## 2 Literature Review
### Machine Learning Applications in Contingency Estimation  
Commonly used ML algorithms in construction management studies include linear regression, support vector machine (SVM), tree-based methods (such as decision trees, random forests, gradient boosting, and XGBoost), and ANNs [9]. Table 1 presents their theoretical underpinnings and strengths. Linear regression predicts continuous outcomes in terms of one or more input variables [25]. It aims to achieve the optimal fit between the input variables and the target by minimizing the ordinary least squares (see Table 1 for the theoretical grounding). This method is easy to understand and interpret, performs well for linear relationships, and is computationally efficient [9; 26]. However, its performance can lag behind more advanced ML algorithms, particularly when capturing complex, non-linear relations [26]. SVM can find an optimal hyperplane to separate the data points in multiple dimensions [9]. SVR, a variant of SVM, extends this concept to regression by fitting a function within a defined margin around the hyperplane to predict continuous outcomes. SVR is robust to outliers and can effectively handle complex, non-linear data [27]. Linear regression and SVR are often employed as foundational models in predictive analysis due to their simplicity and interpretability [28]. Tree-based methods, including decision trees, random forests, gradient boosting, and XGBoost, are known for their versatility and ability to capture complex, non-linear relations [26]. Of these methods, decision trees are the simplest. They are powerful tools for capturing non-linear relationships and identifying feature importance without extensive data preprocessing [9]. However, individual trees can overfit the data. Random forests can address overfitting by combining multiple decision trees and averaging their outcomes [29; 30]. Gradient boosting further improves prediction by sequentially building trees where each tree corrects the errors of its predecessor, producing a strong ensemble model [31]. XGBoost further develops gradient boosting by adding regularization and optimization techniques that reduce overfitting and increase efficiency [32]. Studies in construction management have found that XGBoost provides the highest predictive performance of the tree-based methods [9]. ANNs are inspired by the structure of the human brain, where neurons connect and transmit signals to process information [33]. This structure enables ANNs to identify complex patterns in data, making them highly effective for handling non-linear data, as in cost and contingency estimation [1; 33], project duration prediction [28], and project risk assessment [34] in the construction industry. In the last decade, ML algorithms have been applied to cost and contingency estimation. Although numerous ML models have been developed for cost prediction [31; 32; 35], few studies have focused on cost contingency estimation. Table 2 summarizes the previous studies that applied ML to the predictive analysis of cost contingency. [PERSON] et al. [1] were among the first to use ML for cost contingency estimation in construction projects, employing an ANN to estimate optimal contingency levels. Their approach used an intermediate contingency form--the contingency rate--as the neural network's output variable to predict the owner's contingency. The ANN model developed was based on only four project characteristics (the number of bidders, project letting year, project duration, and contract value), which may limit its capacity to capture the broader uncertainties affecting cost outcomes.