## 2 Materials and Methods
### Imputation Methods
#### 2.2.3 Machine Learning (ML) Methods  
Machine Learning (ML), a branch of Artificial Intelligence (AI), has rapidly evolved into a transformative technology. ML enables systems to learn and improve from experience without explicit programming, making it a key driver of automation in various industries. This automation often involves analyzing vast amounts of data and applying ML algorithms to uncover patterns and insights critical to intelligent decision-making and were successfully used also in data imputation [44]. Common categories of ML algorithms include supervised, unsupervised, semi-supervised, and reinforcement learning, each catering to specific types of data and applications [45]. The effectiveness of ML solutions depends significantly on the quality of data and the choice of algorithms, which can be mostly classified as classification, regression, clustering and deep learning. In the realm of data imputation, ML offers innovative solutions for managing incomplete datasets, a common issue in real-world scenarios [46; 47]. By leveraging the principles of ML, researchers can enhance the accuracy of predictive models and the reliability of data-driven decisions [48]. In our research we focused on the evaluation of four ML regressor techniques. XGBoost (XGB) is a high-performance machine learning system known for its effectiveness and scalability. It is widely used for achieving top results in tasks such as classification, regression, and ranking. XGBoost's success lies in its innovative features, including a sparsity-aware algorithm for handling sparse data [49], a weighted quantile sketch for scalable learning, and support for parallel and distributed computing. Gradient Boosting (GB) is a machine learning technique that combines multiple \"weak\" models, to build a strong predictive model. It works iteratively, adding new models to correct errors made by the ensemble, focusing on refining the model with each step, making it highly adaptable to tasks like regression, classification, and ranking. Its flexibility allows for customization with various loss functions, enabling it to handle diverse applications effectively, capturing complex data patterns and improving accuracy [50]. Random Forest (RF) is a robust machine learning technique that combines multiple decision trees to create a strong predictive model. By introducing randomness during tree construction, random forests enhance model diversity, which improves overall performance [51]. This approach makes them highly effective for handling high-dimensional data and mitigating the risk of overfitting. Widely used across various domains, random forests are valued for their simplicity, versatility, and ability to provide reliable predictions with minimal tuning [52]. CatBoost (CB) is a gradient boosting algorithm specifically designed to address challenges like target leakage and categorical feature handling. It introduces two innovative techniques: ordered boosting, which prevents prediction bias by avoiding target leakage, and an advanced method for processing categorical features effectively. By overcoming statistical issues present in other gradient boosting methods, CatBoost achieves superior performance on diverse datasets [53]. Its design makes it particularly robust for tasks with heterogeneous features and complex data dependencies, outperforming tools like XGBoost and LightGBM in many benchmarks [54]. In our research considering the machine learning-based approach, gaps within a column are predicted using the values from other columns. To ensure the predictor columns are free of missing values, any initial gaps in these columns has been imputed using median imputation. The considered ML approach leverages the inherent periodicity of the data through our dual data arrangement strategy. In the tabular configuration, each row represents a year with months as columns, allowing the ML algorithms to naturally capture seasonal patterns. The chronological sequence arrangement preserves temporal ordering and enables the capture of autoregressive component.