Paper Info
Title
Optimal Upper Bounds for the Divergence of Finite-Dimensional Distributions under a Given Variational Distance.
Abstract
We consider the problem of finding the maximum values of divergences D(P‖Q) and D(Q‖P) for probability distributions P and Q ranging in the finite set $$\mathcal{N}=\left\{1,\;2,...,n\right\}$$ provided that both the variation distance V (P,Q) between them and either the probability distribution Q or (in the case of D(P‖Q)) only the value of the minimal component qmin of the probability distribution Q are given. Precise expressions for the maximum values of these divergences are obtained. In several cases these expressions allow us to write out some explicit formulas and simple upper and lower bounds for them. Moreover, explicit formulas for the maximum of D(P‖Q) for given V (P,Q) and qmin and also for the maximum of D(Q‖P) for given Q and V (P,Q) are obtained for all possible values of these parameters.
Year
DOI
Venue
2019
10.1134/S0032946019030025
Problems of Information Transmission
Keywords
Field
DocType
informational divergence, variational distance, discrete probability distributions
Discrete mathematics,Combinatorics,Finite set,Divergence,Expression (mathematics),Upper and lower bounds,Probability distribution,Mathematics
Journal
Volume
Issue
ISSN
55
3
0032-9460
Citations 
PageRank 
References 
0
0.34
0
Authors
1
Name
Order
Citations
PageRank
Vyacheslav V. Prelov114529.59