On Dykstra's Iterative Fitting Procedure

On Improving the Efficiency of the Iterative Proportional Fitting Procedure

Iterative proportional fitting (IPF) on junction trees is an important tool for learning in graphical models. We identify the propagation and IPF updates on the junction tree as fixed point equations of a single constrained entropy maximization problem. This allows a more efficient message updating protocol than the well known effective IPF of Jiroušek and Přeučil (1995). When the junction tree...

Design of Iterative Proportional Fitting Procedure for Possibility Distributions

We design an iterative proportional fitting procedure (parameterized by a continuous t-norm) for computation of multidimensional possibility distributions from its marginals, and discuss its basic properties.

On the Iterative Proportional Fitting Procedure: Structure of Accumulation Points and L1-error Analysis

Symmetric Iterative Proportional Fitting

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)...

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...