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Robust sparse Bayesian infinite factor models

Author

Listed:
  • Jaejoon Lee

    (Flash Product Engineering Team, Samsung Electronics Co., Ltd)

  • Seongil Jo

    (Inha University)

  • Jaeyong Lee

    (Seoul National University)

Abstract

Most of previous works and applications of Bayesian factor model have assumed the normal likelihood regardless of its validity. We propose a Bayesian factor model for heavy-tailed high-dimensional data based on multivariate Student-t likelihood to obtain better covariance estimation. We use multiplicative gamma process shrinkage prior and factor number adaptation scheme proposed in Bhattacharya and Dunson [Biometrika 98(2):291–306, 2011]. Since a naive Gibbs sampler for the proposed model suffers from slow mixing, we propose a Markov Chain Monte Carlo algorithm where fast mixing of Hamiltonian Monte Carlo is exploited for some parameters in the proposed model. Simulation results illustrate the gain in performance of covariance estimation for heavy-tailed high-dimensional data. We also provide a theoretical result that the posterior of the proposed model is weakly consistent under reasonable conditions. We conclude the paper with the application of the proposed factor model on breast cancer metastasis prediction given DNA signature data of cancer cells.

Suggested Citation

  • Jaejoon Lee & Seongil Jo & Jaeyong Lee, 2022. "Robust sparse Bayesian infinite factor models," Computational Statistics, Springer, vol. 37(5), pages 2693-2715, November.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:5:d:10.1007_s00180-022-01208-5
    DOI: 10.1007/s00180-022-01208-5
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    References listed on IDEAS

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    1. Seth Flaxman & Swapnil Mishra & Axel Gandy & H. Juliette T. Unwin & Thomas A. Mellan & Helen Coupland & Charles Whittaker & Harrison Zhu & Tresnia Berah & Jeffrey W. Eaton & Mélodie Monod & Azra C. Gh, 2020. "Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe," Nature, Nature, vol. 584(7820), pages 257-261, August.
    2. Federico Ferrari & David B. Dunson, 2021. "Bayesian Factor Analysis for Inference on Interactions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1521-1532, July.
    3. Durante, Daniele, 2017. "A note on the multiplicative gamma process," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 198-204.
    4. 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.
    5. Ando, Tomohiro, 2009. "Bayesian factor analysis with fat-tailed factors and its exact marginal likelihood," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1717-1726, September.
    6. A. Bhattacharya & D. B. Dunson, 2011. "Sparse Bayesian infinite factor models," Biometrika, Biometrika Trust, vol. 98(2), pages 291-306.
    7. Carvalho, Carlos M. & Chang, Jeffrey & Lucas, Joseph E. & Nevins, Joseph R. & Wang, Quanli & West, Mike, 2008. "High-Dimensional Sparse Factor Modeling: Applications in Gene Expression Genomics," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1438-1456.
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