Titanic Survival Prediction: A Mathematical Endeavor

Abstract

This study addresses the gap in existing Titanic survival prediction research—where algorithm application dominates while mathematical underpinnings are overlooked—by integrating applied mathematics into three mainstream machine learning models: Logistic Regression, Random Forest, and K-Nearest Neighbors (KNN). Mathematical principles guided the entire workflow: Bayesian probability interpreted how features (e.g., gender, cabin class) contribute to survival likelihood; Gini impurity quantified decision-making logic in tree-based models; statistical distribution theory justified median imputation for missing values (e.g., 19.8% missing in the Age feature); feature engineering further embedded mathematical logic, including constructing Age and Class interaction terms to capture nonlinear dependencies between variables and binning continuous features (Age to AgeBand, Fare to FareBand) to simplify probability distributions for better model adaptability. Experimental results showed Random Forest outperformed the other models, achieving 82.68% accuracy, compared to 81.56% for KNN and 81.01% for Logistic Regression; feature importance analysis identified gender as the most critical predictor (significance score ~0.3), followed by fare (~0.25) and age (~0.24), while survival rates by title (e.g., 79.37% for Mrs, 15.67% for Mr) further reinforced gender’s dominant role in survival prediction. This work enhances the interpretability and methodological rigor of Titanic survival prediction, demonstrating how mathematical theory can ground machine learning applications in theoretical validity.