基于正则化核学习模型的时间序列多步预测的研究与应用

发布时间：2018-03-06 05:22

本文选题：正则化学习　切入点：高斯过程　出处：《兰州大学》2016年博士论文　论文类型：学位论文

【摘要】：统计学习涉及到大量为分析和理解数据而开发的模型,并与计算机科学尤其是机器学习相互融合、促进与发展。在这些模型中,使用正定核进行估计和学习的核方法变得越来越流行,已被广泛应用于诸如回归、预测和分类等问题。但是在将核方法模型应用于实际具体问题如预测、聚类时,还存在着不够灵活、主观选择等不足因素。此外,时间序列预测是根据过去及现在的有关信息,建立适当的模型挖掘事物内在规律及其趋势,从而为社会经济活动中的决策提供科学依据及技术支撑。尽管时间序列的研究早已开展,但由于现实中时间序列的多样性与复杂性,它一直是学术界研究的重点和难点课题。本论文就如何利用基于正则化框架下的核方法对时间序列的多步向前预测展开深入的研究。正则化框架理论为再生希尔伯特空间中的函数学习提供了一般意义的处理办法。基于实际问题的不同,所采取的损失函数也不同,最终获得的模型也不一样。本文第三章在正则化框架下采用二次损失函数,分别从频率论角度和贝叶斯视角进行考察,获得了正则单核学习模型(核岭回归(KRR)和高斯过程模型(GPR)),且就这两种模型的相同和差异进行了对比,并将所获得的正则单核学习模型应用于时间序列的多步迭代向前预测。为克服模型多步向前预测误差将逐步放大的不足与缺陷,本文第三章提出了基于数据驱动的经验小波分解(EWT)信号滤波方法对时间序列数据进行预处理,从而降低噪声数据对预测过程的干扰。另外,第三章构造了三个基于降噪的单核方法的多步预测模型,即两个多步向前预测的复合模型(EWT-KRR,EWT-GPR)和一个多步向前预测的组合模型。其中该组合预测模型是在现有的常见模型(ARIMA)和单核学习模型(LSSVM、SVM和ELM)对预处理之后的时间序列进行多步向前预测的基础上,利用高斯过程模型对预测值进行组合和优化,将确定性预测值转化为不确定预测信息,从而获得更为精确的预测值,同时提供预测的风险。在对所提模型训练过程中,本章提出了运用核距离学习来度量输入数据之间的相似度,同时,提出用耦合模拟退火算法选取模型的参数,以克服模型参数值容易陷入局部最优和稳定性不足的缺陷。在使用单核学习模型(包括上述的核岭回归和高斯过程模型)对时间序列进行预测时,需要为该模型预先选定核函数以进行相应的模型训练与验证。然而,选择合适的用于度量数据之间信息的单一核函数,并非易事。另外,在实际应用中,常会遇到执行多个任务的预测问题,而多次执行单一预测任务是解决问题的方法之一。然而,当预测任务之间存在着相互关联时,多任务同时学习并进行预测就显得非常有必要。鉴于此,本文第四章提出了频率论视角下的混合范数多核学习的预测模型,并形成了两种任务模型,即单一任务多核学习模型和多任务多核学习模型,继而产生了单一任务多核学习的时间序列多步向前迭代预测,以及多任务多核学习的多步向前同步预测。在所提出的多核学习模型中,首先将候选的若干个核函数进行线性组合,在混合范数的限制条件下进行核函数选取与模型训练,以便自动挑选出较为合适的特征表述。此外,在执行时间序列的多个预测值输出时,本章提出了采用布雷格曼距离指标度量两个时间序列之间距离来确定多个时间序列之间的相似性,并将此信息融入到了所提出的模型当中。高斯过程预测模型,虽然在时间序列预测的不确定性和风险方面表现出巨大的优势,但是在应用的过程中,异常数据的出现可能会极大地降低该模型的推理精度,而且核函数的类型和参数的选择亦影响着该模型的预测性能。另外,在实际应用中,时常会遇到执行多输出任务的预测问题。为此,本文第五章提出了贝叶斯视角下的推广的核学习方法预测模型。它是在多元线性模型的基础上,形成的关于函数的双曲线分布的理论模型。具有矩阵变量的广义双曲线分布的良好特性,同时融入了贝叶斯推理和核技巧。此预测模型克服了高斯过程因异常数据所导致的推理精度下降的不足,对带有异常数据的时间序列预测具有良好的稳健性。在上述所提到的核学习模型基础上,我们自然地延伸出两种特殊的模型,即单一输出的核学习回归模型和多输出的核学习回归模型。在应用于时间序列的多步向前预测时,单一输出的核学习模型产生迭代向前分布预测,而多输出的核学习模型则同时产生多步向前的预测分布,以获取时间序列多步向前预测的不确定性和风险。另外,在对所提模型训练过程中,本章提出了用耦合模拟退火算法最大化似然函数以获取最佳模型参数。而且,针对多输出的时间序列预测,本章提出了采用布雷格曼距离指标度量两个时间序列之间的距离进而确定时间序列之间的相关性,并将此作为先验信息融入所提出的模型。为了验证本文建立的模型的预测有效性并拓展其实际价值,本文将它们应用于中国华北地区某风场的风速预测领域中。实验结果表明,相对于传统预测模型,它们的预测性能与精度都有较大的提高。
[Abstract]:Statistical learning involves a large number of data for analyzing and understanding and the development of the model, and the computer science especially machine learning integration, promotion and development. In these models, the use of nuclear positive definite kernel estimation method and learning becomes more and more popular, has been widely used in such as regression, prediction and classification problems. But in the application of kernel method model to actual specific problems such as prediction, clustering, there is not flexible enough, such as lack of subjective choice factors. In addition, the time series prediction is based on past and present relevant information, establish the appropriate mining model inherent law and trend, so as to provide scientific basis and technical support for the social economy in the decision. Although research has long time series to carry out, but in reality because of the diversity and complexity of time series, it has been the focus of academic research and difficult Topic. This paper on how to use regularization kernel method under the framework of time series multi step ahead prediction in-depth study. Based on the framework of regularization theory as a function of regeneration in the Hilbert space learning approach provides a general sense of the same. Based on the practical problems, the loss function is also different. The final model is not the same. The third chapter in the regularization framework using two loss function, respectively from the perspective of frequency and Bayesian perspective, the regular single kernel learning model (kernel ridge regression (KRR) and Gauss model (GPR)), and compare these two kinds of model similarities and differences, and the iteration obtained regular single kernel learning model is applied to time series prediction model forward. In order to overcome the multi step ahead prediction error and the lack of lack of will gradually enlarge the depression, this paper The third chapter puts forward the experience of wavelet decomposition based on data driven (EWT) signal filtering method to preprocess the time-series data, thereby reducing the interference of noise prediction process data. In addition, the third chapter constructs three multi-step predictive model based on single kernel method for noise reduction, the composite model of two multi step ahead prediction the (EWT-KRR, EWT-GPR) model and a multi step ahead prediction. The combination forecasting model is common in the existing models (ARIMA) and single kernel learning model (LSSVM, SVM and ELM) based multi step ahead prediction of time series after pretreatment, using the Gauss model the predictive value of combination and optimization, the deterministic forecasting value into uncertainty forecast information, so as to obtain more accurate predicted at the same time provide the forecast risk. In the proposed model training process, this chapter puts forward the application Nuclear distance learning to measure the similarity between the input data, at the same time, the parameters of coupling with the simulated annealing algorithm selection model, in order to overcome the defects of the model parameter values is easy to fall into local optimum and stability. In the use of single kernel learning model (including the kernel ridge regression and Gauss model) to predict the time series the need for this model, pre selected kernel function for model training and verification. However, it is not easy to choose suitable for single kernel function, measurement data between information. In addition, in practice, often encounter prediction problem to perform multiple tasks, and repeatedly perform a single prediction task is one of the methods to solve the problem. However, when there is correlation between the prediction task, it is very necessary to study and predict multiple tasks at the same time. In view of this, the fourth chapter of this paper presents The frequency of prediction model of mixed norm multiple kernel learning perspective, and has formed two kinds of task model, namely single task and multi kernel learning model and multi task multi kernel learning model, and then created a time series prediction of multiple kernel learning single task and multi step ahead iteration, and multi task multi kernel learning step forward synchronous prediction. In the proposed multi kernel learning model, firstly, a plurality of candidate by linear combination of kernel function, kernel function selection and training model of constraints on mixed norm, in order to automatically select the appropriate features. In addition, the output value in multiple time series prediction is carried out, this chapter puts forward the index Bregman distance metric distance between two time series to determine the similarity between multiple time series, and the information will be integrated into the proposed model. The process of Gauss The prediction model, although uncertainty and risk prediction in time series shows a great advantage, but in the application process, the abnormal data can greatly reduce the reasoning accuracy of the model, and the type of kernel function and its parameters selection also affects the prediction performance of the model. In addition, in the actual in the application, often encounter prediction problem of implementing multiple output tasks. Therefore, the fifth chapter introduces the prediction model of generalized kernel learning methods from the perspective of Bias. It is based on a multivariate linear model, the formation of a hyperbolic function distribution of the theoretical model. The good properties of generalized hyperbolic distribution with matrix variable at the same time, with Bias reasoning and nuclear techniques. This model overcomes the shortcomings of decreased reasoning accuracy Gauss process caused by the abnormal data, with abnormal data Time series prediction robustness. In the above mentioned kernel learning model, we naturally extend two special models, namely single output kernel regression model and multi output kernel regression model. When applied to time series multi-step forward prediction, kernel learning model single output iterative forward distribution prediction, and multi output kernel learning model is also produced multi step ahead predictive distribution, to obtain the time series of multi step ahead predictive uncertainty and risk. In addition, in the training process of the proposed model, this chapter proposes using simulated annealing algorithm to maximize the likelihood of coupling function to obtain the optimal model parameters. Moreover, according to the time sequence of multi output prediction, this chapter puts forward the measure between two time series using Bregman distance index and then determine the time sequence of the The correlation between, and this as a priori information into the proposed model. In order to predict and verify the validity of this model and expand its actual value, this paper applies them to the wind in North China Chinese a wind field prediction field. The experimental results show that compared with the traditional prediction model, the prediction performance and the accuracy of them has been greatly improved.

【学位授予单位】：兰州大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O211.61

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