Tilt-to-length (TTL) coupling noise is a critical issue in space-based gravitational wave detection due to its complex dependence on multiple interacting factors, which complicates the identification of dominant parameters. To address this challenge, we develop a simulation model of the Taiji scientific interferometer, generating noise datasets under multi-parameter conditions. Given the uniqueness of the telescope as well as the convergence behavior of the algorithm, the analysis is structured hierarchically: (i) the telescope level and (ii) the optical bench level. A hierarchical framework combining XGBoost and SHapley Additive exPlanations (SHAP) values is employed to model the intricate relationships between parameters and TTL coupling noise, supplemented by sensitivity analysis. Our results identify pointing jitter and telescope radius as the dominant parameters at the telescope level, while the angles of the plane mirrors and beam splitters are most influential at the optical bench level. The parameter space is reduced from 86 dimensions to 14 dimensions without sacrificing model accuracy. This approach offers actionable insights for optimizing the Taiji interferometer design.