Accumulation Points of the Iterative Proportional Fitting Procedure

  • The asymptotic behavior of the iterative proportional fitting procedure (IPF procedure) is analyzed comprehensively. Given a nonnegative matrix as well as row and column marginals the IPF procedure generates a sequence of matrices, called the IPF sequence, by alternately fitting rows and columns to match their respective marginals. We prove that the IPF sequence has at most two accumulation points. They originate as the limits of the even-step subsequence, and of the odd-step subsequence. The well-known IPF convergence criteria are then retrieved easily. Our proof is based on Csiszár's and Tusnády's (1984) results on the interplay of the I-divergence geometry and alternating minimization procedures.

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Metadaten
Author:Christoph Gietl, Fabian P. Reffel
URN:urn:nbn:de:bvb:384-opus4-19617
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1961
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2012-07)
Type:Preprint
Language:English
Publishing Institution:Universität Augsburg
Release Date:2012/07/09
Tag:iterative proportional fitting; accumulation points; alternating minimization; I-divergence; distributions with given marginals
GND-Keyword:Kontingenztafelanalyse; Statistik; Informationstheorie
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht mit Print on Demand