## 6 Ensemble Approach  
In machine learning, ensemble techniques combine several models to enhance generalization, robustness, and predictive accuracy. By combining the predictions of several models, these techniques take advantage of the wisdom of crowds and frequently provide better outcomes than any one model could on its own. The following are some salient features of ensemble approaches:  
* Diversity: Having a varied set of base models helps ensemble models perform better. Ensemble approaches can capture a broader range of patterns and lower the danger of overfitting by utilizing various algorithms, feature subsets, or training data. * Voting: In ensemble approaches like majority voting or averaging, each base model's forecast is weighted equally. This simple method can be surprisingly effective, especially when the basis models are diverse and exhibit uncorrelated mistakes. * Two well-liked ensemble approaches are used, namely boosting and bagging (also known as bootstrap aggregating): To lower variance, bagging creates several modelsusing arbitrary portions of the training data and averages their predictions. Boosting enhances performance by iteratively training models with the extra weight assigned to incorrectly identified samples. * Stacking: Using a meta-model, stacking, known as meta-learning, aggregates predictions from several base models. Stacking trains is a process known as a meta-model which is used to figure out how to optimally combine the forecasts of base models, as opposed to just average or voting. Stacking frequently results in better performance and can capture more intricate patterns. To summarize, ensemble techniques are effective machine learning tools that can considerably increase model performance and robustness. Ensemble methods provide a viable answer to various prediction challenges across several domains by harnessing the aggregate expertise of multiple models. The experiment involves logistic regression and decision tree models, two standard machine learning techniques for categorization applications. While logistic regression delivers probabilistic predictions and is interpretable, decision trees are more flexible and may capture nonlinear relationships in data. Combining these two algorithms into an ensemble technique can allow for the use of each model's capabilities, improving the overall prediction performance and model durability. The ensemble approach combines logistic regression and decision tree predictions with a majority vote scheme. If both models forecast the same class, the ensemble prediction will match. If the two models disagree, a majority vote decides the ensemble prediction. By combining logistic regression with decision tree predictions, the ensemble may improve the generalization performance and capture a more thorough representation of the underlying data patterns. The logistic regression and decision tree ensemble technique provide a powerful and versatile solution for classification tasks, using the benefits of both methods to improve the predicted accuracy and model interpretability. Let us denote the prediction of logistic regression as \(Clr\) and the prediction of decision trees as \(Edt\). In this ensemble approach, logistic regression outputs probabilities for binary classification, typically between 0 and 1. We can threshold these probabilities to obtain binary predictions (0 or 1). Decision trees directly provide binary predictions based on the features. The ensemble combines the predictions of logistic regression and decision trees using a majority voting scheme. Specifically, if logistic regression and decision trees predict the same class, the ensemble prediction is that class. If logistic regression and decision trees predict different classes, the ensemble prediction is determined by a majority vote among these two predictions. Mathematically, the ensemble prediction \(GEn\) can be defined as  
\[GEn=MV(Clr,Edt) \tag{12}\]  
where \(Clr\) is the prediction of logistic regression, \(Edt\) is the prediction of decision trees, and \(MV(.