Chaotic time series multi-step direct prediction with partial least squares regression

Considering chaotic time series multi-step prediction,multi-step direct prediction model based on partial least squares(PLS)is proposed in this article,where PLS,the method for predicting a set of dependent variables forming a large set of predictors,is used to model the dynamic evolution between the space points and the corresponding future points.The model can eliminate error accumulation with the common single-step local model algorithm,and refrain from the high multi-collinearity problem in the reconstructed state space with the increase of embedding dimension.Simulation predictions are done on the Mackey-Glass chaotic time series with the model.The satisfying prediction accuracy is obtained and the model efficiency verified.In the experiments,the number of extracted components in PLS is set with Cross-validation procedure.     

偏最小二乘法在公共部门绩效多元评估中的应用

将偏最小二乘法（PLS）应用于公共部门绩效的多元评估研究, 首先,回顾总结了PLS建模的特点及建模步骤,并就公共部门绩效评估与普通最小二乘法（OLS）进行了对比;其次,以上海市为例, 建构了上海市公共部门绩效评估PLS方程模型;最后,对模型展开讨论认为：1. PLS建模方法是公共部门绩效多元评估的有效的、可行的方法;2. 对于上海市公共部门绩效多元评估实践来看,评价指标的重要性次序,由大到小依次是：政务公开、办事效率、执法公正、履行职责、清正廉洁和服务态度;而综合来看,评价指标体系对各评价主体评价结果贡献的大小有所不同,影响程度由大到小依次是：上级评价、同级评价、专业评价和公众评价.这些结论, 对于开展公共部门绩效评估的方法论研究,对于公共部门绩效多元评估的理论与实践都具有一定的参考价值.     

Some properties of LSQR for large sparse linear least squares problems

<正> It is well-known that many Krylov solvers for linear systems,eigenvalue problems,andsingular value decomposition problems have very simple and elegant formulas for residual norms.Theseformulas not only allow us to further understand the methods theoretically but also can be usedas cheap stopping criteria without forming approximate solutions and residuals at each step beforeconvergence takes place.LSQR for large sparse linear least squares problems is based on the Lanczosbidiagonalization process and is a Krylov solver.However,there has not yet been an analogouslyelegant formula for residual norms.This paper derives such kind of formula.In addition,the authorgets some other properties of LSQR and its mathematically equivalent CGLS.     

基于偏最小二乘模型的无人机航材需求预测方法

针对无人机航材存在样本数据量少,影响因素多且复杂多变,以及库存需求预测精度不高等问题,对现有经典小样本下航材需求预测方法进行系统分析,并利用偏最小二乘回归方法在处理小样本数据、变量多重相关性等方面的独特优势,提出了基于偏最小二乘的无人机航材需求预测方法.选取无人机的飞行时间、飞行起落次数、操控人员熟练程度、异常环境温度、异常环境湿度、航材故障率、维修人员技术水平、维修资料等参数,对偏最小二乘法进行原理及模型建模步骤分析,构建了无人机航材需求预测模型,并进行航材影响因素研究.实验结果表明:该模型较其它常用预测模型的精度有所提高,预测结果的平均相对误差绝对值为4.87%,表明该方法可以应用于无人机航材需求预测,能够满足实际需要.     

Partially function linear error-in-response models with validation data

This paper considers partial function linear models of the form Y =∫X(t)β(t)dt + g(T)with Y measured with error. The authors propose an estimation procedure when the basis functions are data driven, such as with functional principal components. Estimators of β(t) and g(t) with the primary data and validation data are presented and some asymptotic results are given. Finite sample properties are investigated through some simulation study and a real data application.     

具有内生性的随机变系数模型的PLS估计

在随机变系数模型中,自变量很可能与系数方程中的随机斜率相关,从而引起内生性问题.这样的内生性同样会导致标准的OLS (ordinary least squares)估计量有偏且非一致.本文通过非参方法来解决这种内生性问题.首先设定此种相关性为一个未知方程,将其直接加入模型,再利用PLS (profile least squares)方法进行估计.在给出确定性参数的渐近性质后,本文比较了PLS和OLS估计量的有限样本性质.Monte Carlo结果显示,一般而言,PLS方法都优于OLS方法.最后,本文以社会经济地位对学生成绩的影响为例,考察了PLS和OLS估计值的区别.     

最小二乘支持向量机的预优共轭梯度法

针对Suyken等人提出的最小二乘支持向量机的共轭梯度法在输入样本的个数较大时,需要求解高阶线性方程组这一缺陷,提出了一种新算法。该算法利用分块矩阵的思想将该高阶线性方程组系数矩阵降阶,为了提高收敛速度,克服数值的不稳定性,采用条件预优共轭梯度法求解低阶的线性方程组。通过仿真试验证明用本文方法训练最小二乘支持向量机比共轭梯度法的训练速度提高了将近一倍。     

排水型深V型船形因子的偏最小二乘回归分析与建模

采用偏最小二乘法对排水型深V型船的船形因子进行了回归分析与建模, 给出了回归公式的适用范围, 并与模型试验、 Holtrop船形因子求解法进行了比较分析, 结果表明: 在排水型深V型船型参数中长宽比对船形因子的解释能力最强, 其 次是吃水船长比和底部斜升角与进流角比, 进流段长度比和棱形系数对船形因子的影响较弱; 该回归公式适用范围为 L/▽^1/3= 7.0-7.9、长度傅汝德数 Fr<0.44 内的排水型深V型船型, 结合Holtrop阻力计算公式能有效提高原计算公式的阻力预报精度; 偏最小二乘法对于排水型深 V型船船形因子的回归计算具有较强的实用性.     

Approximate conditional likelihood for generalized linear models with general missing data mechanism

The generalized linear model is an indispensable tool for analyzing non-Gaussian response data, with both canonical and non-canonical link functions comprehensively used. When missing values are present, many existing methods in the literature heavily depend on an unverifiable assumption of the missing data mechanism, and they fail when the assumption is violated. This paper proposes a missing data mechanism that is as generally applicable as possible, which includes both ignorable and nonignorable missing data cases, as well as both scenarios of missing values in response and covariate. Under this general missing data mechanism, the authors adopt an approximate conditional likelihood method to estimate unknown parameters. The authors rigorously establish the regularity conditions under which the unknown parameters are identifiable under the approximate conditional likelihood approach. For parameters that are identifiable, the authors prove the asymptotic normality of the estimators obtained by maximizing the approximate conditional likelihood. Some simulation studies are conducted to evaluate finite sample performance of the proposed estimators as well as estimators from some existing methods. Finally, the authors present a biomarker analysis in prostate cancer study to illustrate the proposed method.     

SIMO系统辅助变量最小二乘盲辨识方法

辅助变量辨识方法是一类重要的辨识方法,然而对于盲辨识,系统输入未知,辅助矩阵的选择就成了难题。针对盲辨识领域研究最多的单输入多输出(SIMO)系统,利用辅助变量方法研究相应的盲辨识方法,其基本思想是联立其中两个子系统进行辨识,利用其他子系统的输出来构造辅助矩阵,从而提出了辅助变量最小二乘盲辨识方法,来获得系统参数估计。还给出所提算法的递推形式,并进行了收敛性分析。仿真例子验证了所提方法的有效性。     

Empirical likelihood confidence region for parameters in linear errors-in-variables models with missing data

The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin (1976) is considered in this paper. A constrained empirical likelihood confidence region for a parameter β ₀ in this model is proposed, which is constructed by combining the score function corresponding to the weighted squared orthogonal distance based on inverse probability with a constrained region of β ₀. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. Simulations show that the coverage rate of the proposed confidence region is closer to the nominal level and the length of confidence interval is narrower than those of the normal approximation of inverse probability weighted adjusted least square estimator in most cases. A real example is studied and the result supports the theory and simulation’s conclusion.     

New results about the relationship between optimally weighted least squares estimate and linear minimum variance estimate

The optimally weighted least squares estimate and the linear minimum variance estimate are two of the most popular estimation methods for a linear model. In this paper, the authors make a comprehensive discussion about the relationship between the two estimates. Firstly, the authors consider the classical linear model in which the coefficient matrix of the linear model is deterministic, and the necessary and sufficient condition for equivalence of the two estimates is derived. Moreover, under certain conditions on variance matrix invertibility, the two estimates can be identical provided that they use the same a priori information of the parameter being estimated. Secondly, the authors consider the linear model with random coefficient matrix which is called the extended linear model; under certain conditions on variance matrix invertibility, it is proved that the former outperforms the latter when using the same a priori information of the parameter. This research is supported in part by the National Natural Science Foundation of China under Grant Nos. 60232010, 60574032, and the Project 863 under Grant No. 2006AA12A104.     

Improved adaptive pruning algorithm for least squares support vector regression

As the solutions of the least squares support vector regression machine(LS-SVRM) are not sparse,it leads to slow prediction speed and limits its applications.The defects of the existing adaptive pruning algorithm for LS-SVRM are that the training speed is slow,and the generalization performance is not satisfactory,especially for large scale problems.Hence an improved algorithm is proposed.In order to accelerate the training speed,the pruned data point and fast leave-one-out error are employed to validate the temporary model obtained after decremental learning.The novel objective function in the termination condition which involves the whole constraints generated by all training data points and three pruning strategies are employed to improve the generalization performance.The effectiveness of the proposed algorithm is tested on six benchmark datasets.The sparse LS-SVRM model has a faster training speed and better generalization performance.     

Two-step estimators in partial linear models with missing response variables and error-prone covariates

A partial linear model with missing response variables and error-prone covariates is considered. The imputation approach is developed to estimate the regression coefficients and the nonparametric function. The proposed parametric estimators are shown to be asymptotically normal, and the estimators for the nonparametric part are proved to converge at an optimal rate. To construct confidence regions for the regression coefficients and the nonparametric function, respectively, the authors also propose the empirical-likelihood-based statistics and investigate the limit distributions of the empirical likelihood ratios. The simulation study is conducted to compare the finite sample behavior for the proposed estimators. An application to an AIDS dataset is illustrated.     

原空间中最小二乘支持向量机的新算法

为了解决原空间中最小二乘支持向量机的解缺乏稀疏性的缺点,提出了Pruning法、MFCV法和IMFCV法并对BDFS法进行了修改和运用。对一个不含有奇异点的系统而言,Pruning法、BDFS法和MFCV法在一定程度上都能实现原空间中最小二乘支持向量机解的稀疏性。BDFS法无论是训练时间还是预测时间都比Pruning法短;和MFCV法比起来,虽然BDFS法的训练时间短,但比MFCV的预测时间长。对一个含有奇异点的系统而言,Pruning法几乎失去了效用;虽然BDFS和MFCV法的训练时间都比IMFCV法的训练时间短,但IMFCV法能成功抑制奇异点从而缩短预测时间。     

基于约束加权最小二乘的无源定位闭式解算方法

针对无源定位问题中可进行伪线性处理的观测方程,提出一种基于约束加权最小二乘的无源定位闭式解算的理论框架。首先,在不限定定位观测量情况下,建立基于约束加权最小二乘的定位模型,推导其无约束最优化形式;然后,只需通过广义特征值分解即可实现辐射源状态估计并给出其解析表达式,并在此基础上证明了该闭式解的全局最优性和减小定位偏差的特性;最后,将该理论框架应用于到达角(angle of arrival, AOA)/到达时间差(time difference of arrival, TDOA)联合定位场景,验证了其有效性。仿真结果表明,所提算法定位精度能够逼近克拉美-罗下限(Cramer-Rao low bound, CRLB),定位偏差明显小于加权最小二乘算法,尤其在连续定位时间较短,噪声强度较大等情况下,验证了所提理论框架的优越性。     

关于稀疏最小二乘支持向量回归机的改进剪枝算法

对于含有奇异点的系统而言,由于一般的剪枝算法不能成功抑制系统中的奇异点,在借鉴支持向量分类机选择支持向量方法的基础上,提出了改进的剪枝算法. 改进的剪枝算法能成功抑制系统中的奇异点,减少支持向量的数目, 增强最小二乘支持向量回归机的泛化能力.另外,仿真实例也验证了改进剪枝算法的有效性. 在 不含有奇异点系统中,改进的剪枝算法退化成了一般的剪枝算法,也就是说一般的剪枝算法是改进剪枝算法的一个特例.     

A two-stage estimation algorithm for a type of current status data

Success-failure life tests are widely used in reliability engineering research to evaluate the storage life of products,where the observed data are the current status data,usually summarized as the form of "binomial life data".For this type of data,this paper proposes a two-stage algorithm to estimate some commonly used lifetime distributions.This algorithm is automatic,intuitively appealing and simple to implement.Simulation studies show that compared with some existing methods,the proposed algorithm is more stable and efficient,especially in small sample situations,and it can also be extended to deal with some complicated lifetime distributions.     

最小二乘支持向量机的参数优选方法及应用

支持向量机是一种新型的学习方法,该方法以结构风险最小化原则取代传统机器学习中的经验风险最小化原则,在小样本的机器学习中显示出了优异的性能.传统的支持向量机是解凸二次规划问题,而最小二乘支持向量机是解等式线性方程,显得尤为方便,通过建立适当的性能指标,用遗传算法优化最小二乘支持向量机的有关参数,并在非线性经济系统中应用.用最小二乘支持向量机对非线性经济系统进行预测并与其它方法的预测结果比较,结果证明,该模型的预测精确度是令人满意的,文中提出的方法是可行的.     

基于最小二乘近似支持向量回归模型的电子商务信用风险预警

随着制约电子商务发展的基础性问题如交易支付和物流配送等问题的逐步解决,电子商务交易双方的信用问题已凸显为电子商务发展的瓶颈. 在国内外研究现状的基础上, 构建电子商务信用风险的预警指标体系,并建立电子商务信用风险预警的最小二乘近似支持向量回归模型. 同时,利用相关样本数据进行了实证分析, 并根据实证结果给出不同的预警管理对策.