## 2 ML Methodologies
### Supervised Learning
#### 2.1.2 Regression
We also provide applications and publication references for validation. Table 7 provides a concise overview of various nonlinear regression algorithms. Nonlinear regression is a powerful approach for modeling relationships between variables when the underlying patterns are not strictly linear. These algorithms are essential tools in data analysis and machine learning, enabling the modeling of complex, nonlinear associations in various applications. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Category** & **Algorithm** & **Description** & **Applications** & **Ref.** \\ \hline Regression and water resources management & Ordinary least squares (OLS) & Minimizes the sum of squared differences between observed and predicted values. & River flow forecasting, reservoir management. & [84] \\ \hline Hydrological modeling and prediction & Ridge regression & Adds L2 regularization to OLS, helps prevent overfitting by adding a penalty for large coefficients. & Groundwater level prediction, water quality modeling. & [85] \\ \hline Water quality analysis and pollution tracking & Lasso regression & Adds L1 regularization to OLS, encourages sparse coefficient selection by penalizing nonessential features. & Streamflow modeling, feature selection in hydrology. & [86] \\ \hline Hydrological modeling and data fusion & Elastic net regression & Combines L1 (lasso) and L2 (ridge) regularization to balance feature selection and coefficient shrinkage. & Hydrological modeling, water resource Optimization. & [87] \\ \hline Water resource allocation and management & Bayesian linear regression & Uses Bayesian framework to estimate model parameters and uncertainty in predictions. & Flood risk assessment, climate change impact modeling. & [88] \\ \hline Environmental data analysis and modeling & Stepwise regression & Iteratively adds or removes predictors to build the best-fitting model. & Water resource allocation, reservoir operation optimization. & [89] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Linear regression algorithms for water resources management. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Algorithm** & **Ref.** & **Description** \\ \hline Polynomial regression & [90] & Fits a polynomial function to the data by including higher-order terms of the input variables. It can capture nonlinear relationships by introducing polynomial features, allowing for more flexible curve fitting. & Find a polynomial function to the data by including higher-order terms of the input variables. It can capture nonlinear relationships by introducing polynomial features, allowing for more flexible curve fitting. & [85] \\ \hline Support vector regression (SVR) & [91] & Uses support vector machines to perform regression. It aims to find a nonlinear function that best fits the data by mapping the input variables to a higher-dimensional feature space. SVR uses a loss function that allows for a certain tolerance or margin around the predicted values, providing flexibility to capture nonlinear patterns. & [86] \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Nonlinear regression algorithms.