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Accumulation points of the iterative proportional fitting procedure

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  • Christoph Gietl
  • Fabian Reffel

Abstract

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 (Stat Decis Suppl Issue 1:205–237, 1984 ) results on the interplay of the I-divergence geometry and alternating minimization procedures. Copyright Springer-Verlag Berlin Heidelberg 2013

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  • Christoph Gietl & Fabian Reffel, 2013. "Accumulation points of the iterative proportional fitting procedure," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(6), pages 783-798, August.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:6:p:783-798
    DOI: 10.1007/s00184-012-0415-7
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    Cited by:

    1. Friedrich Pukelsheim, 2014. "Biproportional scaling of matrices and the iterative proportional fitting procedure," Annals of Operations Research, Springer, vol. 215(1), pages 269-283, April.

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