Table 2 The description of the machine learning methods adopted in this paper, \(({\textbf{X}}, {\textbf{Y}})\) means the dataset in pair; \(\beta\) the parameters of the models, \(\lambda\) the hyperparameter
From: A comparison of machine learning methods for ozone pollution prediction
Model | Formulation | Kernel |
|---|---|---|
Linear Regression | \({\textbf{Y}} = {\textbf{X}} \beta\) | None |
Linear Regression with l2 regularizer | \({\textbf{Y}} = {\textbf{X}} \beta + \lambda \Vert \beta \Vert ^2\) | None |
Lasso | \({\textbf{Y}} = {\textbf{X}} \beta + \lambda \Vert \beta \Vert ^1\) | None |
Partial Linear Least Square Regression | Regression of decomposed \({\textbf{Y}}\) and \({\textbf{X}}\) | None |
GRP (Exponential kernel) | \({\textbf{Y}} \sim {\mathcal {N}} ({\textbf{X}} \beta , \Sigma )\) | Eq. 10 |
GRP (DotProd kernel) | \({\textbf{Y}} \sim {\mathcal {N}} ({\textbf{X}} \beta , \Sigma )\) | Eq. 13 |
GRP (Matérn kernel) | \({\textbf{Y}} \sim {\mathcal {N}} ({\textbf{X}} \beta , \Sigma )\) | Eq. 12 |
SVR (linear kernel) | Eq. 3 | Eq. 14 |
SVR (Polynomial kernel) | Eq. 3 | Eq. 15 |
SVR (Radial basis kernel) | Eq. 3 | Eq. 11 |
SVR (Sigmoid kenerl) | Eq. 3 | Eq. 16 |
MLP_1 | Layer shape [10, 5, 1] | None |
MLP_2 | Layer shape [10, 5, 2, 1] | None |
RF | Depth 7, Criterion: squared error | None |
Bagging | 10 decision trees as base learner | None |
GBoost | Criterion: Friedman MSE | None |
AdaBoost | 50 decision trees as base learner | None |
HistGBoost | Criterion: squared error | None |
LightGBM | 31 leaves and Criterion: squared error | None |