Parameter Estimation for Unnormalized Discrete Models via Empirically Localized Deformed Bregman Divergence
This study addresses the core computational bottleneck of evaluating normalization constants in parameter estimation for discrete models. To overcome this challenge, we propose a novel normalization-free estimation framework that integrates empirical localization with deformed Bregman divergence. By leveraging empirical localization techniques, the proposed method effectively circumvents the computation of global normalization constants, substantially reducing computational overhead. Furthermore, the incorporation of deformed Bregman divergence reconstructs the objective function, endowing the estimator with rigorous statistical properties. Both theoretical analysis and empirical evaluations demonstrate that our approach significantly lowers computational costs and enhances estimation efficiency while exhibiting superior robustness against anomalous noise. Ultimately, this work establishes a new paradigm for efficient parameter estimation in large-scale discrete probabilistic models.