Open Access
February, 1975 $I$-Divergence Geometry of Probability Distributions and Minimization Problems
I. Csiszar
Ann. Probab. 3(1): 146-158 (February, 1975). DOI: 10.1214/aop/1176996454


Some geometric properties of PD's are established, Kullback's $I$-divergence playing the role of squared Euclidean distance. The minimum discrimination information problem is viewed as that of projecting a PD onto a convex set of PD's and useful existence theorems for and characterizations of the minimizing PD are arrived at. A natural generalization of known iterative algorithms converging to the minimizing PD in special situations is given; even for those special cases, our convergence proof is more generally valid than those previously published. As corollaries of independent interest, generalizations of known results on the existence of PD's or nonnegative matrices of a certain form are obtained. The Lagrange multiplier technique is not used.


Download Citation

I. Csiszar. "$I$-Divergence Geometry of Probability Distributions and Minimization Problems." Ann. Probab. 3 (1) 146 - 158, February, 1975.


Published: February, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0318.60013
MathSciNet: MR365798
Digital Object Identifier: 10.1214/aop/1176996454

Keywords: 15-A48 , 49-F22 , 60-00-E05 , 62-B10 , Contingency tables , distributions with given marginals , Geometry of probability distributions , iterative proportional fitting procedure , minimum discrimination information

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 1 • February, 1975
Back to Top