Assessing the impact of climate variability on maize yields in the different regions of Ghana—A machine learning perspective

for this model given the dependent variable Y as: Y ¼ XK j¼1 Cj � 1Rj X ð Þ ð3Þ Where Y is the predicted value which is maize in this case, K is the number of terminal nodes or leaves in the decision tree, Cj is the constant value assigned to the jth leaf node, representing the predicted value of Y for that region, 1Rj X ð Þ represent an indicator function that takes the value 1 if the output vector X falls within the rectangular region Rj and 0 otherwise. Random forest. The ensemble learning method known as a random forest produces numer- ous decision trees during training and outputs the mean prediction (regression) or mode of the classes (classification) of the individual trees. Each tree in a random forest is trained using a different subset of the characteristics and a different portion of the training data. By averag- ing all the trees’ projections, the final prediction is produced. In this study, the Random Forest regression was considered. Mathematically, given an input vector X (Climate variables), the random forest model predicts the output ^y (maize yield) as: ^y ¼ 1 T XT t¼1 ft X ð Þ þ ε ð4Þ In this study, Eq 4 can be written as: Yt ¼ 1 T XT t¼1 ft x1;t ; x2;t ; x3;t ; x4;t ; x5;t � þ εt ð5Þ Where T represents the number of decision trees in the ensemble, ft is the function that maps the independent variables (climate variables) to the dependent variable Y(maize yield). Yt is the maize yield; x1,t = average temperature; x2,t = maximum temperature; x3,t = minimum tem-

perature; x4,t = precipitation; x5,t = CO2, εt is the error term or residual that represents the dif- ference between the predicted value and the actual value of the dependent variable and ft(x) is the prediction of the tth tree. In a random forest model, the function is a combination of multi- ple decision trees that each provide a prediction for the dependent variable. Support vector machine. A support vector machine is a type of supervised learning tech- nique that can be used for classification as well as regression. The SVM finds a hyperplane that optimally separates the input into various groups (in classification) or predicts the output val- ues (in regression). The hyperplane is chosen in such a way that the margin between the differ- ent classes is maximized. Mathematically, the hyperplane is defined by the equation: w � x þ b ¼ 0 ð6Þ Where w is the weight vector, x is the input vector, and b is the bias term. The prediction ^y for a new input vector x is given by: ^y ¼ sign w � x þ b ð Þ ð7Þ The "sign" refers to the sign of the output of the decision tree model. The output of a deci- sion tree is a discrete set of values based on the rules and splits that the tree has learned from the training data. The sign function is used to map these discrete values to either +1 or -1. The positive sign (+1) indicates that the sample is predicted to belong to the positive class (or have a positive target value), while the negative sign (-1) indicates that the sample is predicted to belong to the negative class (or have a negative target value).

Gradient boosting. Gradient Boosting is an ensemble technique that combines predictions generated by different weak models to produce a powerful forecasting model. The "gradient" in the term "gradient boosting" refers to the fact that the technique iteratively adds new models PLOS ONE Impact of climate variability on maize yields in Ghana PLOS ONE | https://doi.org/10.1371/journal.pone.0305762 June 25, 2024 8 / 24