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Table 6 Statistic indicators of the nineteen machine learning methods on ozone prediction for testing data with one-time-lagged ozone values

From: A comparison of machine learning methods for ozone pollution prediction

Model

RMSE \(\downarrow\)

MAE \(\downarrow\)

MAPE \(\downarrow\)

R-square \(\uparrow\)

J2 \(\downarrow\)

Time (min)

Linr

3.315/3.217

2.171/2.289

0.12/0.248

0.954/0.911

0.942

0.01

Linr_l2

3.315/3.22

2.173/2.293

0.121/0.249

0.954/0.911

0.944

0

Lasso

5.867/7.614

4.624/6.66

0.458/1.448

0.857/0.836

1.684

0.01

PLSR

4.987/6.558

3.849/5.405

0.213/0.63

0.897/0.629

1.729

0.01

GRP_Expo

2.685/4.166

1.797/3.086

0.097/0.414

0.97/0.86

2.407

7.79

GRP_DotProd

3.315/3.215

2.17/2.286

0.12/0.249

0.954/0.911

0.941

15.59

GRP_Matern

0.0/20.863

0.0/17.878

0.0/1.0

1.0/0.0

inf

21.61

SVR_linear

3.388/3.032

2.087/1.979

0.114/0.213

0.952/0.921

0.801

0.01

SVR_poly

3.903/5.351

2.678/3.778

0.222/0.624

0.937/0.801

1.88

5.37

SVR_rbf

3.097/3.189

1.998/2.277

0.12/0.298

0.96/0.914

1.06

6.04

SVR_sigmoid

4.501/4.079

3.352/3.241

0.215/0.521

0.916/0.86

0.821

6.92

MLP_1

3.315/3.199

2.174/2.234

0.126/0.232

0.954/0.912

0.931

0.28

MLP_2

15.514/21.707

12.668/19.503

1.287/4.222

0.0/0.0

1.958

1.09

RF

3.07/3.416

2.002/2.451

0.114/0.272

0.961/0.9

1.238

0.05

Bagging

1.381/3.731

0.863/2.756

0.046/0.281

0.992/0.881

7.299

0.16

GBoost

3.068/3.663

2.001/2.719

0.115/0.278

0.961/0.885

1.425

0.29

AdaBoost

4.908/6.396

3.942/5.485

0.326/0.985

0.912/0.844

1.698

0.12

HistGBoost

2.806/3.604

1.855/2.667

0.102/0.284

0.967/0.889

1.65

0.89

LightGBM

6.568/8.834

5.241/7.857

0.527/1.682

0.821/0.804

1.809

0.01

  1. The value before slash represents the loss value in the training dataset and the latter in the testing dataset (training/testing), the best performance is bold and the line colored grey means over-fitting. In addition, the \(\uparrow\) means the model is better when the value is larger, and the \(\downarrow\) means the model is better when the value is smaller