVS) in linear mixed models. We extended the computational algorithm of SSVS to fit models from split-plot mixture design by introducing the algorithm of the Stochastic Search Variable Selection for Split-plot Design (SSVS-SPD). The motivation of this extension is that we have two different levels of the experimental units, one for the whole plots and the other for subplots in the split-plot mixture design.

Variable selection for skew-normal mixture of joint location and scale models

Although there are many papers on variable selection methods based on mean model in the nite mixture of regression models,little work has been done on how to select signi cant explanatory variables in the modeling of the variance parameter.In this paper,we propose and study a novel class of models:a skew-normal mixture of joint location and scale models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population.The problem of variable selection for the proposed models is considered.In particular,a modi ed Expectation-Maximization(EM)algorithm for estimating the model parameters is developed.The consistency and the oracle property of the penalized estimators is established.Simulation studies are conducted to investigate the nite sample performance of the proposed methodolo-gies.An example is illustrated by the proposed methodologies.

Online quantitative analysis of soluble solids content in navel oranges using visible-nearinfrared spectroscopy and variable selection methods

Variable selection is applied widely for visible-near infrared(Vis-NIR)spectroscopy analysis of internal quality in fruits.Different spectral variable selection methods were compared for online quantitative analysis of soluble solids content(SSC)in navel oranges.Moving window partial least squares(MW-PLS),Monte Carlo uninformative variables elimination(MC-UVE)and wavelet transform(WT)combined with the MC-UVE method were used to select the spectral variables and develop the calibration models of online analysis of SSC in navel oranges.The performances of these methods were compared for modeling the Vis NIR data sets of navel orange samples.Results show that the WT-MC-UVE methods gave better calibration models with the higher correlation cofficient(r)of 0.89 and lower root mean square error of prediction(RMSEP)of 0.54 at 5 fruits per second.It concluded that Vis NIR spectroscopy coupled with WT-MC-UVE may be a fast and efective tool for online quantitative analysis of SSC in navel oranges.

Comparative Study of Variable Selection Using Genetic Algorithm with Various Types of Chromosomes

In this study,different methods of variable selection using the multilinear step-wise regression（MLR） and support vector regression（SVR） have been compared when the performance of genetic algorithms（GAs） using various types of chromosomes is used.The first method is a GA with binary chromosome（GA-BC） and the other is a GA with a fixed-length character chromosome（GA-FCC）.The overall prediction accuracy for the training set by means of 7-fold cross-validation was tested.All the regression models were evaluated by the test set.The poor prediction for the test set illustrates that the forward stepwise regression（FSR） model is easier to overfit for the training set.The results using SVR methods showed that the over-fitting could be overcome.Further,the over-fitting would be easier for the GA-BC-SVR method because too many variables fleetly induced into the model.The final optimal model was obtained with good predictive ability（R2 = 0.885,S = 0.469,Rcv2 = 0.700,Scv = 0.757,Rex2 = 0.692,Sex = 0.675） using GA-FCC-SVR method.Our investigation indicates the variable selection method using GA-FCC is the most appropriate for MLR and SVR methods.

VARIABLE SELECTION BY PSEUDO WAVELETS IN HETEROSCEDASTIC REGRESSION MODELS INVOLVING TIME SERIES

A simple but efficient method has been proposed to select variables in heteroscedastic regression models. It is shown that the pseudo empirical wavelet coefficients corresponding to the significant explanatory variables in the regression models are clearly larger than those nonsignificant ones, on the basis of which a procedure is developed to select variables in regression models. The coefficients of the models are also estimated. All estimators are proved to be consistent.

Fuzzy identification of nonlinear dynamic system based on selection of important input variables

Input variables selection(IVS) is proved to be pivotal in nonlinear dynamic system modeling. In order to optimize the model of the nonlinear dynamic system, a fuzzy modeling method for determining the premise structure by selecting important inputs of the system is studied. Firstly, a simplified two stage fuzzy curves method is proposed, which is employed to sort all possible inputs by their relevance with outputs, select the important input variables of the system and identify the structure.Secondly, in order to reduce the complexity of the model, the standard fuzzy c-means clustering algorithm and the recursive least squares algorithm are used to identify the premise parameters and conclusion parameters, respectively. Then, the effectiveness of IVS is verified by two well-known issues. Finally, the proposed identification method is applied to a realistic variable load pneumatic system. The simulation experiments indi cate that the IVS method in this paper has a positive influence on the approximation performance of the Takagi-Sugeno(T-S) fuzzy modeling.

Ensemble Variable Selection for Naive Bayes to Improve Customer Behaviour Analysis

Executing customer analysis in a systemic way is one of the possible solutions for each enterprise to understand the behavior of consumer patterns in an efficient and in-depth manner.Further investigation of customer patterns helps thefirm to develop efficient decisions and in turn,helps to optimize the enter-prise’s business and maximizes consumer satisfaction correspondingly.To con-duct an effective assessment about the customers,Naive Bayes(also called Simple Bayes),a machine learning model is utilized.However,the efficacious of the simple Bayes model is utterly relying on the consumer data used,and the existence of uncertain and redundant attributes in the consumer data enables the simple Bayes model to attain the worst prediction in consumer data because of its presumption regarding the attributes applied.However,in practice,the NB pre-mise is not true in consumer data,and the analysis of these redundant attributes enables simple Bayes model to get poor prediction results.In this work,an ensem-ble attribute selection methodology is performed to overcome the problem with consumer data and to pick a steady uncorrelated attribute set to model with the NB classifier.In ensemble variable selection,two different strategies are applied:one is based upon data perturbation(or homogeneous ensemble,same feature selector is applied to a different subsamples derived from the same learning set)and the other one is based upon function perturbation(or heterogeneous ensemble different feature selector is utilized to the same learning set).Further-more,the feature set captured from both ensemble strategies is applied to NB indi-vidually and the outcome obtained is computed.Finally,the experimental outcomes show that the proposed ensemble strategies perform efficiently in choosing a steady attribute set and increasing NB classification performance efficiently.