Latent Variable Modeling and Dynamic Weight Optimization System: A Unified Framework for Multi-Source Evaluation

Abstract

This paper proposes an inverse inference framework for audience voting based on latent variable modeling and maximum likelihood estimation. By introducing latent performance variables, it integrates judge scores and audience preferences into a constrained probabilistic measurement system to indirectly reconstruct incomplete voting data. Dynamic structural equations are adopted to account for temporal dependence and historical voting inertia, while elimination constraints are converted into penalty terms for likelihood optimization. To enhance numerical stability and convergence efficiency, the L-BFGS quasi-Newton algorithm combined with an alternating iteration strategy is applied for parameter estimation. Bootstrap resampling is further used to quantify estimation uncertainty and evaluate model robustness. Based on the inferred audience votes, this study compares ranking-based and percentage-based aggregation mechanisms and assesses their performance via correlation and consistency indicators. Finally, a dynamic weighting optimization framework is constructed, and Pareto optimization is employed to balance evaluation consistency and ranking diversity. Cross-season experimental results reveal that the proposed framework achieves excellent performance in improving elimination consistency, reducing extreme ranking deviations and enhancing the coordination of multi-source evaluations. It possesses strong universality and practical application value.