Shape-Constrained Estimation Using Nonnegative Splines

We consider the problem of nonparametric estimation of unknown smooth functions in the presence of restrictions on the shape of the estimator and on its support using polynomial splines. We provide a general computational framework that treats these estimation problems in a unified manner, without the limitations of the existing methods. Applications of our approach include computing optimal spline estimators for regression, density estimation, and arrival rate estimation problems in the presence of various shape constraints. Our approach can also handle multiple simultaneous shape constraints. The approach is based on a characterization of nonnegative polynomials that leads to semidefinite programming (SDP) and second-order cone programming (SOCP) formulations of the problems. These formulations extend and generalize a number of previous approaches in the literature, including those with piecewise linear and B-spline estimators. We also consider a simpler approach in which nonnegative splines are approximated by splines whose pieces are polynomials with nonnegative coefficients in a nonnegative basis. A condition is presented to test whether a given nonnegative basis gives rise to a spline cone that is dense in the space of nonnegative continuous functions. The optimization models formulated in the article are solvable with minimal running time using off-the-shelf software. We provide numerical illustrations for density estimation and regression problems. These examples show that the proposed approach requires minimal computational time, and that the estimators obtained using our approach often match and frequently outperform kernel methods and spline smoothing without shape constraints. Supplementary materials for this article are provided online.     

Fast Nonparametric Quantile Regression With Arbitrary Smoothing Methods

The calculation of nonparametric quantile regression curve estimates is often computationally intensive, as typically an expensive nonlinear optimization problem is involved. This article proposes a fast and easy-to-implement method for computing such estimates. The main idea is to approximate the costly nonlinear optimization by a sequence of well-studied penalized least squares-type nonparametric mean regression estimation problems. The new method can be paired with different nonparametric smoothing methods and can also be applied to higher dimensional settings. Therefore, it provides a unified framework for computing different types of nonparametric quantile regression estimates, and it also greatly broadens the scope of the applicability of quantile regression methodology. This wide applicability and the practical performance of the proposed method are illustrated with smoothing spline and wavelet curve estimators, for both uni- and bivariate settings. Results from numerical experiments suggest that estimates obtained from the proposed method are superior to many competitors. This article has supplementary material online.     

基于SVM回归模型的混合气体组分种类光谱识别方法

针对混合气体红外光谱分析中无法采用同一模型同时进行混合气体组分浓度的定量分析和组分种类的定性分析的问题,本文提出了基于SVM回归模型的混合气体组分种类光谱识别方法.通过详细推导,证明混合气体组分种类识别完全可以通过组分浓度分析的SVM回归模型来求解,混合气体组分种类识别是一种特殊的回归.实验结果显示,该方法的混合气体组分种类的正确识别率不小于92.5%.     

基于分类回归树的个人信用客观评分指标体系(英文)

本文提出了一种客观的个人信用指标体系.首先利用分类回归树量化每个指标对信用状况的影响程度,并以此量化值为每个指标设置不同的评分权重;然后通过定义风险度量值来确定指标中各个取值的评分,进而建立了新的评估指标体系.通过选取现实样本数据对指标体系做了实证分析,分析结果表明,新建的指标体系能很好地对借款人进行风险评价.     

Optimization of heterogeneous Catalyst-assisted fatty acid methyl esters biodiesel production from Soybean oil with different Machine learning methods

There is a growing attention to the bio and renewable energies due to fast depletion of fossil fuels as well as the global warming problem. Here, we developed a modeling and simulation method by means of artificial intelligence (AI) for prediction of the bioenergy production from vegetable bean oil. AI methods are well known for prediction of complex and nonlinear process. Three distinct Adaptive Boosted models including Huber regression, LASSO, and Support Vector Regression (SVR) as well as artificial neural network (ANN) were applied in this study to predict actual yield of Fatty acid methyl esters (FAME) production. All boosted utilizing the Adaptive boosting algorithm. The important influencing parameters on the biodiesel production such as the catalyst loading (CAO/Ag, wt%) and methanol to oil (Soybean oil) molar ratio were selected as the input variables of models while the yield of FAME production was selected as output. Model hyper-parameters were tuned to maintain generality while improving prediction accuracy. The models were evaluated using three distinct metrics Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and R². Error rates of 8.16780E-01, 4.43895E-01, 2.06692E + 00, and 3.92713 E-01 were obtained with the MAE metric for boosted Huber, SVR, LASSO and ANN models. On the other hand, the RMSE error of these models were about 1.092E-02, 1.015E-02, 2.669E-02, and 1.01174E-02, respectively. Finally, the R-square score were calculated for boosted Huber, boosted SVR, and boosted LASSO as 0.976, 0.990, 0.872, and 0.99702, respectively. Therefore, it can be concluded that although the boosted SVR and ANN models were better models for prediction of process efficiency in terms of error, but all algorithms had high accuracy. The optimum yield of 83.77% and 81.60% for biodiesel production were observed at optimum operating values from boosted SVR and ANN models, respectively.     

Determining the Zn Content of Cherry in Field Using VNIR Spectroscopy

Visible and near-infrared(VNIR)spectroscopy is an eco-friendly method used for estimating plant nutrient deficiencies.The aim of this study was to investigate the possibility of using VNIR method for estimating Zn content in cherry orchard leaves under field conditions.The study was conducted in 3different locations in Isparta region of Turkey.Fifteen cherry orchards containing normal and Zn deficient plants were chosen,and 60 leaf samples were collected from each location.The reflectance spectra of the leaves were measured with an ASD FieldSpec HandHeld spectroradiometer and a plant probe.The Zn contents of leaf samples were predicted through laboratory analysis.The spectral reflectance measurements were used to estimate the Zn levels using stepwise multiple linear regression analysis method.Prediction models were created using the highest coefficient of determination value.The results show that Zn content of cherry trees can be estimated using the VNIR spectroscopic method(87.5相似文献   

Multivariate optimization and comparison between conventional extraction (CE) and ultrasonic-assisted extraction (UAE) of carotenoid extraction from cashew apple

Carotenoids are an essential component of cashew and can be used in pharmaceuticals, cosmetics, natural pigment, food additives, among other applications. The present work focuses on optimizing and comparing conventional and ultrasound-assisted extraction methods. Every optimization step took place with a 1:1 (w:w) mixture of yellow and red cashew apples lyophilized and ground in a cryogenic mill. A Simplex-centroid design was applied for both methods, and the solvents acetone, methanol, ethanol, and petroleum ether were evaluated. After choosing the extractor solvent, a central composite design was applied to optimize the sample mass (59–201 mg) and extraction time (6–34 min). The optimum conditions for the extractor solvent were 38% acetone, 30% ethanol, and 32% petroleum ether for CE and a mixture of 44% acetone and 56% methanol for UAE. The best experimental conditions for UAE were a sonication time of 19 min and a sample mass of 153 mg, while the CE was 23 min and 136 mg. Comparing red and yellow cashews, red cashews showed a higher carotenoid content in both methodologies. The UAE methodology was ca. 21% faster, presented a more straightforward composition of extracting solution, showed an average yield of superior carotenoid content in all samples compared to CE. Therefore, UAE has demonstrated a simple, efficient, fast, low-cost adjustment methodology and a reliable alternative for other applications involving these bioactive compounds in the studied or similar matrix.     

Robust Autocorrelation Estimation

In this article, we introduce a new class of robust autocorrelation estimators based on interpreting the sample autocorrelation function as a linear regression. We investigate the efficiency and robustness properties of the estimators that result from employing three common robust regression techniques. We discuss the construction of robust autocovariance and positive definite autocorrelation estimates, and their application to AR model fitting. We perform simulation studies with various outlier configurations to compare the different estimators.     

水溶液中Cr^3＋的火焰原子吸收光谱法测试条件的优化

为优化火焰原子吸收光谱法测定水溶液中的Cr^3＋的测试条件,分别采用单因素简单比较法、正交实验设计极差分析及正交实验回归方法考察了光谱通带n,空心阴极灯电流I,燃烧器高度h以及乙炔/空气流量比P对于仪器灵敏度的影响。结果表明单因素简单比较法获得的实验条件最优。乙炔/空气流量比P对火焰原子吸收仪器灵敏度影响最大、其次是光谱通带n,燃烧器高度h和灯电流I的影响很小。测定水溶液中的Cr^3＋时仪器灵敏度最佳的实验条件为：乙炔/空气流量比P=0.4;光谱通带n=0.2nm;灯电流I=5mA;燃烧器高度h=5cm。