使用Matlab拟合竞价与曝光次数关系并评估模型性能

%20读取Excel数据%0Adata%20%3D%20xlsread%28'Impression%26%26CPC.xlsx',%20'Sheet1',%20'A2:B212'%29;%20%20假设数据在Sheet1中，曝光次数在第一列，竞价在第二列%0A%0Aimpressions%20%3D%20data%28%3A%2C%201%29;%20%20曝光次数数据%0Abid%20%3D%20data%28%3A%2C%202%29;%20%20竞价数据%0A%0A%20%20%20%20%2F%20%20找到空位置的索引%0Amissing_idx%20%3D%20isnan%28impressions%29%20%7C%20isnan%28bid%29;%0A%0A%20%20%20%20%2F%20%20将空位置填充为中位数%0Aimpressions%28missing_idx%29%20%3D%20median%28impressions%28~missing_idx%29%29;%0Abid%28missing_idx%29%20%3D%20median%28bid%28~missing_idx%29%29;%0A%0A%20%20%20%20%2F%20%20画出散点图%0Ascatter%28bid%2C%20impressions%29;%0Axlabel%28'竞价'%29;%0Aylabel%28'曝光次数'%29;%0Atitle%28'竞价与曝光次数关系散点图'%29;%0A%0A%20%20%20%20%2F%20%20定义模型函数%0Amodel%20%3D%20%40%28x%2C%20bid%29%20x%281%29%20*%20exp%28x%282%29%20*%20%28x%283%29%20*%20bid%20%2B%20x%284%29%29%29%20.%20sin%282pix%285%29bid%29;%0A%0A%20%20%20%20%2F%20%20定义误差函数（最小二乘法）%0AerrorFunc%20%3D%20%40%28x%29%20sum%28%28model%28x%2C%20bid%29%20-%20impressions%29.^2%29;%0A%0A%20%20%20%20%2F%20%20初始参数值%0Ax0%20%3D%20%5B1%2C%200.1%2C%200.1%2C%200.1%2C%200.1%5D;%0A%0A%20%20%20%20%2F%20%20使用fminsearch函数进行参数估计%0Ax%20%3D%20fminsearch%28errorFunc%2C%20x0%29;%0A%0A%20%20%20%20%2F%20%20输出估计的参数值%0Aa%20%3D%20x%281%29;%0Ab%20%3D%20x%282%29;%0Ac%20%3D%20x%283%29;%0Ad%20%3D%20x%284%29;%0AT%20%3D%20x%285%29;%0A%0A%20%20%20%20%2F%20%20打印参数值%0Afprintf%28'估计的参数值： '%29;%0Afprintf%28'a%20%3D%20%.2f '%2C%20a%29;%0Afprintf%28'b%20%3D%20%.2f '%2C%20b%29;%0Afprintf%28'c%20%3D%20%.2f '%2C%20c%29;%0Afprintf%28'd%20%3D%20%.2f '%2C%20d%29;%0Afprintf%28'T%20%3D%20%.2f '%2C%20T%29;%0A%0A%20%20%20%20%2F%20%20代入参数绘制曲线图（包括剔除填充数据后的散点图）%0Ax_vals%20%3D%20linspace%28min%28bid%29%2C%20max%28bid%29%2C%20100%29;%20%20%20%20生成横坐标数据%0Ay_vals%20%3D%20model%28x%2C%20x_vals%29;%20%20%20%20计算纵坐标数据%0A%0Afigure;%20%20%20%20创建新的图形窗口%0Ascatter%28bid%2C%20impressions%29;%20%20%20%20绘制原始数据的散点图%0Ahold%20on;%0Ascatter%28bid%28~missing_idx%29%2C%20impressions%28~missing_idx%29%2C%20'filled'%2C%20'MarkerFaceColor'%2C%20'r'%29;%20%20%20%20绘制剔除填充数据后的散点图%0Aplot%28x_vals%2C%20y_vals%2C%20'g--'%2C%20'LineWidth'%2C%202%29;%20%20%20%20绘制拟合曲线%0A%0Axlabel%28'竞价'%29;%0Aylabel%28'曝光次数'%29;%0Atitle%28'竞价与曝光次数关系散点图及拟合曲线'%29;%0Alegend%28'原始数据'%2C%20'剔除填充数据后的数据'%2C%20'拟合曲线'%29;%0A%0A%20%20%20%20%2F%20%20随机选取80%的数据作为训练集，20%的数据作为测试集%0An%20%3D%20size%28data%2C%201%29;%0Atrain_idx%20%3D%20randperm%28n%2C%20round%280.8*n%29%29;%20%20%20%20随机选取80%的索引作为训练集%0Atest_idx%20%3D%20setdiff%281%3An%2C%20train_idx%29;%20%20%20%20剩余的索引作为测试集%0A%0Atrain_data%20%3D%20data%28train_idx%2C%20%3A%29;%0Atest_data%20%3D%20data%28test_idx%2C%20%3A%29;%0A%0Atrain_impressions%20%3D%20train_data%28%3A%2C%201%29;%0Atrain_bid%20%3D%20train_data%28%3A%2C%202%29;%0A%0Atest_impressions%20%3D%20test_data%28%3A%2C%201%29;%0Atest_bid%20%3D%20test_data%28%3A%2C%202%29;%0A%0A%20%20%20%20%2F%20%20重新进行参数估计%0Atrain_missing_idx%20%3D%20isnan%28train_impressions%29%20%7C%20isnan%28train_bid%29;%0Atrain_impressions%28train_missing_idx%29%20%3D%20median%28train_impressions%28~train_missing_idx%29%29;%0Atrain_bid%28train_missing_idx%29%20%3D%20median%28train_bid%28~train_missing_idx%29%29;%0A%0Aoptions%20%3D%20optimset%28'MaxIter'%2C%201000%29;%20%20%20%20设置最大迭代次数为1000%0Ax%20%3D%20fminsearch%28%40%28x%29%20sum%28%28model%28x%2C%20train_bid%29%20-%20train_impressions%29.^2%29%2C%20x0%2C%20options%29;%0A%0A%20%20%20%20%2F%20%20使用训练集的参数进行预测%0Atrain_predictions%20%3D%20model%28x%2C%20train_bid%29;%0Atest_predictions%20%3D%20model%28x%2C%20test_bid%29;%0A%0A%20%20%20%20%2F%20%20计算训练集和测试集的均方误差%0Atrain_mse%20%3D%20sum%28%28train_predictions%20-%20train_impressions%29.^2%29%20%2F%20length%28train_impressions%29;%0Atest_mse%20%3D%20sum%28%28test_predictions%20-%20test_impressions%29.^2%29%20%2F%20length%28test_impressions%29;%0A%0Afprintf%28'训练集均方误差：%.2f '%2C%20train_mse%29;%0Afprintf%28'测试集均方误差：%.2f '%2C%20test_mse%2