2020/08/13 by Vincenzo Bonnici, Bonnici, Vincenzo
Computer Science · Decision Sciences · Physics and Astronomy · #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Multi-Criteria Decision Making #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2008.05932
openalex publication_date 2020/08/13 · openalex created_date 2020/12/21 · openalex updated_date 2026/07/28
This work presents an upper-bound to value that the Kullback-Leibler (KL) divergence can reach for a class of probability distributions called quantum distributions (QD). The aim is to find a distribution U which maximizes the KL divergence from a given distribution P under the assumption that P and U have been generated by distributing a given discrete quantity, a quantum. Quantum distributions naturally represent a wide range of probability distributions that are used in practical applications. Moreover, such a class of distributions can be obtained as an approximation of any probability distribution. The retrieving of an upper-bound for the entropic divergence is here shown to be possible under the condition that the compared distributions are quantum distributions over the same quantum value, thus they become comparable. Thus, entropic divergence acquires a more powerful meaning when it is applied to comparable distributions. This aspect should be taken into account in future developments of divergences. The theoretical findings are used for proposing a notion of normalized KL divergence that is empirically shown to behave differently from already known measures.