🤖 AI Summary
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.
📝 Abstract
Estimation of parameter of probabilistic models is an important task in the field of machine learning.For models of discrete variables, calculation of the normalization constant of model is sometimes difficult and a lot of researches have been done to avoid the calculation of the normalization constant. In this paper, we tackle with the difficulty by combining a technique of empirical localization and a deformed Bregman divergence.The technique of empirical localization makes it possible to drastically reduce computational cost of the calculation of the normalization constant, and in addition, appropriate choice of the deformation for the Bregman divergence can invest the proposed estimator with various kinds of favorable statistical properties, such as efficiency or robustness against outlier noise.