Divergence Family Contribution to Data Evaluation in Blockchain Via Alpha-EM and Log-EM Algorithms

Abstract

This study interrelates three adjacent topics in data evaluation. The first is the establishment of a relationship between Bregman divergence and probabilistic alpha-divergence. In particular, we demonstrate that square-root-order probability normalization enables the unification of these two divergence families. This yields a new alpha-divergence, which can be used to jointly derive the alpha-EM algorithm (alpha-expectation-maximization algorithm) and the traditional log-EM algorithm. The second topic is the application of the alpha-EM algorithm in the evaluation of graders scoring raw data over a network. We estimate multinomial mixture distributions in this evaluation problem. We note that the convergence speed of the alpha-EM algorithm is significantly higher than that of the log-EM algorithm. Finally, the third topic is the use of this increase in convergence speed to assign the winning evaluator and miner in a blockchain environment. This is achieved by proof-of-review using evaluation scores, which is a class of proof-of-stake. In the second and third topics, we select terminology from wine tasting for brevity in the exposition. However, this formulation can be applied to a broader class of data in a network environment comprising blockchains.