An Improved Iterative Proportional Scaling Procedure for Gaussian Graphical Models

“…Standard approaches for regularization selection are known to result in overly dense graphs [12]. In this work, we divide the problem of learning the precision matrix into two steps: we first apply the BINCO method [13] to learn the sparsity structure of the graphical model; next we determine the non-zero elements in the precision matrix via Iterative Proportional Fitting (IPF) [14].…”

Section: Introductionmentioning

confidence: 99%

Copula Gaussian graphical model for discrete data

Dauwels

et al. 2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

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Copula Gaussian graphical models are capable of describing dependencies between a large number of heterogeneous variables. In this paper, low-complexity algorithms are proposed for learning copula Gaussian graphical models from discrete data. The proposed approach is Monte-Carlo expectation maximization: in the E-step, an efficient Gibbs sampler is applied, and in the M-step, the sparse graphical model is inferred by solving a penalized maximize likelihood problem. The regularization parameter is determined through the BINCO method proposed by Li et al. Numerical results for both synthetic and real data demonstrate the effectiveness of the proposed approach.

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“…We also apply the chordal graph theory to retrieve the Markov structure to reduce the computational time using the recursive summation/integration technique. Our technique is then similar to those used in the efficient computation of maximum-likelihood estimator of graphical models (e.g., Badsberg and Malvestuto 2001;Hara and Takemura 2010;Xu et al 2011Xu et al , 2012Xu et al , 2014.…”

Section: Introductionmentioning

confidence: 99%

Multiplicity adjustment for temporal and spatial scan statistics using Markov property

Kuriki

Takahashi

Hara

2018

Jpn J Stat Data Sci

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We discuss computation of the conditional expectation in a multinomial distribution. The problem is motivated by the evaluation of the multiplicity-adjusted p-value of scan statistics in spatial epidemiology. We propose a recursive summation/integration technique using the Markov property, which is extracted from a chordal graph defined by temporal and spatial structures. This methodology can be applied to a class of distributions, including the Poisson distribution (that is, the conditional distribution is the multinomial). To illustrate the approach, we present the real data analyses for detecting temporal and spatial clustering.

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An Improved Iterative Proportional Scaling Procedure for Gaussian Graphical Models

Cited by 16 publications

References 24 publications

A new algorithm for decomposition of graphical models

A new algorithm for decomposition of graphical models

Copula Gaussian graphical model for discrete data

Multiplicity adjustment for temporal and spatial scan statistics using Markov property

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