Symmetric Iterative Proportional Fitting
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چکیده
This supplement consists of several parts that refer directly to specific topics in the paper: A Proof of Equation (2) B Proof of Lemma 3.1 (Symmetric biproportional fit) C Technical details on why ”local affinity” is sufficient in Section 4.1 D Proof of Theorem 4.2 (Convergence of PSIPF) E Proof of Lemma 4.4 (L1-monotony) F Proof of Lemma 4.5 (Volume bounds) G Proof of Lemma 4.6 (Limit points) H Proof of Lemma 4.7 (Strong convergence) I Proof (sketch) of Proposition 5.2 (Strictly positive feasibility)
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Symmetric Iterative Proportional Fitting
Iterative Proportional Fitting (IPF) generates from an input matrix W a sequence of matrices that converges, under certain conditions, to a specific limit matrix Ŵ . This limit is the relative-entropy nearest solution to W among all matrices of prescribed row marginals r and column marginals c. We prove this known fact by a novel strategy that contributes a pure algorithmic intuition. Then we f...
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