基于贝叶斯线性回归bayesian时间序列预测，bayes时间序列预测，MATLAB代码 评价指标包括:R2、MAE、MSE

%% 清空环境变量 warning off % 关闭报警信息 close all % 关闭开启的图窗 clear % 清空变量 clc % 清空命令行 %% 导入数据 f = xlsread('windspeed.xls','Sheet1','B2:B1001'); [x,y]=data_process(f,12); %步长为12 n=size(x,1); m=round(n*0.7); %前70%训练，对最后30%进行预测 P_train=x(1:m,:)'; T_train=y(1:m,:)'; P_test=x(m+1:end,:)'; T_test=y(m+1:end,:)'; M = size(P_train,2); % 测试集—200个 N = size(T_test,2); outdim=1; %输出的维度 f_ = size(P_train, 1); % 输入特征维度 %% 数据归一化 [p_train, ps_input] = mapminmax(P_train, 0, 1); p_test = mapminmax('apply', P_test, ps_input); [t_train, ps_output] = mapminmax(T_train, 0, 1); t_test = mapminmax('apply', T_test, ps_output); %% 矩阵转置 p_train = p_train'; p_test = p_test'; t_train = t_train'; t_test = t_test'; %% 设置参数 sigma_squared = 0.01; % 输出的协方差的方差 eta_sqaured = 0.02; % beta的协方差的方差 %% 训练模型 model = bayesian_regression(p_train, t_train, sigma_squared, eta_sqaured); %% 仿真测试 t_sim1 = sim_bayes(model, p_train); t_sim2 = sim_bayes(model, p_test ); %% 数据反归一化 T_sim1 = mapminmax('reverse', t_sim1', ps_output); T_sim2 = mapminmax('reverse', t_sim2', ps_output); % T_sim1=double(T_sim1); % T_sim2=double(T_sim2); %% 均方根误差 error1 = sqrt(sum((T_sim1 - T_train).^2) ./ M); error2 = sqrt(sum((T_sim2 - T_test ).^2) ./ N); %% R2 R1 = 1 - norm(T_train - T_sim1)^2 / norm(T_train - mean(T_train))^2; R2 = 1 - norm(T_test - T_sim2)^2 / norm(T_test - mean(T_test ))^2; %% MAE mae1 = sum(abs(T_sim1 - T_train)) ./ M ; mae2 = sum(abs(T_sim2 - T_test )) ./ N ; %% 绘图 %% 测试集结果 figure; plotregression(T_test,T_sim2,['回归图']); figure; ploterrhist(T_test-T_sim2,['误差直方图']); %% 均方根误差 RMSE error1 = sqrt(sum((T_sim1 - T_train).^2)./M); error2 = sqrt(sum((T_test - T_sim2).^2)./N); %% %决定系数 R1 = 1 - norm(T_train - T_sim1)^2 / norm(T_train - mean(T_train))^2; R2 = 1 - norm(T_test - T_sim2)^2 / norm(T_test - mean(T_test ))^2; %% %均方误差 MSE mse1 = sum((T_sim1 - T_train).^2)./M; mse2 = sum((T_sim2 - T_test).^2)./N; %% %RPD 剩余预测残差 SE1=std(T_sim1-T_train); RPD1=std(T_train)/SE1; SE=std(T_sim2-T_test); RPD2=std(T_test)/SE; %% 平均绝对误差MAE MAE1 = mean(abs(T_train - T_sim1)); MAE2 = mean(abs(T_test - T_sim2)); %% 平均绝对百分比误差MAPE MAPE1 = mean(abs((T_train - T_sim1)./T_train)); MAPE2 = mean(abs((T_test - T_sim2)./T_test)); %% 训练集绘图 figure %plot(1:M,T_train,'r-*',1:M,T_sim1,'b-o','LineWidth',1) plot(1:M,T_train,'r-',1:M,T_sim1,'b-','LineWidth',1.5) legend('真实值','Bayes预测值') xlabel('预测样本') ylabel('预测结果') string={'训练集预测结果对比';['(R^2 =' num2str(R1) ' RMSE= ' num2str(error1) ' MSE= ' num2str(mse1) ' RPD= ' num2str(RPD1) ')' ]}; title(string) %% 预测集绘图 figure plot(1:N,T_test,'r-',1:N,T_sim2,'b-','LineWidth',1.5) legend('真实值','Bayes预测值') xlabel('预测样本') ylabel('预测结果') string={'测试集预测结果对比';['(R^2 =' num2str(R2) ' RMSE= ' num2str(error2) ' MSE= ' num2str(mse2) ' RPD= ' num2str(RPD2) ')']}; title(string) %% 测试集误差图 figure ERROR3=T_test-T_sim2; plot(T_test-T_sim2,'b-*','LineWidth',1.5) xlabel('测试集样本编号') ylabel('预测误差') title('测试集预测误差') grid on; legend('Bayes预测输出误差') %% 绘制线性拟合图 %% 训练集拟合效果图 figure plot(T_train,T_sim1,'*r'); xlabel('真实值') ylabel('预测值') string = {'训练集效果图';['R^2_c=' num2str(R1) ' RMSEC=' num2str(error1) ]}; title(string) hold on ;h=lsline; set(h,'LineWidth',1,'LineStyle','-','Color',[1 0 1]) %% 预测集拟合效果图 figure plot(T_test,T_sim2,'ob'); xlabel('真实值') ylabel('预测值') string1 = {'测试集效果图';['R^2_p=' num2str(R2) ' RMSEP=' num2str(error2) ]}; title(string1) hold on ;h=lsline(); set(h,'LineWidth',1,'LineStyle','-','Color',[1 0 1]) %% 求平均 R3=(R1+R2)./2; error3=(error1+error2)./2; %% 总数据线性预测拟合图 tsim=[T_sim1,T_sim2]'; S=[T_train,T_test]'; figure plot(S,tsim,'ob'); xlabel('真实值') ylabel('预测值') string1 = {'所有样本拟合预测图';['R^2_p=' num2str(R3) ' RMSEP=' num2str(error3) ]}; title(string1) hold on ;h=lsline(); set(h,'LineWidth',1,'LineStyle','-','Color',[1 0 1]) %% 打印出评价指标 disp(['-----------------------误差计算--------------------------']) disp(['评价结果如下所示：']) disp(['平均绝对误差MAE为：',num2str(MAE2)]) disp(['均方误差MSE为： ',num2str(mse2)]) disp(['均方根误差RMSEP为： ',num2str(error2)]) disp(['决定系数R^2为： ',num2str(R2)]) disp(['剩余预测残差RPD为： ',num2str(RPD2)]) disp(['平均绝对百分比误差MAPE为： ',num2str(MAPE2)]) grid