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Bayesian sparse convex clustering via global-local shrinkage priors

Author

Listed:
  • Kaito Shimamura

    (NTT Advanced Technology Corporation
    The University of Electro-Communications)

  • Shuichi Kawano

    (The University of Electro-Communications)

Abstract

Sparse convex clustering is to group observations and conduct variable selection simultaneously in the framework of convex clustering. Although a weighted $$L_1$$ L 1 norm is usually employed for the regularization term in sparse convex clustering, its use increases the dependence on the data and reduces the estimation accuracy if the sample size is not sufficient. To tackle these problems, this paper proposes a Bayesian sparse convex clustering method based on the ideas of Bayesian lasso and global-local shrinkage priors. We introduce Gibbs sampling algorithms for our method using scale mixtures of normal distributions. The effectiveness of the proposed methods is shown in simulation studies and a real data analysis.

Suggested Citation

  • Kaito Shimamura & Shuichi Kawano, 2021. "Bayesian sparse convex clustering via global-local shrinkage priors," Computational Statistics, Springer, vol. 36(4), pages 2671-2699, December.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:4:d:10.1007_s00180-021-01101-7
    DOI: 10.1007/s00180-021-01101-7
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    References listed on IDEAS

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    1. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, vol. 97(2), pages 465-480.
    2. Yixin Wang & David M. Blei, 2019. "Frequentist Consistency of Variational Bayes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1147-1161, July.
    3. Kaito Shimamura & Masao Ueki & Shuichi Kawano & Sadanori Konishi, 2019. "Bayesian generalized fused lasso modeling via NEG distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(16), pages 4132-4153, August.
    4. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    5. Sylvia Frühwirth-Schnatter & Gertraud Malsiner-Walli, 2019. "From here to infinity: sparse finite versus Dirichlet process mixtures in model-based clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 33-64, March.
    6. J. A. Hartigan & M. A. Wong, 1979. "A K‐Means Clustering Algorithm," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 28(1), pages 100-108, March.
    7. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    8. Annalisa Cadonna & Sylvia Frühwirth-Schnatter & Peter Knaus, 2020. "Triple the Gamma—A Unifying Shrinkage Prior for Variance and Variable Selection in Sparse State Space and TVP Models," Econometrics, MDPI, vol. 8(2), pages 1-36, May.
    9. Anirban Bhattacharya & Debdeep Pati & Natesh S. Pillai & David B. Dunson, 2015. "Dirichlet--Laplace Priors for Optimal Shrinkage," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1479-1490, December.
    10. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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