Probability Measures with given Marginals and Conditionals: I-projections and Conditional Iterative Proportional Fitting
نویسنده
چکیده
The iterative proportional fitting procedure (IPF-P) is an algorithm to compute approximately probability measures with prescribed marginals. We propose two extensions of the IPF-P, called conditional iterative proportional fitting procedures (CIPF-P), so that, additionally, given conditional distributions are taken into account. This modification is carried out by using the geometrical interpretation of the IPF-P as successive application of I-projections. Finally, we establish the convergence of both CIPF-Ps in the finite discrete case.
منابع مشابه
An Iterative Procedure for General Probability Measures to Obtain I-projections onto Intersections of Convex Sets by Bhaskar Bhattacharya
The iterative proportional fitting procedure (IPFP) was introduced formally by Deming and Stephan in 1940. For bivariate densities, this procedure has been investigated by Kullback and Rüschendorf. It is well known that the IPFP is a sequence of successive I-projections onto sets of probability measures with fixed marginals. However, when finding the I-projection onto the intersection of arbitr...
متن کاملAn Iterative Procedure for General Probability Measures to Obtain I-projections onto Intersections of Convex Sets
The iterative proportional fitting procedure (IPFP) was introduced formally by Deming and Stephan in 1940. For bivariate densities, this procedure has been investigated by Kullback and Rüschendorf. It is well known that the IPFP is a sequence of successive I-projections onto sets of probability measures with fixed marginals. However, when finding the I-projection onto the intersection of arbitr...
متن کاملDesign 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.
متن کاملIPFP and Further Experiments
Iterative Proportional Fitting Procedure is commonly used in probability theory for construction of a joint probability distribution from a system of its marginals. A similar idea can be used in case of belief functions thanks to special operators of composition defined in this framework. In this paper, a formerly designed IPF procedure is further studied. We propose a modification of compositi...
متن کاملModifying Bayesian Networks by Probability Constraints
This paper deals with the following problem: modify a Bayesian network to satisfy a given set of probability constraints by only change its conditional probability tables, and the probability distribution of the resulting network should be as close as possible to that of the original network. We propose to solve this problem by extending IPFP (iterative proportional fitting procedure) to probab...
متن کامل