# Ensemble Machine Learning for Monkeypox Transmission Time Series Forecasting
## 2 Materials and Methods
### Architecture of Stacking  
The stacking model architecture is designed to include six base learner models: adaptive boosting regression (Adaboost), gradient boosting regression (GBOOST), random forest regression, ordinary least square regression (OLS), least absolute shrinkage selection operator regression (LASSO), and ridge regression (RIDGE), as well as a random forest meta-model that combines the predictions of the base models. The level 0 models are the base models, while the level 1 model is the meta-model. As a result, the stacking ensemble approach consists of original (training) data, primary level models, primary level prediction, secondary level models, and final prediction. The fundamental stacking architecture is as follows:  
* Original data: The dataset is divided into training data and test data.
* Base models: Level-0 models include adaptive boosting regression (Adaboost), gradient boosting regression (GBOOST), random forest regression (RFR), ordinary least square regression (OLS), least absolute shrinkage selection operator regression (LASSO), and ridge regression (RIDGE). These models employ training data to provide assembled predictions (level 0).
* Level-0 Predictions: Each base model produces various level-0 predictions when it is activated on a set of training data.
* Meta Model: To aggregate the predictions of the base models as effectively as possible, the stacking model's architecture consists of a single meta-model that uses random forest regression. An alternate name for the meta-model is the level-1 model.
* Level-1 Prediction: The meta-model learns how to combine the predictions of the base models in the best way possible and is trained on the various predictions made by individual base models. For instance, data that was not used to train the base models is fed to the meta-model, predictions are made, and these predictions, along with the expected outputs, provide the input and output pairs of the training dataset that was used to fit the meta-model. See Figure 1 (The architecture of the proposed system).  
The proposed system makes use of stacking ensemble learning (SEL) techniques for time series forecasting. Experiments were conducted using COVID-19 datasets [95] as the training sets, while as the test sets for each of the datasets, we employed the monkey pox dataset. The extracted features that are used for the prediction are confirmed_cases, suspected_cases, hospitalized, travel_history_yes and travel_history_no. COVID-19 was employed as the training set, while monkey pox was used as the test set. Six models were used in the architecture of the proposed stacking ensemble learning system. The primary goal of this research is to predict monkey pox transmission rates on different continents around the world using stacking ensemble machine learning. This is achieved by stacking the six models (adaptive boosting regression, gradient boosting regression, random forest regression, regularized regression (the least absolute shrinkage selection operator, ridge regression), and ordinary least squares stacking ensemble learning methods).