使用MATLAB拟合竞价与曝光次数关系并评估模型性能

%E8%AF%BB%E5%8F%96Excel%E6%95%B0%E6%8D%AE data%20%3D%20xlsread('Impression%26%26CPC.xlsx',%20'Sheet1',%20'A2:B212');%20%E5%81%87%E8%AE%A2%E6%95%B0%E6%8D%AE%E5%9C%A8Sheet1%E4%B8%AD%EF%BC%8C%E6%98%BE%E5%85%89%E6%AC%A1%E6%95%B0%E5%9C%A8%E7%AC%AC%E4%B8%80%E5%88%97%EF%BC%8C%E7%AB%9E%E4%BB%B7%E5%9C%A8%E7%AC%AC%E4%BA%8C%E5%88%97%0A%0Aimpressions%20%3D%20data(:,%201);%20%E6%98%BE%E5%85%89%E6%AC%A1%E6%95%B0%E6%95%B0%E6%8D%AE%0Abid%20%3D%20data(:,%202);%20%E7%AB%9E%E4%BB%B7%E6%95%B0%E6%8D%AE%0A%0A%2F%2F%20%E6%89%BE%E5%88%B0%E7%A9%BA%E4%BD%8D%E7%BD%AE%E7%9A%84%E7%B4%A2%E5%BC%95%0Amissing_idx%20%3D%20isnan(impressions)%20%7C%20isnan(bid);%0A%0A%2F%2F%20%E5%B0%86%E7%A9%BA%E4%BD%8D%E7%BD%AE%E5%A1%AB%E5%85%85%E4%BA%86%E4%B8%AD%E4%BD%8D%E6%95%B0%0Aimpressions(missing_idx)%20%3D%20median(impressions(~missing_idx));%0Abid(missing_idx)%20%3D%20median(bid(~missing_idx));%0A%0A%2F%2F%20%E7%94%BB%E5%87%BA%E6%95%A3%E7%82%B9%E5%9B%BE%0Ascatter(bid,%20impressions);%0Axlabel('竞价');%0Aylabel('曝光次数');%0Atitle('竞价与曝光次数关系散点图');%0A%0A%2F%2F%20%E5%AE%9A%E4%B9%89%E6%A8%A1%E5%9E%8B%E5%87%BD%E6%95%B0%0Amodel%20%3D%20@(x,%20bid)%20x(1)%20*%20exp(x(2)%20*%20(x(3)%20*%20bid%20+%20x(4)))%20.%20sin(2pi*x(5)bid);%0A%0A%2F%2F%20%E5%AE%9A%E4%B9%89%E8%AF%AF%E5%8F%82%E5%87%BD%E6%95%B0%EF%BC%88%E6%9C%80%E5%B0%8F%E4%BA%8C%E7%A7%92%E6%B3%95%EF%BC%89%0AerrorFunc%20%3D%20@(x)%20sum((model(x,%20bid)%20-%20impressions).^2);%0A%0A%2F%2F%20%E5%88%9D%E5%A7%8B%E5%8F%82%E6%95%B0%E5%80%BC%0Ax0%20%3D%20[1,%200.1,%200.1,%200.1,%200.1];%0A%0A%2F%2F%20%E4%BD%BF%E7%94%A8fminsearch%E5%87%BD%E6%95%B0%E8%BF%9B%E8%A1%8C%E5%8F%82%E6%95%B0%E4%BC%B0%E8%AE%A1%0Ax%20%3D%20fminsearch(errorFunc,%20x0);%0A%0A%2F%2F%20%E8%BE%93%E5%87%BA%E4%BC%B0%E8%AE%A1%E7%9A%84%E5%8F%82%E6%95%B0%E5%80%BC%0Aa%20%3D%20x(1);%0Ab%20%3D%20x(2);%0Ac%20%3D%20x(3);%0Ad%20%3D%20x(4);%0AT%20%3D%20x(5);%0A%0A%2F%2F%20%E6%89%93%E5%8D%B0%E5%8F%82%E6%95%B0%E5%80%BC%0Afprintf('估计的参数值： ');%0Afprintf('a = %.2f ',%20a);%0Afprintf('b = %.2f ',%20b);%0Afprintf('c = %.2f ',%20c);%0Afprintf('d = %.2f ',%20d);%0Afprintf('T = %.2f ',%20T);%0A%0A%2F%2F%20%E4%BB%A3%E5%85%A5%E5%8F%82%E6%95%B0%E7%BB%98%E5%88%B6%E6%9B%B2%E7%BA%BF%E5%9B%BE%EF%BC%88%E5%9C%A8%E5%8C%85%E9%99%A4%E5%A1%AB%E5%85%85%E6%95%B0%E6%8D%AE%E5%90%8E%E7%9A%84%E6%95%A3%E7%82%B9%E5%9B%BE%EF%BC%89%0Ax_vals%20%3D%20linspace(min(bid),%20max(bid),%20100);%20%2F%2F%20%E7%94%9F%E6%88%90%E6%A8%AA%E5%8F%8D%E5%8F%8D%E6%A0%87%E6%95%B0%E6%8D%AE%0Ay_vals%20%3D%20model(x,%20x_vals);%20%2F%2F%20%E8BA%8F%E7%AE%97%E7%BA%B3%E5%8F%8D%E5%8F%8D%E6%A0%87%E6%95%B0%E6%8D%AE%0A%0Afigure;%20%2F%2F%20%E5%88%9B%E5%BB%BA%E6%96%B0%E7%9A%84%E5%9B%BE%E5%BD%A2%E7%AA%97%E5%8F%A3%0Ascatter(bid,%20impressions);%20%2F%2F%20%E7%BB%98%E5%88%B6%E5%8E%9F%E5%A7%8B%E6%95%B0%E6%8D%AE%E7%9A%84%E6%95%A3%E7%82%B9%E5%9B%BE%0Ahold%20on;%0Ascatter(bid(~missing_idx),%20impressions(~missing_idx),%20'filled',%20'MarkerFaceColor',%20'r');%20%2F%2F%20%E7%BB%98%E5%88%B6%E6%8C%81%E9%99%A4%E5%A1%AB%E5%85%85%E6%95%B0%E6%8D%AE%E5%90%8E%E7%9A%84%E6%95%A3%E7%82%B9%E5%9B%BE%0Aplot(x_vals,%20y_vals,%20'g--',%20'LineWidth',%202);%20%2F%2F%20%E7%BB%98%E5%88%B6%E6%8C%81%E5%90%88%E6%9B%B2%E7%BA%BF%0A%0Axlabel('竞价');%0Aylabel('曝光次数');%0Atitle('竞价与曝光次数关系散点图及拟合曲线');%0Alegend('原始数据',%20'剔除填充数据后的数据',%20'拟合曲线');%0A%0A%2F%2F%20%E9%9A%8F%E6%9C%BA%E9%80%89%E5%8F%9680%%E7%9A%84%E6%95%B0%E6%8D%AE%E4%BD%9C%E4%B8%BA%E8%AE%AD%E7%BB%83%E9%9B%86%EF%BC%8C20%%E7%9A%84%E6%95%B0%E6%8D%AE%E4%BD%9C%E4%B8%BA%E6%B5%8B%E8%AF%95%E9%9B%86%0An%20%3D%20size(data,%201);%0Atrain_idx%20%3D%20randperm(n,%20round(0.8n));%20%2F%2F%20%E9%9A%8F%E6%9C%BA%E9%80%89%E5%8F%9680%%E7%9A%84%E7%B4%A2%E5%BC%95%E4%BD%9C%E4%B8%BA%E8%AE%AD%E7%BB%83%E9%9B%86%0Atest_idx%20%3D%20setdiff(1:n,%20train_idx);%20%2F%2F%20%E5%89%A9%E4%BD%8F%E7%9A%84%E7%B4%A2%E5%BC%95%E4%BD%9C%E4%B8%BA%E6%B5%8B%E8%AF%95%E9%9B%86%0A%0Atrain_data%20%3D%20data(train_idx,%20:);%0Atest_data%20%3D%20data(test_idx,%20:);%0A%0Atrain_impressions%20%3D%20train_data(:,%201);%0Atrain_bid%20%3D%20train_data(:,%202);%0A%0Atest_impressions%20%3D%20test_data(:,%201);%0Atest_bid%20%3D%20test_data(:,%202);%0A%0A%2F%2F%20%E9%87%8D%E6%96%B0%E8%BF%9B%E8%A1%8C%E5%8F%82%E6%95%B0%E4%BC%B0%E8%AE%A1%0Atrain_missing_idx%20%3D%20isnan(train_impressions)%20%7C%20isnan(train_bid);%0Atrain_impressions(train_missing_idx)%20%3D%20median(train_impressions(~train_missing_idx));%0Atrain_bid(train_missing_idx)%20%3D%20median(train_bid(~train_missing_idx));%0A%0Ax%20%3D%20fminsearch(@(x)%20sum((model(x,%20train_bid)%20-%20train_impressions).^2),%20x0);%0A%0A%2F%2F%20%E4%BD%BF%E7%94%A8%E8%AE%AD%E7%BB%83%E9%9B%86%E7%9A%84%E5%8F%82%E6%95%B0%E8%BF%9B%E8%A1%8C%E9%A2%84%E6%B5%8B%0Atrain_predictions%20%3D%20model(x,%20train_bid);%0Atest_predictions%20%3D%20model(x,%20test_bid);%0A%0A%2F%2F%20%E8BA%8F%E7%AE%97%E8%AE%AD%E7%BB%83%E9%9B%86%E5%92%8C%E6%B5%8B%E8%AF%95%E9%9B%86%E7%9A%84%E5%9D%87%E6%96%B9%E8%AF%AF%E5%B7%AE%0Atrain_mse%20%3D%20sum((train_predictions%20-%20train_impressions).^2)%20/%20length(train_impressions);%0Atest_mse%20%3D%20sum((test_predictions%20-%20test_impressions).^2)%20/%20length(test_impressions);%0A%0Afprintf('训练集均方误差：%.2f ',%20train_mse);%0Afprintf('测试集均方误差：%.2f ',%20test_mse);%0A