Computing the maximum-entropy extension of given discrete probability distributions

Malvestuto, Francesco M.

doi:10.1016/0167-9473(89)90046-7

Cited by 13 publications

(5 citation statements)

References 18 publications

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“…We see that the numerator of α (t) 0 consists of the diagonal square terms when we expand the square of denominator in the form of (16). We now give a proof of Proposition 3.1.…”

Section: Analysis Of Behavior Close To the Maximum Likelihood Estimatementioning

confidence: 75%

“…Consider (15) and (16). If the signs of the terms on the right hand side of (16) are "random" then we can expect that α (t) 0 is close to 1.…”

Section: Analysis Of Behavior Close To the Maximum Likelihood Estimatementioning

confidence: 99%

“…In this paper, we propose another generalization of IPS based on decomposable submodels. Decomposable models or graph decompositions have been already considered by Jiroušek [12], Jiroušek and Přeučil [13] and Malvestuto [16]. However they used decomposable models for efficient implementation of conventional IPS in the form of treecomputation.…”

Section: Introductionmentioning

confidence: 99%

“…Extension of IPS to continuous case was studied in Kullback [14] and Rüschendorf [17]. Effective algorithms and implementations of IPS have been also studied by many authors, including [1], [9], [12], [13], [16].…”

Section: Introductionmentioning

confidence: 99%

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Iterative proportional scaling via decomposable submodels for contingency tables

Endo¹,

Takemura²

2009

Computational Statistics & Data Analysis

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We propose iterative proportional scaling (IPS) via decomposable submodels for maximizing likelihood function of a hierarchical model for contingency tables. In ordinary IPS the proportional scaling is performed by cycling through the members of the generating class of a hierarchical model. We propose to adjust more marginals at each step. This is accomplished by expressing the generating class as a union of decomposable submodels and cycling through the decomposable models. We prove convergence of our proposed procedure, if the amount of scaling is adjusted properly at each step. We also analyze the proposed algorithms around the maximum likelihood estimate (MLE) in detail. Faster convergence of our proposed procedure is illustrated by numerical examples.

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“…We see that the numerator of α (t) 0 consists of the diagonal square terms when we expand the square of denominator in the form of (16). We now give a proof of Proposition 3.1.…”

Section: Analysis Of Behavior Close To the Maximum Likelihood Estimatementioning

confidence: 75%

“…Consider (15) and (16). If the signs of the terms on the right hand side of (16) are "random" then we can expect that α (t) 0 is close to 1.…”

Section: Analysis Of Behavior Close To the Maximum Likelihood Estimatementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Iterative proportional scaling via decomposable submodels for contingency tables

Endo¹,

Takemura²

2009

Computational Statistics & Data Analysis

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show abstract

“…Although the intention is somewhat different, the algorithm is effectively identical to IPFP (Onuki, 2013). The popularity of the procedure can also be explained by the fact that it provides a solution for the so called maximum entropy (ME) problem (Malvestuto, 1989, Upper, 2011, Elsinger et al, 2013. In Computer Sciences, flows within router networks are often estimated using Raking and so called Gravity Models (see Zhang et al, 2003).…”

Section: Introductionmentioning

confidence: 99%

Regression-based Network Reconstruction with Nodal and Dyadic Covariates and Random Effects

Lebacher,

Kauermann

2019

Preprint

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Network (or matrix) reconstruction is a general problem which occurs if the margins of a matrix are given and the matrix entries need to be predicted. In this paper we show that the predictions obtained from the iterative proportional fitting procedure (IPFP) or equivalently maximum entropy (ME) can be obtained by restricted maximum likelihood estimation relying on augmented Lagrangian optimization. Based on the equivalence we extend the framework of network reconstruction towards regression by allowing for exogenous covariates and random heterogeneity effects. The proposed estimation approach is compared with different competing methods for network reconstruction and matrix estimation. Exemplary, we apply the approach to interbank lending data, provided by the Bank for International Settlement (BIS). This dataset provides full knowledge of the real network and is therefore suitable to evaluate the predictions of our approach. It is shown that the inclusion of exogenous information allows for superior predictions in terms of L 1 and L 2 errors. Additionally, the approach allows to obtain prediction intervals via bootstrap that can be used to quantify the uncertainty attached to the predictions.

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Introduction to probabilistic methods of knowledge representation and processing

Jiroušek¹

1992

Advanced Topics in Artificial Intelligence

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Computing the maximum-entropy extension of given discrete probability distributions

Cited by 13 publications

References 18 publications

Iterative proportional scaling via decomposable submodels for contingency tables

Iterative proportional scaling via decomposable submodels for contingency tables

Regression-based Network Reconstruction with Nodal and Dyadic Covariates and Random Effects

Introduction to probabilistic methods of knowledge representation and processing

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