On Global-local Shrinkage Priors for Count Data

Hamura, Yasuyuki; Irie, Kaoru

doi:10.48550/arxiv.1907.01333

Cited by 3 publications

(1 citation statement)

References 18 publications

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“…For the heavily-tailed distribution that comprises the finite mixture, Student's tdistribution is still regarded thin-tailed for its outlier sensitivity. We propose the use of distributions that has been utilized in the robust inference for high-dimensional count data (Hamura et al, 2019) for their extremely-heavy tails. This is another scale mixture of normals by the gamma distribution with the hierarchical structure on shape parameters, which allows the posterior inference by a simple but efficient Gibbs sampler.…”

Section: Introductionmentioning

confidence: 99%

Log-Regularly Varying Scale Mixture of Normals for Robust Regression

Hamura¹,

Irie²

2020

Preprint

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Linear regression with the classical normality assumption for the error distribution may lead to an undesirable posterior inference of regression coefficients due to the potential outliers. This paper considers the finite mixture of two components with thin and heavy tails as the error distribution, which has been routinely employed in applied statistics. For the heavily-tailed component, we introduce the novel class of distributions; their densities are log-regularly varying and have heavier tails than those of Cauchy distribution, yet they are expressed as a scale mixture of normal distributions and enable the efficient posterior inference by Gibbs sampler. We prove the robustness to outliers of the posterior distributions under the proposed models with a minimal set of assumptions, which justifies the use of shrinkage priors with unbounded densities for the high-dimensional coefficient vector in the presence of outliers. The extensive comparison with the existing methods via simulation study shows the improved performance of our model in point and interval estimation, as well as its computational efficiency. Further, we confirm the posterior robustness of our method in the empirical study with the shrinkage priors for regression coefficients.

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Section: Introductionmentioning

confidence: 99%

Log-Regularly Varying Scale Mixture of Normals for Robust Regression

Hamura¹,

Irie²

2020

Preprint

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Minimax Predictive Density for Sparse Count Data

Yano

Kaneko

Komaki

2018

Preprint

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This paper discusses predictive densities under the Kullback-Leibler loss in high-dimensional sparse count data models. In particular, Poisson sequence models under sparsity constraints are discussed. Sparsity in count data implies zero-inflation. We present a class of Bayes predictive densities that attain exact asymptotic minimaxity in sparse Poisson sequence models. We also show that our class with an estimator of unknown sparsity level plugged-in is adaptive in the exact minimax sense. For application, we extend our results to settings with quasi-sparsity and with missing-completely-at-random observations. The simulation studies as well as applications to real data demonstrate the efficiency of the proposed Bayes predictive densities.

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Shrinkage with Robustness: Log-Adjusted Priors for Sparse Signals

Hamura¹,

Irie²

2020

Preprint

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We introduce a new class of distributions named log-adjusted shrinkage priors for the analysis of sparse signals, which extends the three parameter beta priors by multiplying an additional log-term to their densities. The proposed prior has density tails that are heavier than even those of the Cauchy distribution and realizes the tail-robustness of the Bayes estimator, while keeping the strong shrinkage effect on noises. We verify this property via the improved posterior mean squared errors in the tail. An integral representation with latent variables for the new density is available and enables fast and simple Gibbs samplers for the full posterior analysis. Our log-adjusted prior is significantly different from existing shrinkage priors with logarithms for allowing its further generalization by multiple log-terms in the density. The performance of the proposed priors is investigated through simulation studies and data analysis.

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On Global-local Shrinkage Priors for Count Data

Cited by 3 publications

References 18 publications

Log-Regularly Varying Scale Mixture of Normals for Robust Regression

Log-Regularly Varying Scale Mixture of Normals for Robust Regression

Minimax Predictive Density for Sparse Count Data

Shrinkage with Robustness: Log-Adjusted Priors for Sparse Signals

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