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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Author:Christoph Gietl, Fabian P. Reffel
Frontdoor URL
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2012-07)
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
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand