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- Iterative_proportional_fitting abstract "The iterative proportional fitting procedure (IPFP, also known as biproportional fitting in statistics, RAS algorithm in economics and matrix raking or matrix scaling in computer science) is an iterative algorithm for estimating cell values of a contingency table such that the marginal totals remain fixed and the estimated table decomposes into an outer product.First introduced by Deming and Stephan in 1940 (they proposed IPFP as an algorithm leading to a minimizer of the Pearson X-squared statistic, which it does not, and even failed to prove convergence), it has seen various extensions and related research. A rigorous proof of convergence by means of differential geometry is due to Fienberg (1970). He interpreted the family of contingency tables of constant crossproduct ratios as a particular (IJ − 1)-dimensional manifold of constant interaction and showed that the IPFP is a fixed-point iteration on that manifold. Nevertheless, he assumed strictly positive observations. Generalization to tables with zero entries is still considered a hard and only partly solved problem.An exhaustive treatment of the algorithm and its mathematical foundations can be found in the book of Bishop et al. (1975). The first general proof of convergence, built on non-trivial measure theoretic theorems and entropy minimization, is due to Csiszár (1975).Relatively new results on convergence and error behavior have been published by Pukelsheim and Simeone (2009). They proved simple necessary and sufficient conditions for the convergence of the IPFP for arbitrary two-way tables (i.e. tables with zero entries) by analysing an -error function.Other general algorithms can be modified to yield the same limit as the IPFP, for instance the Newton–Raphson method andthe EM algorithm. In most cases, IPFP is preferred due to its computational speed, numerical stability and algebraic simplicity.".
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- Iterative_proportional_fitting subject Category:Categorical_data.
- Iterative_proportional_fitting subject Category:Statistical_algorithms.
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- Iterative_proportional_fitting type Algorithm105847438.
- Iterative_proportional_fitting type CategoricalData.
- Iterative_proportional_fitting type Cognition100023271.
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- Iterative_proportional_fitting type Event100029378.
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- Iterative_proportional_fitting type Procedure101023820.
- Iterative_proportional_fitting type PsychologicalFeature100023100.
- Iterative_proportional_fitting type Rule105846932.
- Iterative_proportional_fitting type StatisticalAlgorithms.
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- Iterative_proportional_fitting comment "The iterative proportional fitting procedure (IPFP, also known as biproportional fitting in statistics, RAS algorithm in economics and matrix raking or matrix scaling in computer science) is an iterative algorithm for estimating cell values of a contingency table such that the marginal totals remain fixed and the estimated table decomposes into an outer product.First introduced by Deming and Stephan in 1940 (they proposed IPFP as an algorithm leading to a minimizer of the Pearson X-squared statistic, which it does not, and even failed to prove convergence), it has seen various extensions and related research. ".
- Iterative_proportional_fitting label "Iterative proportional fitting".
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- Iterative_proportional_fitting isPrimaryTopicOf Iterative_proportional_fitting.