Conjugate and conditional conjugate Bayesian analysis of discrete graphical models of marginal independence

Ntzoufras, Ioannis; Tarantola, Claudia

doi:10.1016/j.csda.2013.04.005

Cited by 7 publications

(16 citation statements)

References 34 publications

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“…4 Probability Based MCMC Samplers 4.1 Initial Set-up and Data Augmentation for MCMC Following the notation of Ntzoufras and Tarantola (2013), we can divide the class of graphical log-linear marginal models in two major categories: homogeneous and non-homogeneous models. A bi-directed graph is named homogeneous if it does not include a bi-directed 4-chain or a chordless 4-cycle as subgraphs.…”

Section: Likelihood Specification and Posterior Inferencementioning

confidence: 99%

“…interactions). Moreover, we can exploit the advantages of the conditional conjugacy of the algorithm of Ntzoufras and Tarantola (2013) in order to obtain efficient proposals based on probability parameters.…”

Section: Likelihood Specification and Posterior Inferencementioning

confidence: 99%

“…Some context specific results have been presented by e.g. Silva and Ghahramani (2009a), Bartolucci et al (2012) and Ntzoufras and Tarantola (2013). For graphical log-linear marginal models, no conjugate analysis is available.…”

Section: Introductionmentioning

confidence: 99%

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Probability Based Independence Sampler for Bayesian Quantitative Learning in Graphical Log-Linear Marginal Models

Ntzoufras¹,

Tarantola²,

Lupparelli³

2019

Bayesian Anal.

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Bayesian methods for graphical log-linear marginal models have not been developed in the same extent as traditional frequentist approaches. In this work, we introduce a novel Bayesian approach for quantitative learning for such models. These models belong to curved exponential families that are difficult to handle from a Bayesian perspective. Furthermore, the likelihood cannot be analytically expressed as a function of the marginal log-linear interactions, but only in terms of cell counts or probabilities. Posterior distributions cannot be directly obtained, and MCMC methods are needed.Finally, a well-defined model requires parameter values that lead to compatible marginal probabilities.Hence, any MCMC should account for this important restriction. We construct a fully automatic and efficient MCMC strategy for quantitative learning for graphical log-linear marginal models that handles these problems. While the prior is expressed in terms of the marginal log-linear interactions, we build an MCMC algorithm that employs a proposal on the probability parameter space. The corresponding proposal on the marginal log-linear interactions is obtained via parameter transformation. By this strategy, we achieve to move within the desired target space. At each step, we directly work with welldefined probability distributions. Moreover, we can exploit a conditional conjugate setup to build an 1 efficient proposal on probability parameters. The proposed methodology is illustrated by a simulation study and a real dataset.

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Section: Likelihood Specification and Posterior Inferencementioning

confidence: 99%

Section: Likelihood Specification and Posterior Inferencementioning

confidence: 99%

See 1 more Smart Citation

Probability Based Independence Sampler for Bayesian Quantitative Learning in Graphical Log-Linear Marginal Models

Ntzoufras¹,

Tarantola²,

Lupparelli³

2019

Bayesian Anal.

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“…The compatibility between the different transformation families is automatically introduced by the use of common imaginary data, as the power‐priors are nothing more than rescaled posterior distributions given the imaginary data

{boldy}^{*}

. Similar strategies have been introduced in common model selection problems, such as the well‐known g‐prior of Zellner (), and in graphical models (Ntzoufras & Tarantola, , for example). Some interesting properties of this class of power‐priors are described in Ibrahim, Chen & Sinha ().…”

Section: Bayesian Formulationmentioning

confidence: 99%

Bayesian transformation family selection: Moving toward a transformed Gaussian universe

2015

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The problem of transformation selection is thoroughly treated from a Bayesian perspective. Several families of transformations are considered with a view to achieving normality: the Box–Cox, the Modulus, the Yeo & Johnson, and the Dual transformation. Markov chain Monte Carlo algorithms have been constructed in order to sample from the posterior distribution of the transformation parameter λT associated with each competing family T. We investigate different approaches to constructing compatible prior distributions for λT over alternative transformation families. Selection and discrimination between different transformation families are attained via posterior model probabilities. Although there is no choice of transformation family that can be universally applied to all problems, empirical evidence suggests that some particular data structures are best treated by specific transformation families. For example, skewness is associated with the Box–Cox family while fat‐tailed distributions are efficiently treated using the Modulus transformation. The Canadian Journal of Statistics 43: 600–623; 2015 © 2015 Statistical Society of Canada

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“…The classic Bayes school uses different parametric distributions on different parts of θ according to the natures of learning tasks and empirical experiences. Typical examples are those of conjugate priors (Diaconis and Ylvisaker 1979;Ntzoufras and Tarantola 2013). Extensive studies along this line have been made in the machine learning literature, especially on Dirichlet-multinomial for Gaussian mixture.…”

Section: Bayes Approach and Automatic Model Selectionmentioning

confidence: 99%

Further advances on Bayesian Ying-Yang harmony learning

2015

Appl Inform

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After a short tutorial on the fundamentals of Bayes approaches and Bayesian Ying-Yang (BYY) harmony learning, this paper introduces new progresses. A generic information harmonising dynamics of BYY harmony learning is proposed with the help of a Lagrange variety preservation principle, which provides Lagrange-like implementations of Ying-Yang alternative nonlocal search for various learning tasks and unifies attention, detection, problem-solving, adaptation, learning and model selection from an information harmonising perspective. In this framework, new algorithms are developed to implement Ying-Yang alternative nonlocal search for learning Gaussian mixture and several typical exemplars of linear matrix system, including factor analysis (FA), mixture of local FA, binary FA, nonGaussian FA, de-noised Gaussian mixture, sparse multivariate regression, temporal FA and temporal binary FA, as well as a generalised bilinear matrix system that covers not only these linear models but also manifold learning, gene regulatory networks and the generalised linear mixed model. These algorithms are featured with a favourable nature of automatic model selection and a unified formulation in performing unsupervised learning and semi-supervised learning. Also, we propose a principle of preserving multiple convex combinations, which leads alternative search algorithms. Finally, we provide a chronological outline of the history of BYY learning studies.

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Conjugate and conditional conjugate Bayesian analysis of discrete graphical models of marginal independence

Cited by 7 publications

References 34 publications

Probability Based Independence Sampler for Bayesian Quantitative Learning in Graphical Log-Linear Marginal Models

Probability Based Independence Sampler for Bayesian Quantitative Learning in Graphical Log-Linear Marginal Models

Bayesian transformation family selection: Moving toward a transformed Gaussian universe

Further advances on Bayesian Ying-Yang harmony learning

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