Bregman divergence as general framework to estimate unnormalized statistical models
This provides a theoretical unification for researchers in machine learning and statistics, but it is incremental as it builds on and connects established methods.
The paper tackles the problem of estimating unnormalized statistical models for continuous or discrete random variables by proposing the Bregman divergence as a general framework, showing that it unifies existing methods like noise-contrastive estimation, ratio matching, and score matching.
We show that the Bregman divergence provides a rich framework to estimate unnormalized statistical models for continuous or discrete random variables, that is, models which do not integrate or sum to one, respectively. We prove that recent estimation methods such as noise-contrastive estimation, ratio matching, and score matching belong to the proposed framework, and explain their interconnection based on supervised learning. Further, we discuss the role of boosting in unsupervised learning.