基于马尔科夫模型的回归研究及其应用  

Regression Research and Application Based on Markov Model

作　　者：何成刚[1,2] 丁宏强 陈思宝[1,2] 罗斌[1] 王家鑫 HE Cheng-gang;Chris HQDING;CHEN Si-bao;LUO Bin;WANG Jia-xin(School of Computer Science and Technology,Anhui University,Hefei 230031,China;Key Lab of Intelligent Computing and Signal Processing of Ministry of Education,Hefei 230039,China;Department of Computer Science and Engineering,University of Texas at Arlington,Arlington TX76019,USA)

机构地区：[1]安徽大学计算机科学与技术学院,安徽合肥230031 [2]安徽大学计算智能与信号处理教育部重点实验室,安徽合肥230039 [3]美国德州大学阿灵顿分校计算机科学与工程系,美国阿灵顿TX76019

出　　处：《计算机技术与发展》2022年第4期8-14,38,共8页Computer Technology and Development

基　　金：国家自然科学基金资助项目(61976004,61572030,61671018);国家自然科学基金面上项目(61673020);国际(地区)合作与交流重点项目(61860206004);安徽大学科学研究建设经费(Y040418282)。

摘　　要：在国内外回归分析方法的研究中,神经网络、支持向量机等传统方法被广泛使用,但是由于其计算量太大而且对计算模型和数据的准确性要求很高,在实际的应用中局限性强。为了解决这些难题,对Markov理论和相关模型进行了深入的研究。首先将多元回归和Markov模型进行结合,提出了基于多元回归的Markov模型,解决了转移矩阵难以确定的问题,并将其应用于国民收入预测中,减少了运算复杂度并且解决了实际应用中的局限性,提高了模型的鲁棒性。同时将Markov模型和Regime Switching Model进行结合,提出了基于Markov-switch的回归算法,使用状态转移矩阵来处理数据,实验结果表明该算法可以有效地提高预测效率和大幅度减少运算时间,并且在UCI数据集上进行验证和传统方法相比,标准差减少72.72%、相关系数提高2%、运行时间减少了50%。In the research of regression method at home and abroad,traditional methods such as neural network and support vector machine are widely used.However,due to its large amount of calculation and high requirements on the accuracy of the calculation model and data,it has strong limitations in application.Combined multiple regression with Markov model,we propose a Markov model based on multiple regression,which solves the problem that the transfer matrix is difficult to determine,and apply it to national income prediction,which reduces the computational complexity and solves the limitation in application,and improves the robustness of the model.At the same time,the Markov model and Regime Switching Model are combined,and a regression algorithm based on Markov-switch is proposed.The experiment shows that the proposed algorithm can effectively improve the prediction efficiency and greatly shorten the calculation time.It is verified on the UCI data set and compared with traditional methods,the standard deviation is reduced by 72.72%,the correlation coefficient is increased by 2%,and the running time is reduced by 50%.

关 键 词：MARKOV模型 多元回归 Markov-switch回归算法 减少运算量 缩短运算时间 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]