## 3 Methodology
### CatBoost  
CatBoost is a gradient boosting technique that proficiently manages categorical features without requiring considerable preparation [21]. It presents novel methodologies, including ordered boosting and target statistics, to address prediction shift and overfitting. Ordered boosting employs a permutation-based methodology to guarantee that each model is trained on novel data, hence mitigating the bias associated with conventional gradient boosting techniques.  
Figure 1: Application of XGBoost algorithm for PV system efficiency estimation.  
The technique employs symmetric decision trees, which facilitate the reduction in prediction time and the preservation of balanced tree topologies. CatBoost's proficiency in handling categorical variables and its resilience to overfitting render it a useful instrument for datasets characterized by intricate patterns and interactions, exemplified by the internal features of PV systems [22].  
1. LightGBM  
LightGBM is a gradient- boosting framework optimized for efficiency and scalability, especially applicable to extensive datasets with high dimensionality [23]. It presents two innovative methodologies: Gradient-based One-Side Sampling (GOSS) and Exclusive Feature Bundling (EFB). GOSS preserves instances with substantial gradients while eliminating those with minimal gradients, so substantially decreasing the quantity of data instances without markedly impacting accuracy. EFB minimizes the feature set by consolidating mutually exclusive features, therefore reducing computational expenses. LightGBM constructs trees in a leaf-wise manner (best-first) instead of a level-wise approach, resulting in accelerated convergence and enhanced accuracy. This method may lead to overfitting if not adequately regularized. In our research, LightGBM's rapid training performance and minimal memory consumption enabled us to effectively manage high-dimensional data and conduct swift iterations during model optimization.  
1. Adaptive Boosting (AdaBoost)  
AdaBoost is an ensemble learning technique that integrates several weak learners to create a robust predictive model [24]. It operates by incrementally modifying the weights of training cases, placing greater emphasis on those that prior models inaccurately predicted. Each successive weak learner is trained to rectify the faults of its predecessor, and the final model consolidates the predictions of all learners, weighted according to their performance. AdaBoost, in technical terms, minimizes an exponential loss function, rendering it susceptible to noisy data and outliers. Notwithstanding this sensitivity, it possesses the benefit of diminishing both bias and variance, hence enhancing its efficacy in regression tasks. AdaBoost's iterative emphasis on challenging cases in PV efficiency prediction improves its capacity to model intricate linkages within the data.  
1. Histogram-Based Gradient Boosting  
Histogram-Based Gradient Boosting is an efficient variant of gradient boosting that enhances the training speed by converting continuous features into discrete bins or histograms [25]. This discretization diminishes the quantity of split points to evaluate during tree construction, resulting in expedited computation and decreased memory consumption. The technique identifies appropriate split points using histogram bins, effectively mimicking continuous features with minimal information loss. This strategy is especially beneficial for extensive datasets where computational efficiency is paramount. Simplifying continuous variables preserves competitive performance while decreasing training duration. In our work, the Histogram-Based Gradient Boosting technique enabled us to effectively simulate the PV efficiency data, achieving a compromise between precision and computational resource consumption.