Relation between Pearson correlation coefficient and ML models

In linear regression, selecting the most relevant independent variables based on their correlation coefficient with the dependent variable can be a useful approach. However, it's important to note that correlation coefficient is only one metric for feature selection, and other factors such as domain knowledge, feature importance, and multicollinearity should also be taken into account.

In DNN regression and XGBoost, the approach to feature selection is often different. These algorithms can handle large numbers of features, so it's common to include all available features in the model and let the algorithm determine which features are most important for prediction.

In DNN regression, feature selection can be done using techniques such as regularization and dropout, which help to prevent overfitting and improve the generalization performance of the model. Regularization involves adding a penalty term to the loss function that encourages the weights of less important features to be closer to zero, while dropout randomly drops out units from the neural network during training to prevent over-reliance on any single feature.

In XGBoost, feature selection can be done using techniques such as feature importance and pruning. Feature importance is a metric that assigns a score to each feature based on its contribution to the overall predictive performance of the model. Pruning involves removing features that do not improve the performance of the model, based on a threshold determined by the user.

Overall, while correlation coefficient can be a useful metric for feature selection in linear regression, it may not be the best approach in other types of regression models such as DNN regression and XGBoost. In these cases, other techniques such as regularization, dropout, feature importance, and pruning may be more appropriate for selecting relevant features and improving the performance of the model.