-
摘要:
将遍历搜索法引入带空间结构的人工神经网络模型，提出一种新的模型估计和空间数据样本外预测方法。该方法基于人工神经网络，结合空间自回归模型思想，在网络模型中引入空间滞后项来考虑变量的空间效应，提出使用遍历搜寻最优解的方式替代传统极大似然法进行空间自回归系数估计和建模。结合样本外数据和空间结构，扩展空间权重矩阵并代入所提模型进行样本外预测，充分发挥了人工神经网络模型泛化能力强的特点。仿真分析指出：在合理考虑空间效应的情况下，所提模型的预测效果较普通人工神经网络有显著提升；而且当空间变量间存在非线性关系时，所提模型的预测精度同样优于空间自回归模型。
Abstract:In this paper, grid-search method is introduced into artificial neural network model incorporating spatial structure, which is a new method of model estimation, to do out-of-sample prediction. This method is based on the artificial neural network algorithm, is combined with the idea of spatial autoregressive model, and introduces the spatial lag term in the model to consider the spatial effect of variables. Meanwhile, instead of maximum likelihood method, it uses the method of grid-search for the optimal solution to estimate and model the spatial autoregressive coefficient. Then, combined with the out-of-sample data and spatial structure, the spatial matrix is extended and the new model is brought in to make out-of-sample prediction, which gives full play to the strong generalization ability of the neural network model. Finally, the simulation results show that, compared with ordinary artificial neural network, the prediction effect of the new model is significantly improved when the spatial effect is considered reasonably, and the prediction accuracy is better than that of the spatial autoregressive model when there is a nonlinear relationship between spatial variables.
-
图 1 带空间结构的人工神经网络流程图
Figure 1. Flow chart of artificial neural network incorporating spatial structure
图 4 带空间结构的人工神经网络估计值与期望值之间的关系(y1和y2)
Figure 4. Relationship between estimated value and expected value applying artificial neural network incorporating spatial structure (y1 and y2)
表 1 因变量莫兰检验结果
Table 1. Moran's I test results of dependent variable
自变量 Moran’s I p y1 0.088 < 2×10-16 y2 0.093 < 2×10-16 
下载: 导出CSV
表 2 不同
Table 2. Comparison of model prediction error under different
MSE y1 y2 0 8.48 31.15 0.49 0.81* 14.61 0.61 1.12 13.87* 注：“*”为同组数据预测误差最小的模型。
下载: 导出CSV
表 3 不同模型的预测误差
Table 3. Prediction error of different model
模型 MSE y1 y2 普通线性回归模型 8.00 124.92 空间自回归模型 0.14*( 
110.69( 
普通人工神经网络模型 8.50 22.95 带空间结构的人工神经网络模型 1.39( 
10.70*( 
注：“*”为同组数据预测误差最小的模型。
下载: 导出CSV
表 4 带空间结构的人工神经网络(SNN)模型与普通人工神经网络的仿真实验结果
Table 4. Simulation results comparison of artificial neural network incorporating spatial structure andclassic neural network
方法 样本数(模型) MSE ρ=0.1 ρ=0.3 ρ=0.5 y1(线性生成法) 40(SNN) 2.238(0.07) 2.035(0.27) 2.060(0.51) 40(NN) 2.821 2.844 2.762 80(SNN) 1.659(0.22) 1.474(0.34) 1.428(0.57) 80(NN) 2.949 2.844 2.762 400(SNN) 1.121(0.13) 0.918(0.31) 0.711(0.54) 400(NN) 2.138 2.283 2.107 y2(非线性生成法) 40(SNN) 57.834(0.57) 64.127(0.84) 50.593(0.82) 40(NN) 84.415 85.857 69.412 80(SNN) 22.328(0.26) 22.857(0.40) 21.374(0.64) 80(NN) 30.272 29.732 31.566 400(SNN) 18.466(0.14) 14.030(0.38) 11.859(0.58) 400(NN) 23.753 20.758 20.801 注：括号内数值为ρ的估计量。
下载: 导出CSV
表 5 自变量名称及分类
Table 5. Name and classification of independent variables
类别 变量 经济发展 GDP 实际GDP增速 人均GDP 地方一般公共预算支出 地方一般公共预算-科学和技术 总耗电量 产业结构 规模以上工业企业数量 规模以上工业企业工业总产值 第一产业增加值占GDP的比重 第二产业增加值占GDP的比重 第三产业增加值占GDP的比重 人口结构 人口 人口密度 一产从业人员比例 二产从业人员比例 三产从业人员比例 城市建成面积 城市绿地面积 房地产开发企业投资完成金额 城市化 固定资产投资完成额 公共汽车数量 出租车数量 城市液化石油气总供气量 城市液化石油气国内天然气供应总量
下载: 导出CSV
-
[1] ANSELIN L.Spatial econometrics:Methods and models[M].Berlin:Springer, 1988. [2] CLIFF A D, ORD J K.Spatial autocorrelation[M].London:Pion, 1981. [3] QU X, LEE L F.Estimating a spatial autoregressive model with an endogenous spatial weight matrix[J].Journal of Econometrics, 2015, 184(2):209-232. doi: 10.1016/j.jeconom.2014.08.008 [4] 王惠文, 顾杰, 黄文阳, 等.京津冀地区大气严重污染的主要影响因素分析[J].数学的实践与认识, 2017, 47(20):86-91. https://www.cnki.com.cn/Article/CJFDTOTAL-SSJS201720011.htmWANG H W, GU J, HUANG W Y, et al.The study on main influence factors of the serious atmosphere pollution in Beijing-Tianjin-Hebei region[J].Mathematics in Practice and Theory, 2017, 47(20):86-91(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-SSJS201720011.htm [5] 孙坚强, 缪旖璇, 张世泽.粤港澳大湾区的科技创新与经济增长[J].华南理工大学学报(社会科学版), 2019, 21(3):7-16. https://www.cnki.com.cn/Article/CJFDTOTAL-HNLS201903001.htmSUN J Q, MIAO Y X, ZHANG S Z.Technology innovation and economic growth of Guangdong-Hong Kong-Macao Greater Bay Area[J].Journal of South China University of Technolog(Social Science Edition), 2019, 21(3):7-16(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HNLS201903001.htm [6] HAYKIN S.Neural networks:A comprehensive foundation[J].Neural Networks A Comprehensive Foundation, 1994, 31(5):71-80. doi: 10.1145/541500 [7] RUMELHART D E, HINTON G E, WILLIAMS R J.Learning representations by back propagating errors[J].Nature, 1986, 323:533-536. doi: 10.1038/323533a0 [8] 朱大奇.人工神经网络研究现状及其展望[J].江南大学学报(自然科学版), 2004, 3(1):103-110. doi: 10.3969/j.issn.1671-7147.2004.01.027ZHU D Q.The research progress and prospects of artificial neural netwoks[J].Journal of Southern Yangtze University(Nature Science Edition), 2004, 3(1):103-110(in Chinese). doi: 10.3969/j.issn.1671-7147.2004.01.027 [9] MANN S, BENWELL G L.The integration of ecological, neural and spatial modeling for monitoring and prediction for semi-arid landscapes[J].Computers and Geosciences, 1996, 22(9):1003-1012. doi: 10.1016/S0098-3004(96)00038-6 [10] LUK K C, BALL J E, SHARMA A.A study of optimal model lag and spatial inputs to artificial neural network for rainfall forecasting[J].Journal of Hydrology, 2000, 227(1):56-65. [11] PATRICK L M, CHRISTOPHER K W.Bayesian recurrent neural network models for forecasting and quantifying uncertainty in spatial-temporal data[J].Entropy, 2019, 21(2):184. doi: 10.3390/e21020184 [12] 池娇, 焦利民.住宅房地产价格评估的空间型BP神经网络模型[J].地理空间信息, 2017, 15(2):86-90. doi: 10.3969/j.issn.1672-4623.2017.02.027CHI J, JIAO L M.Spatial BP neural networks in evaluation of residential real estate price[J].Geospatial Information, 2017, 15(2):86-90(in Chinese). doi: 10.3969/j.issn.1672-4623.2017.02.027 [13] WANG W, ZHAO S, JIAO L, et al.Estimation of PM 2.5 concentrations in China using a spatial back propagation neural network[J].Scientific Report, 2017, 9(1):1-10. [14] ORD K.Estimation methods for models of spatial interaction[J].Journal of the American Statal Association, 1975, 70(349):120-126. doi: 10.1080/01621459.1975.10480272 [15] GOULARD M, LAURENT T, THOMAS-AGNAN C.About predictions in spatial autoregressive models:Optimal and almost optimal strategies[J].Spatial Economic Analysis, 2017, 12(2-3):304-325. doi: 10.1080/17421772.2017.1300679 [16] 刘会.当代中国农村土地流转的工业条件研究-基于全局莫兰指数与空间计量模型的研究[J].财经理论研究, 2017(6):23-32. https://www.cnki.com.cn/Article/CJFDTOTAL-NCXB201706003.htmLIU H.An empirical analysis on the industry condition rural land transfer in contemporary China-with the Moran's I test and methods of SEM and SAR[J].Journal of Financial and Economic Theory, 2017(6):23-32(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-NCXB201706003.htm [17] 朱庆生, 周冬冬, 黄伟.BP神经网络样本数据预处理应用研究[J].世界科技研究与发展, 2012, 34(4):624-626. doi: 10.3969/j.issn.1006-6055.2012.04.024ZHU Q S, ZHOU D D, HUANG W.Application research of preprocess in BP neural network sample data[J].World Sci-Tech Research and Development, 2012, 34(4):624-626(in Chinese). doi: 10.3969/j.issn.1006-6055.2012.04.024 -
下载:
点击查看大图
计量
- 文章访问数: 681
- HTML全文浏览量: 109
- PDF下载量: 327
- 被引次数: 0
