【作者】 张仕光；

【导师】 米据生； 胡清华；

【作者基本信息】 河北师范大学 ， 应用数学， 2014， 博士

【摘要】 回归模型注重挖掘数据的线性或非线性结构规律,它为研究人员和工程师利用数据进行学习提供了强大的工具.回归模型已成功应用于研究和应用等各个领域,包括社会科学、经济学、金融学、电网运行的风功率预测等.经典的核岭回归模型和基于高斯噪声特性的-支持向量回归模型都假设噪声特性服从高斯分布.然而在许多实际应用领域中,如风功率预报、相关电磁波的到达方向估计问题等,噪声特性不服从高斯分布,而服从Beta分布、拉普拉斯分布,或者别的分布.此时,经典的回归技术不是最优的.利用Bayesian方法,得到一般噪声特性的损失函数,构造了新的基于噪声特性的核岭回归模型(GN-KRR)框架结构;提出了新的基于噪声特性的-支持向量回归模型(GN-SVR)通用框架.基于高斯噪声特性的核岭回归模型(GN-KRR)、-支持向量回归模型(GN-SVR)都假设噪声特性服从均值为0、同方差2的高斯分布.作者利用持续法统计得到,风速预报误差不服从均值为0、同方差2的高斯分布,而服从均值为0,异方差2i(i1,2,, l)的高斯分布.此时模型GN-KRR和GN-SVR不是最优的.利用异方差噪声特性的损失函数,提出了新的基于异方差噪声特性-支持向量回归模型(HGN-SVR)框架结构.在ε-支持向量回归和粗糙-支持向量回归模型的基础上,研究了新的粗糙-支持向量回归模型.利用固定对称边界粗糙-不敏感损失函数,构造固定对称边界粗糙ε-支持向量回归模型;利用固定非对称边界粗糙-不敏感损失函数,构造固定非对称边界粗糙-支持向量回归模型.通过引进拉格朗日函数和根据KKT条件,得到了粗糙-支持向量回归模型的对偶问题.作者根据Karush-Kuhn-Tucker (KKT)条件,通过构造拉格朗日泛函,得到了模型GN-KRR、 GN-SVR、 HGN-SVR的对偶问题.利用增广拉格朗日乘子法求解模型GN-KRR、GN-SVR的最优解,利用随机梯度下降法求解模型HGN-SVR的最优解.将上述三类模型应用于短期风速预报中,实验结果表明提出的噪声特性回归模型的有效性.更多还原

【Abstract】 Regression is an old topic in the domain of learning functions from a set of samples. Itprovides researchers and engineers with a powerful tool to extract hidden rules of data. Thetrained model is used to predict future events with the information of past or present events.Regression analysis is now successfully applied in nearly all fields of science and technology,including the social sciences, economics, finance, wind power prediction for grid operation.However, this domain is still attracting much attention from research and application domains.The main research contents of this work are as follows.The classical kernel ridge regression (KRR) and-Support vector regression (-SVR)techniques are aimed at discovering a linear or nonlinear structure hidden in original data.They make an assumption that the noise distribution is Gaussian. However, it is reported thatthe noise models in some real-world practical applications, such as wind power forecastingand direction of the direction-of-arrival of coherent electromagnetic waves impingingestimation problem, do not satisfy Gaussian distribution, but beta distribution, Laplaciandistribution, or other models. In these cases the current regression techniques are not optimal.Using Bayesian approach, we derive an optimal loss function for a general noise model. Wepropose a new framework of kernel ridge regression for the general noise mode (N KRR)and a novel-support vector regression model for the general noise model (N-SVR),respectively.The classical GN KRR and GN-SVRtechniques take an assumption that the noiseis Gaussian with zero mean and the same variance. However, it is found that the noise modelsin some practical applications satisfy Gaussian distribution with zero mean andheteroscedasticity, such as wind speed forecasting. In this case, the derived models are notoptimal. Using the optimal loss function for heteroscedastic noise model, propose a newframework of-SVRfor heteroscedastic noise model (HN-SVR).Two new rough-support vector regression models are proposed based on-supportvector regression, rough-support vector regression and rough set theory. Firstly, a roughboundary-insensitive tube is defined with fixed symmetrical boundary rough ε-insensitive loss function and the method of optimization and-support vector regressionmodel. Then we design a fixed symmetrical boundary rough-support vector regressionmodel (RFSM ε-SVR). Secondly, we extend the model to the case that asymmetrical lossfunction is considered. Finally, according to Karush-Kuhn-Tucker (KKT) conditions, wederive their dual problems by introducing the Lagrangian functional into rough-supportvector regression models.According to Karush-Kuhn-Tucker (KKT) conditions, we derive their dual problems byintroducing the Lagrangian functional into N-KRR, N-SVRand HN-SVR. The AugmentedLagrangian Multiplier (ALM) method is applied to solve the dual models of the modelsN-KRR and N-SVR. The Stochastic Gradient Descent (SGD) method is applied to solvethe model HGN-SVR. We test the proposed techniques to short-term wind speed prediction.Experimental results confirm the effectiveness of the proposed models.更多还原