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A Bayesian model for biclustering with applications

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  • Jian Zhang

Abstract

Summary. The paper proposes a Bayesian method for biclustering with applications to gene microarray studies, where we want to cluster genes and experimental conditions simultaneously. We begin by embedding bicluster analysis into the framework of a plaid model with random effects. The corresponding likelihood is then regularized by the hierarchical priors in each layer. The resulting posterior, which is asymptotically equivalent to a penalized likelihood, can attenuate the effect of high dimensionality on cluster predictions. We provide an empirical Bayes algorithm for sampling posteriors, in which we estimate the cluster memberships of all genes and samples by maximizing an explicit marginal posterior of these memberships. The new algorithm makes the estimation of the Bayesian plaid model computationally feasible and efficient. The performance of our procedure is evaluated on both simulated and real microarray gene expression data sets. The numerical results show that our proposal substantially outperforms the original plaid model in terms of misclassification rates across a range of scenarios. Applying our method to two yeast gene expression data sets, we identify several new biclusters which show the enrichment of known annotations of yeast genes.

Suggested Citation

  • Jian Zhang, 2010. "A Bayesian model for biclustering with applications," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(4), pages 635-656, August.
    • Handle: RePEc:bla:jorssc:v:59:y:2010:i:4:p:635-656
    DOI: 10.1111/j.1467-9876.2010.00716.x
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    References listed on IDEAS

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    1. P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
    2. Qiu Xing & Klebanov Lev & Yakovlev Andrei, 2005. "Correlation Between Gene Expression Levels and Limitations of the Empirical Bayes Methodology for Finding Differentially Expressed Genes," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
    3. Turner, Heather & Bailey, Trevor & Krzanowski, Wojtek, 2005. "Improved biclustering of microarray data demonstrated through systematic performance tests," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 235-254, February.
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    Cited by:

    1. Jian Zhang, 2017. "Screening and clustering of sparse regressions with finite non-Gaussian mixtures," Biometrics, The International Biometric Society, vol. 73(2), pages 540-550, June.
    2. Xinghua Fang & Jian Zhou & Hongya Zhao & Yizeng Chen, 2022. "A biclustering-based heterogeneous customer requirement determination method from customer participation in product development," Annals of Operations Research, Springer, vol. 309(2), pages 817-835, February.

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