强相关数据回归函数的小波估计

讨论了在强相关数据情形下对回归函数的小波估计,并且给出了估计量的均方误差的一个渐近展开表示式． 对研究估计量的优劣,所推导的近似表示式显得非常重要．对一般的回归函数核估计,如果回归函数不是充分光滑,这个均方误差表示式并不成立A·D2但对小波估计,即使回归函数间断连续,这个均方误差表示式仍然成立．因此,小波估计的收敛速度要比核估计来得快,从而小波估计在某种程度上改进了现有的核估计．     

基于回归分析的机场拥挤预测问题研究

及时有效的预测机场拥挤状态并辅助机场管理部门采取相应缓解拥挤的措施,将有助于提高机场的服务质量和运行效率.提出了利用回归分析的方法对机场拥挤问题进行研究.利用已有的历史航班数据挖掘出与机场拥挤最为相关的因素,并将其作为预测变量来预测响应变量.使用到两种回归分析方法即:普通最小二乘回归(OLS)和支持向量回归(SVR).使用历史数据来训练模型,并将这两种训练模型用于真实数据集上做测试,且取得较好的预测效果.实验结果证明该方法在机场拥挤预测问题上的可用性和有效性.     

连续时间下非参数回归模型的误差密度估计

本文研究连续时间下非参数回归的误差密度估计问题，给出误差密度的一个核估计量，利用回归函数的核估计在紧区间上一致均收敛的结论证明了该统计量渐近无偏差，均方相合法，并说明了该核估计中窗宽选取的办法。     

基于VAR—GM(1.1)—SVR模型的房地产价格预测研究

为提高房地产价格预测精度,克服传统统计数据真实性低、时效性差的缺点,本文以网络搜索数据为基础,首先通过斯皮尔曼相关分析和时差相关分析筛选出与房地产价格具有高度相关性的先行关键词,并利用向量自回归模型(VAR)和GM(1.1)模型分别预测房地产价格;然后构建基于向量自回归模型和GM(1.1)模型的VAR—GM(1.1)—SVR模型将以上两个模型的预测结果进行预测融合,并以西安市数据为例进行验证,得出均方误差(MSE)和标准平均方差(NMSE)分别为0.97和0.03,优于单一模型预测效果.     

基于最大相关熵准则回归模型的大盘指数预测

大盘指数是衡量股票市场运行情况的“晴雨表”,是投资者洞察股票市场发展态势和制定投资策略的重要依据.大盘指数的变化趋势与经济发展状况、宏观经济政策、投资者心态等诸多复杂因素密切相关,具有明显的随机性和不确定性,这导致精准预测大盘指数的变化趋势成为一个富有挑战性的问题.文章基于最大相关熵准则,使用一种新的回归预测模型,该方法将实际输出与理想输出视为两个随机变量,并采用相关熵度量它们之间的相似程度,进而基于最大熵准则构建一种新的回归模型优化函数,用于指导回归系数的确定.在实际操作中,通常基于有限样本,采用高斯核函数的Parzen窗方法估计两个随机变量的相关熵,因此可借助高斯核函数的核宽调节,解决最小均方误差准则回归模型对异常数据和随机噪声敏感性问题,从而提升预测精度.基于实测数据的实验结果表明:与自回归模型、差分自回归模型以及深度学习方法等相比,文章所提方法能有效降低异常数据对预测精度的影响,预测误差小,鲁棒性强.     

基于改进萤火虫优化算法的SVR空气污染物浓度预测模型

为了对空气污染物浓度进行准确预测,提出了基于改进萤火虫优化方法(IGSO)的支持向量机回归(SVR)空气污染物浓度预测模型.首先,利用佳点集理论、拥挤度以及变步长策略对萤火虫优化算法进行改进;其次,根据空气污染物浓度时间序列数据构造训练集,运用IGSO算法寻找SVR的最优参数;最后,利用基于最优参数的SVR实现对空气污染物浓度的预测.通过两部分的实验说明文章所提方法的性能.1)在8个标准测试函数上进行多次对比实验,结果显示IGSO算法相比于基于其他改进策略的萤火虫优化方法能够寻找到更优的目标函数值且方差较小,实验表明改进萤火虫优化算法在稳定性及求解精度方面性能较优.2)对京津冀地区空气污染物浓度进行实验,结果显示如下,首先,相比于萤火虫优化算法、粒子群优化算法以及遗传算法,文章基于IGSO对SVR参数的多次寻优结果波动较小,并且所得SVR模型的交叉验证误差及其方差较小;其次,与基于上述其他优化算法的SVR、基于网格搜索的SVR以及BP神经网络相比,文章方法对测试集的预测精度较高.因此,基于IGSO的SVR空气污染物浓度预测模型具有较高稳定性及预测精度.     

固定设计下半参数回归模型核估计的渐近性质

研究一类新的半参数回归模型回归函数的核估计问题,其中误差项为一阶非参数自回归过程.通过重复利用Watson-Nadaraya核估计方法,构造了回归函数及误差回归函数的估计量分别为β,g(·)和ρ(·),在适当的条件下,证明了估计量β,g(·)和ρ(·)的渐近正态性.     

基于主成分和GBDT对血糖值的预测

为了通过众多的医学指标更准确地预测血糖值,将运用主成分分析耦合GBDT做回归·首先运用主成分分析将39个原指标综合成18个新指标,并对这18个累积贡献率达95%的新指标做变量特征重要性分析,再结合18个新指标运用GBDT做回归.其中有关血糖值的数据来源于天池精准医疗大赛-人工智能辅助糖尿病遗传风险预测.将含有5642个样本值的一组血糖值数据按照7:3的比例分成两组,分别称为训练集和测试集,运用训练集中的数据建立回归模型,得出回归模型的均方根误差为0.0053,再利用测试集中的数据预测血糖值,并与测试集中的真实值作比较,得出均方根误差为0.0063,这说明预测出的血糖值较为准确,能够保障血糖值预测的精度.     

基于改进的SVR模型在年降水量预测中的应用

鉴于降水量数据的高维非线性性和周期性,建立了支持向量回归(SVR)预测模型用于降水量预测,由于对该模型输入特征的选取极为重要,因此提出了一种基于季节自回归(SARI)的输入特征选取方法.利用已有的降水量数据建立SARI模型,通过观察模型表达式提取建立SVR模型所需的输入特征用于训练支持向量机,并通过网格参数寻优法确定SVR模型的参数,进行降水量预测.实例分析中,应用此模型对黄土丘陵半干旱区域的降水量进行预测,将预测结果与季节时间序列(SARIMA)模型的预测结果进行对比,结果表明,模型具有更高的预测精度和拟合优度,可以用于降水量的预测.     

单位球上散乱数据核正则化回归的误差分析

给出基于二次损失的单位球盖(单位球)上确定型散乱数据核正则化回归误差的上界估计,将学习误差估计转化为核函数积分的误差分析,借助于学习理论中的K-泛函与光滑模的等价性刻画了学习速度.研究结果表明学习速度由网格范数所控制.     

Robust kernel ridge regression based on M-estimation

Ridge regression (RR) and kernel ridge regression (KRR) are important tools to avoid the effects of multicollinearity. However, the predictions of RR and KRR become inappropriate for use in regression models when data are contaminated by outliers. In this paper, we propose an algorithm to obtain a nonlinear robust prediction without specifying a nonlinear model in advance. We combine M-estimation and kernel ridge regression to obtain the nonlinear prediction. Then, we compare the proposed method with some other methods.     

Hazard Rate Regression Using Ordinary Nonparametric Regression Smoothers

Abstract

This article proposes a method for nonparametric estimation of hazard rates as a function of time and possibly multiple covariates. The method is based on dividing the time axis into intervals, and calculating number of event and follow-up time contributions from the different intervals. The number of event and follow-up time data are then separately smoothed on time and the covariates, and the hazard rate estimators obtained by taking the ratio. Pointwise consistency and asymptotic normality are shown for the hazard rate estimators for a certain class of smoothers, which includes some standard approaches to locally weighted regression and kernel regression. It is shown through simulation that a variance estimator based on this asymptotic distribution is reasonably reliable in practice. The problem of how to select the smoothing parameter is considered, but a satisfactory resolution to this problem has not been identified. The method is illustrated using data from several breast cancer clinical trials.     

Robust Depth-Weighted Wavelet for Nonparametric Regression Models

In the nonparametric regression models, the original regression estimators including kernel estimator, Fourier series estimator and wavelet estimator are always constructed by the weighted sum of data, and the weights depend only on the distance between the design points and estimation points. As a result these estimators are not robust to the perturbations in data. In order to avoid this problem, a new nonparametric regression model, called the depth-weighted regression model, is introduced and then the depth-weighted wavelet estimation is defined. The new estimation is robust to the perturbations in data, which attains very high breakdown value close to 1/2. On the other hand, some asymptotic behaviours such as asymptotic normality are obtained. Some simulations illustrate that the proposed wavelet estimator is more robust than the original wavelet estimator and, as a price to pay for the robustness, the new method is slightly less efficient than the original method.     

A robust support vector regression with a linear-log concave loss function

Support vector regression (SVR) is one of the most popular nonlinear regression techniques with the aim to approximate a nonlinear system with a good generalization capability. However, SVR has a major drawback in that it is sensitive to the presence of outliers. The ramp loss function for robust SVR has been introduced to resolve this problem, but SVR with ramp loss function has a non-differentiable and non-convex formulation, which is not easy to solve. Consequently, SVR with the ramp loss function requires smoothing and Concave-Convex Procedure techniques, which transform the non-differentiable and non-convex optimization to a differentiable and convex one. We present a robust SVR with linear-log concave loss function (RSLL), which does not require the transformation technique, where the linear-log concave loss function has a similar effect as the ramp loss function. The zero norm approximation and the difference of convex functions problem are employed for solving the optimization problem. The proposed RSLL approach is used to develop a robust and stable virtual metrology (VM) prediction model, which utilizes the status variables of process equipment to predict the process quality of wafer level in semiconductor manufacturing. We also compare the proposed approach to existing SVR-based methods in terms of the root mean squared error of prediction using both synthetic and real data sets. Our experimental results show that the proposed approach performs better than existing SVR-based methods regardless of the data set and type of outliers (ie, X-space and Y-space outliers), implying that it can be used as a useful alternative when the regression data contain outliers.     

Global sensitivity analysis using support vector regression

Global sensitivity analysis (GSA) plays an important role in exploring the respective effects of input variables on response variables. In this paper, a new kernel function derived from orthogonal polynomials is proposed for support vector regression (SVR). Based on this new kernel function, the Sobol’ global sensitivity indices can be computed analytically by the coefficients of the surrogate model built by SVR. In order to improve the performance of the SVR model, a kernel function iteration scheme is introduced further. Due to the excellent generalization performance and structural risk minimization principle, the SVR possesses the advantages of solving non-linear prediction problems with small samples. Thus, the proposed method is capable of computing the Sobol’ indices with a relatively limited number of model evaluations. The proposed method is examined by several examples, and the sensitivity analysis results are compared with the sparse polynomial chaos expansion (PCE), high dimensional model representation (HDMR) and Gaussian radial basis (RBF) SVR model. The examined examples show that the proposed method is an efficient approach for GSA of complex models.     

基于粒子群-支持向量机定量降水集合预报方法

首先对ECMWF不同物理量场预报因子群进行自然正交展开,选取能充分反映每个预报因子场主要信息的第一主分量作为模型输入.进一步利用粒子群算法对支持向量回归机的相关参数进行优化,以南宁市8个气象站单站逐日降水作为预报对象,建立粒子群-支持向量回归集合预报模型,进行单站逐日降水的数值预报产品释用预报方法研究.利用模型对2015年5-6月南宁市8站进行了逐日降水预报业务试验,结果表明,模型具有较好的预报效果.并提出了利用隶属函数建立可信度函数对不同的预报模型进行评价.     

Treed Regression

Abstract

Given a data set consisting of n observations on p independent variables and a single dependent variable, treed regression creates a binary tree with a simple linear regression function at each of the leaves. Each node of the tree consists of an inequality condition on one of the independent variables. The tree is generated from the training data by a recursive partitioning algorithm. Treed regression models are more parsimonious than CART models because there are fewer splits. Additionally, monotonicity in some or all of the variables can be imposed.     

删失数据回归误差项的非参数密度估计的一致相合性(英文)

回归误差项是不可观测的. 由于回归误差项的密度函数在实际中有许多应用, 故使用非参数方法对其进行估计就成为回归分析中的一个基本问题. 针对完全观测数据回归模型, 曾有作者对此问题进行了研究. 然而在实际应用中, 经常会有数据被删失的情况发生, 在此情况下, 可以利用删失回归残差, 并使用核估计的方法对回归误差项的密度函数进行估计. 本文研究了该估计的大样本性质, 并证明了估计量的一致相合性.     

增量式Huber-支持向量回归机算法研究

传统的面向支持向量回归的一次性建模算法中样本增加时,均需从头开始学习,而增量式算法可以充分利用上一阶段的学习成果。SVR的增量算法通常基于ε-不敏感损失函数,该损失函数对大的异常值比较敏感,而Huber损失函数对异常值敏感度低。所以在有噪声的情况下,Huber损失函数是比ε-不敏感损失函数更好的选择,在现实情况当中。基于此,本文提出了一种基于Huber损失函数的增量式Huber-SVR算法,该算法能够持续地将新样本信息集成到已经构建好的模型中,而不是重新建模。与增量式ε-SVR算法和增量式RBF算法相比,在对真实数据进行预测建模时,增量式Huber-SVR算法具有更高的预测精度。     

Additive Function-on-Function Regression

We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself, as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function. We discuss prediction of a new response trajectory, propose an inference procedure that accounts for total variability in the predicted response curves, and construct pointwise prediction intervals. The estimation/inferential procedure accommodates realistic scenarios, such as correlated error structure as well as sparse and/or irregular designs. We investigate our methodology in finite sample size through simulations and two real data applications. Supplementary material for this article is available online.