向量多项式优化问题的数值方法

向量多项式优化问题中的目标函数和约束条件都是由多项式描述的.先将多目标多项式函数分别通过主要目标法、线性加权和法和理想点法等转化为单目标多项式函数,再利用Lasserre松弛方法求解该多项式优化问题,从而得到原向量多项式优化问题的弱有效解或有效解.数值实验结果表明该数值方法是有效的.     

基于L_1范数支持向量分类机的算法扰动设计

普通向量分类机算法普遍有效率低下、算法复杂的缺点,为了进一步降低计算量,提高算法效率,提出了支持向量机算法.该算法将二次规划问题转换为线性规划问题,同时可以进行优化降次.结果显示,在数据量较大的情况下可以迅速并较为准确地处理大量数据,面对较为困难的数据处理时可以实现数据的有效分类.     

特征值在高等代数中的作用

以高等代数中的定义、定理和例题为依据,论述了特征值具有化繁为简的作用,它还是实对称矩阵和二次型的本质所在.特别地,它是解决许多代数问题的重要工具.     

An Adaptive Multiscale Ensemble Learning Paradigm for Nonstationary and Nonlinear Energy Price Time Series Forecasting

For forecasting nonstationary and nonlinear energy prices time series, a novel adaptive multiscale ensemble learning paradigm incorporating ensemble empirical mode decomposition (EEMD), particle swarm optimization (PSO) and least square support vector machines (LSSVM) with kernel function prototype is developed. Firstly, the extrema symmetry expansion EEMD, which can effectively restrain the mode mixing and end effects, is used to decompose the energy price into simple modes. Secondly, by using the fine‐to‐coarse reconstruction algorithm, the high‐frequency, low‐frequency and trend components are identified. Furthermore, autoregressive integrated moving average is applicable to predicting the high‐frequency components. LSSVM is suitable for forecasting the low‐frequency and trend components. At the same time, a universal kernel function prototype is introduced for making up the drawbacks of single kernel function, which can adaptively select the optimal kernel function type and model parameters according to the specific data using the PSO algorithm. Finally, the prediction results of all the components are aggregated into the forecasting values of energy price time series. The empirical results show that, compared with the popular prediction methods, the proposed method can significantly improve the prediction accuracy of energy prices, with high accuracy both in the level and directional predictions. Copyright © 2016 John Wiley & Sons, Ltd.     

LEARNING CAUSAL GRAPHS OF NONLINEAR STRUCTURAL VECTOR AUTOREGRESSIVE MODEL USING INFORMATION THEORY CRITERIA

Detection and clarification of cause-effect relationships among variables is an important problem in time series analysis. Traditional causality inference methods have a salient limitation that the model must be linear and with Gaussian noise. Although additive model regression can effectively infer the nonlinear causal relationships of additive nonlinear time series, it suffers from the limitation that contemporaneous causal relationships of variables must be linear and not always valid to test conditional independence relations. This paper provides a nonparametric method that employs both mutual information and conditional mutual information to identify causal structure of a class of nonlinear time series models, which extends the additive nonlinear times series to nonlinear structural vector autoregressive models. An algorithm is developed to learn the contemporaneous and the lagged causal relationships of variables. Simulations demonstrate the effectiveness of the nroosed method.     

基于网络关注度的大宗商品市场预测研究

随着大宗商品市场化的加快和电子信息技术的快速发展,以互联网为载体的网络信息将方便快捷地传递到市场及市场参与者.本文从海量开源数据出发,利用搜索引擎平台,提取核心信息构建网络关注度指标,并提出了基于网络关注度的大宗商品价格预测模型.通过引入具有不同核函数的支持向量回归模型,分别建立了针对单个市场(原油、铜以及玉米)的网络关注度预测模型和综合考虑市场间联动性的多市场网络关注度预测模型.实证结果表明,网络关注度对于市场价格的变动有显著的格兰杰因果关系,引入网络关注度指标和相关市场信息能显著提高预测精度.     

Forecasting key US macroeconomic variables with a factor‐augmented Qual VAR

In this paper, we first extract factors from a monthly dataset of 130 macroeconomic and financial variables. These extracted factors are then used to construct a factor‐augmented qualitative vector autoregressive (FA‐Qual VAR) model to forecast industrial production growth, inflation, the Federal funds rate, and the term spread based on a pseudo out‐of‐sample recursive forecasting exercise over an out‐of‐sample period of 1980:1 to 2014:12, using an in‐sample period of 1960:1 to 1979:12. Short‐, medium‐, and long‐run horizons of 1, 6, 12, and 24 months ahead are considered. The forecast from the FA‐Qual VAR is compared with that of a standard VAR model, a Qual VAR model, and a factor‐augmented VAR (FAVAR). In general, we observe that the FA‐Qual VAR tends to perform significantly better than the VAR, Qual VAR and FAVAR (barring some exceptions relative to the latter). In addition, we find that the Qual VARs are also well equipped in forecasting probability of recessions when compared to probit models.     

基于离散Morse理论的优化模型

根据Forman的离散Morse理论的特点，提出一种基于离散Morse理论的优化模型. 该模型利用在3维空间点构建离散Morse函数进行最优化的算法，得到了问题的最优解或近似最优解，同时也证明了构建的函数确实是复形上的离散Morse函数. 这是一个全新的尝试. 实验在4个典型的测试函数中进行，结果证明了该模型的有效性，且该模型尤其适用于解决大数据量的优化问题.     

考虑决策者心理行为特征的激励型变权决策方法研究

系统研究了激励型变权向量,首先定义了考虑决策者心理行为的激励型变权向量,提出了与之对应的状态变权向量,分别讨论了激励型变权向量的基本类型;其次深入研究了效用函数诱导出激励型变权特性;然后,定义了激励型变权的风险规避系数,分别研究了几类激励型变权向量与风险规避系数的关系.提出一种新的基于激励型变权向量的多属性决策方法;最后,通过实例说明了该理论是有效的和合理的.     

三角网格模型五轴加工刀轴矢量调整及优化

为消除全局干涉,提出了一种基于K-D树及刀具离散的高效刀轴矢量调整算法.算法首先以有限个点离散表示刀具,然后利用K-D树快速查找刀具的可能干涉点,并在此基础上计算调整后的刀轴矢量.为避免过大的刀轴矢量突变,提出一种分角度区域方法优化刀轴矢量.实例验证表明:算法能够高效实现全局干涉避免及刀轴矢量优化.