## 3 Materials and Methods
### Stage 1: Data Collection and Preprocessing  
In this stage, data were collected and preprocessed, which included data cleaning, feature selection, and feature scaling. A total of 122 infrastructure project cases were collected from the Hong Kong Public Works Department. Projects were included based on their classification as infrastructure, which was determined according to official categorization by the department. Specifically, the dataset encompassed projects related to transportation (e.g., roads, bridges, and tunnels), utilities (e.g., water supply and drainage systems), and public facilities (e.g., government buildings and hospitals). Only completed projects with available records on cost estimates, contingency allocations, and actual expenditures were considered to ensure data reliability and comparability. During the data collection process, relevant project data, including project characteristics, project estimates (PEs), contract contingencies, and approved PEs under public budget allocation, were gathered. Data cleaning was performed to remove duplicates and address missing data. The dataset was constructed by integrating various types of projects, including land development projects (LDPs), roads and highways (RH), water treatment projects (WTPs), sewage treatment projects (STPs), and other public functional projects (PFPs, e.g., hospitals, schools, and government offices). Given the integration of diverse project types, potential duplicates were identified and removed using the drop_duplicates() function in Pandas to ensure unique entries across the dataset. Missing data were handled through either imputation or removal, depending on the extent of the missing values, to maintain dataset reliability and facilitate accurate predictions [36; 50]. Features with more than 30% missing data were excluded, while those with less than 30% missing data were retained, and the missing values were imputed [51]. For this study, two imputation approaches were considered: (i) replacing missing values with the mean or median or (ii) estimating the missing values more precisely based on underlying data patterns [52]. Although the first method is straightforward, it can reduce data variability and introduce bias. Therefore, the second approach was adopted, and a linear regression model was used for imputation. This method preserved the data patterns and improved the consistency of the predictive models. A set of seven input variables, including PE, contract contingency, approved PE, project type, starting and completion years, and project scope, was created and used for model development. These variables were selected because they represent key factors influencing the cost and contingency outcomes in infrastructure projects. Specifically, the PE and approved PE capture the project's initial cost assessments [45]; contract contingency reflects the risk management buffer embedded into the project budget [2]; and project type accounts for variations in project characteristics. The starting and completion years were included to reflect temporal aspects, such as inflation and regulatory changes [28; 32]. The construction  
Figure 1: Research design. floor area variable indicated project size. This set of input variables was deemed appropriate as it encompasses both financial planning and inherent project characteristics, which are vital for modeling cost performance and contingency materialization and, therefore, provide a robust foundation for prediction models. After data cleaning, the \"project scope\" variable was excluded due to a missing data rate of more than 30%. The six remaining features were retained for model development. The target variable value, cost contingency, was calculated in terms of final cost, project estimate, and contract contingency due to the absence of direct data records for cost contingency values. The materialized cost contingency is defined as the difference between the final cost and the project cost [3].