The Annals of Applied Statistics

The Gibbs-plaid biclustering model

Thierry Chekouo, Alejandro Murua, and Wolfgang Raffelsberger

Full-text: Open access

Abstract

We propose and develop a Bayesian plaid model for biclustering that accounts for the prior dependency between genes (and/or conditions) through a stochastic relational graph. This work is motivated by the need for improved understanding of the molecular mechanisms of human diseases for which effective drugs are lacking, and based on the extensive raw data available through gene expression profiling. We model the prior dependency information from biological knowledge gathered from gene ontologies. Our model, the Gibbs-plaid model, assumes that the relational graph is governed by a Gibbs random field. To estimate the posterior distribution of the bicluster membership labels, we develop a stochastic algorithm that is partly based on the Wang–Landau flat-histogram algorithm. We apply our method to a gene expression database created from the study of retinal detachment, with the aim of confirming known or finding novel subnetworks of proteins associated with this disorder.

Article information

Source
Ann. Appl. Stat., Volume 9, Number 3 (2015), 1643-1670.

Dates
Received: January 2014
Revised: March 2015
First available in Project Euclid: 2 November 2015

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1446488755

Digital Object Identifier
doi:10.1214/15-AOAS854

Mathematical Reviews number (MathSciNet)
MR3418739

Zentralblatt MATH identifier
06526002

Keywords
Clustering relational graph autologistic model Wang–Landau algorithm plaid model gene expression gene ontology retinal detachment

Citation

Chekouo, Thierry; Murua, Alejandro; Raffelsberger, Wolfgang. The Gibbs-plaid biclustering model. Ann. Appl. Stat. 9 (2015), no. 3, 1643--1670. doi:10.1214/15-AOAS854. https://projecteuclid.org/euclid.aoas/1446488755


Export citation

References

  • Akaike, H. (1974). A new look at the statistical model identification. IEEE Trans. Automat. Control AC-19 716–723.
  • Allan, J., Carbonell, J., Doddington, G., Yamron, J. and Yang, Y. (1998). Topic detection and tracking pilot study: Final report. In Proc. DARPA Broadcast News Transcription and Understandingepl Workshop 194–218. Morgan Kaufmann, San Francisco, CA.
  • Ashburner, M., Ball, C. A., Blake, J. A., Bolsteing, D., Butler, H., Cherry, J. M., Davis, A. P., Dolinski, K., Dwight, S. S., Eppig, J. T., Harris, M. A., Hill, D. P., Issel-Tarver, L., Kasarskis, A., Lewis, S., Matese, J. C., Richardson, J. E., Ringwald, M., Rubin, G. M. and Sherlock, G. (2000). Geneontology: Tool for the unification of biology the gene ontology consortium. Nat. Genet. 25 25–29.
  • Atchadé, Y. F. and Liu, J. S. (2010). The Wang–Landau algorithm in general state spaces: Applications and convergence analysis. Statist. Sinica 20 209–233.
  • Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems. J. R. Stat. Soc. Ser. B. Stat. Methodol. 36 192–236.
  • Besag, J. (2001). Markov chain Monte Carlo for statistical inference. Working Paper 9, Center for Statistics and the Social Sciences, Univ. Washington, Seattle, WA.
  • Blatt, M., Wiseman, S. and Domany, E. (1996). Superparamagnetic clustering of data. Phys. Rev. Lett. 76 3251–3254.
  • Caldas, J. and Kaski, S. (2008). Bayesian biclustering with the plaid model. In Proceedings of the IEEE International Workshop on Machine Learning for Signal Processing XVIII (J. Príncipe, D. Erdogmus and T. Adali, eds.) 291–296. Cancun, Mexico.
  • Calza, S., Raffelsberger, W., Ploner, A., Sahel, J., Leveillard, T. and Pawitan, Y. (2007). Filtering genes to improve sensitivity in oligonucleotide microarray data analysis. Nucleic Acids Res. 35 e102.
  • Chekouo, T. and Murua, A. (2015). The penalized biclustering model and related algorithms. J. Appl. Stat. 42 1255–1277.
  • Chekouo, T., Murua, A. and Raffelsberger, W. (2015). Supplement to “The Gibbs-plaid biclustering model.” DOI:10.1214/15-AOAS854SUPP.
  • Cheng, Y. and Church, G. M. (2000). Biclustering of expression data. In Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology (P. Bourne et al., eds.) 93–103. AAAI Press, Menlo Park, CA.
  • Cho, R. J., Campbell, M. J., Winzeler, E. A., Steinmetz, L., Conway, A., Wodicka, L., Wolfsberg, T. G., Gabrielian, A. E., Landsman, D., Lockhart, D. J. and Davis, R. W. (1998). A genome-wide transcriptional analysis of the mitotic cell cycle. Mol. Cell 2 65–73.
  • Cho, H., Dhillon, I. S., Guan, Y. and Sra, S. (2004). Minimum sum-squared residue co-clustering of gene expression data. In Proceedings of the 4th SIAM Conference on Data Mining 114–125.
  • de Lichtenberg, U., Jensen, L. J., Brunak, S. and Bork, P. (2005). Dynamic complex formation during the yeast cell cycle. Science 307 724–727.
  • Delyfer, M.-N., Raffelsberger, W., Mercier, D., Korobelnik, J.-F., Gaudric, A., Charteris, D. G., Tadayoni, R., Metge, F., Caputo, G., Barale, P.-O., Ripp, R., Muller, J.-D., Poch, O., Sahel, J.-A. and Léveillard, T. (2011). Transcriptomic analysis of human retinal detachment reveals both inflammatory response and photoreceptor death. PLoS ONE 6 e28791.
  • Edgar, R., Domrachev, M. and Lash, A. E. (2002). Gene expression omnibus: NCBI gene expression and hybridization array data repository. Nucleic Acids Res. 30 207–210.
  • Franklin, A. J., Yu, M. and Maturi, R. K. (2002). Tobacco smoking negatively affects the outcome of retinal detachment repair. Investigative Ophthalmology and Vision Science 43 635.
  • Gentleman, R., Carey, V. J., Huber, W., Irizarry, R. A. and Dudoit, S., eds. (2005). Bioinformatics and Computational Biology Solutions Using R and Bioconductor. Springer, New York.
  • Getz, G., Levine, E., Domany, E. and Zhang, M. Q. (2000). Super-paramagnetic clustering of yeast gene expression profiles. Phys. A 279 457–464.
  • Geyer, C. J. and Thompson, E. A. (1995). Annealing Markov chain Monte Carlo with applications to ancestral inference. J. Amer. Statist. Assoc. 90 909–920.
  • Gu, J. and Liu, S. J. (2008). Bayesian biclustering of gene expression data. BMC Genomics 9 (Suppl. 1) 113–120. From The 2007 Int. Conf. on Bioinformatics & Computational Biology (BIOCOMP$'$07), Las Vegas, Nevada, USA (2007).
  • Guérin, E., Raffelsberger, W., Pencreach, E., Maier, A., Neuville, A., Schneider, A., Bachellier, P., Rohr, S., Petitprez, A., Poch, O., Moras, D., Oudet, P., Larsen, A. K., Gaub, M. P. and Guenot, D. (2012). In vivo topoisomerase I inhibition attenuates the expression of Hypoxia Inducible Factor 1 alpha target genes and decreases tumor angiogenesis. Molecular Medicine 18 83–94.
  • Hackstadt, A. J. and Hess, A. M. (2009). Filtering for increased power for microarray data analysis. BMC Bioinformatics 10 11.
  • Hang, S., You, Z. and Chun, L. Y. (2009). Incorporating biological knowledge into density-based clustering analysis of gene expression data. In Proceedings of the 2009 Sixth International Conference on Fuzzy Systems and Knowledge Discovery, China, Vol. 05. FSKD ’09 52–56. IEEE Press, Piscataway, NJ.
  • Hartigan, J. A. (1972). Direct clustering of a data matrix. J. Amer. Statist. Assoc. 67 123–129.
  • Hochreiter, S., Bodenhofer, U., Heusel, M., Mayr, A., Mitterecker, A., Kasim, A., Khamiakova, T., Sanden, S. V., Lin, D., Talloen, W., Bijnens, L., Göhlmann, H. W. H., Shkedy, Z. and Clevert, D.-A. (2010). FABIA: Factor analysis for bicluster acquisition. Bioinformatics 26 1520–1527.
  • Ising, E. (1925). Beitrag zur Theorie des Ferromagnetismus. Zeitschrift für Physik A Hadrons and Nuclei 31 253–258.
  • Jensen, L. J., Kuhn, M., Stark, M., Chaffron, S., Creevey, C., Muller, J., Doerks, T., Julien, P., Roth, A., Simonovic, M., Bork, P. and von Mering, C. (2009). STRING 8—A global view on proteins and their functional interactions in 630 organisms. Nucleic Acids Res. 37 D412–D416.
  • Jolliffe, A. K. and Derry, W. B. (2013). The TP53 signaling network in mammals and worms. Brief Funct. Genomics 12 129–141.
  • Kanehisa, M. and Goto, S. (2000). KEGG: Kyoto encyclopedia of genes and genomes. Nucleic Acids Res. 28 27–30.
  • Kerr, G., Ruskin, H. J., Crane, M. and Doolan, P. (2008). Techniques for clustering gene expression data. Comput. Biol. Med. 38 283–293.
  • Kluger, Y., Basri, R., Chang, J. T. and Gerstein, M. (2003). Spectral biclustering of microarray cancer data: Co-clustering genes and conditions. Genome Research 13 703–716.
  • Lazzeroni, L. and Owen, A. (2002). Plaid models for gene expression data. Statist. Sinica 12 61–86.
  • Lin, D. (1998). An information-theoretic definition of similarity. In Proceedings of the 15th International Conference on Machine Learning 296–304. Morgan Kaufmann, San Francisco, CA.
  • Lord, P., Stevens, R., Brass, A. and Goble, C. (2003). Semantic similarity measures as tools for exploring the gene ontology. Pac. Symp. Biocomput. 8 601–612.
  • Madeira, S. C. and Oliveira, A. L. (2004). Biclustering algorithms for biological data analysis: A survey. IEEE Transactions on Computational Biology and Bioinformatics 1 24–45.
  • Mewes, H. W., Heumann, K., Kaps, A., Mayer, K., Pfeiffer, F., Stocker, S. and Frishman, D. (1999). MIPS: A database for genomes and protein sequences. Nucleic Acids Res. 27 44–48.
  • Murua, A., Stanberry, L. and Stuetzle, W. (2008). On Potts model clustering, kernel $K$-means, and density estimation. J. Comput. Graph. Statist. 17 629–658.
  • Murua, A. and Wicker, N. (2014). The conditional-Potts clustering model. J. Comput. Graph. Statist. 23 717–739.
  • Newton, M. A., Kendziorski, C. M., Richmond, C. S., Blattner, F. R. and Tsui, K. W. (2001). On differential variability of expression ratios: Improving statistical inference about gene expression changes from microarray data. J. Comput. Biol. 8 37–52.
  • Park, M. Y., Hastie, T. and Tibshirani, R. (2007). Averaged gene expressions for regression. Biostatistics 8 212–227.
  • Prelić, A., Bleuler, S., Zimmermann, P., Wille, A., Bühlmann, P., Gruissem, W., Hennig, L., Thiele, L. and Zitzler, E. (2006). A systematic comparison and evaluation of biclustering methods for gene expression data. Bioinformatics 22 1122–1129.
  • Purdom, E. and Holmes, S. P. (2005). Error distribution for gene expression data. Stat. Appl. Genet. Mol. Biol. 4 Art. 16, 35 pp. (electronic).
  • Resnik, P. (1999). Semantic similarity in a taxonomy: An information based measure and its application to problems of ambiguity in natural language. J. Artificial Intelligence Res. 11 95–130.
  • Rustici, G., Mata, J., Kivinen, K., Lió, P., Penkett, C. J., Burns, G., Hayles, J., Brazma, A., Nurse, P. and Bähler, J. (2004). Periodic gene expression program of the fission yeast cell cycle. Nat. Genet. 36 809–817.
  • Santamaria, R., Quintales, L. and Theron, R. (2007). Methods to bicluster validation and comparison in microarray data. In Intelligent Data Engineering and Automated Learning—IDEAL 2007. Lecture Notes in Computer Science 4881. Springer, Berlin.
  • Sokal, A. (1997). Monte Carlo methods in statistical mechanics: Foundations and new algorithms. In Functional Integration (Cargèse, 1996) (C. DeWitt-Morette, P. Cartier and A. Folacci, eds.). NATO Adv. Sci. Inst. Ser. B Phys. 361 131–192. Springer, New York.
  • Stanberry, L., Murua, A. and Cordes, D. (2008). Functional connectivity mapping using the ferromagnetic Potts spin model. Human Brain Mapping 29 422–440.
  • Stark, G. R. and Darnell, J. E. Jr. (2012). The JAK-STAT pathway at twenty. Immunity 36 503–514.
  • Stingo, F. C., Chen, Y. A., Tadesse, M. G. and Vannucci, M. (2011). Incorporating biological information into linear models: A Bayesian approach to the selection of pathways and genes. Ann. Appl. Stat. 5 1978–2002.
  • Swendsen, R. H. and Wang, J.-S. (1987). Nonuniversal critical dynamics in Monte Carlo simulations. Phys. Rev. Lett. 58 86–88.
  • Tanay, A., Sharan, R. and Shamir, R. (2002). Discovering statistically significant biclusters in gene expression data. Bioinformatics 18 136–144.
  • Tanay, A., Sharan, R. and Shamir, R. (2005). Biclustering algorithms: A survey. In Handbook of Computational Molecular Biology (S. Aluru, ed.). Chapman & Hall/CRC, Boca Raton, FL.
  • Tavazoie, S., Hughes, J. D., Campbell, M. J., Cho, R. J. and Church, G. M. (1999). Systematic determination of genetic network architecture. Nat. Genet. 22 281–285.
  • Turner, H., Bailey, T. and Krzanowski, W. (2005). Improved biclustering of microarray data demonstrated through systematic performance tests. Comput. Statist. Data Anal. 48 235–254.
  • Vannucci, M. and Stingo, F. C. (2010). Bayesian models for variable selection that incorporate biological information. In Bayesian Statistics 9 (J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West, eds.) 659–678. Oxford Univ. Press, London.
  • Vignes, M. and Forbes, F. (2009). Gene clustering via integrated Markov models combining individual and pairwise features. IEEE/ACM Transactions on Computational Biology and Bioinformatics 6 260–270.
  • Wang, F. and Landau, D. P. (2001). Efficient, multiple-range random walk algorithm to calculate the density of states. Phys. Rev. Lett. 86 2050–2053.
  • Ward, J. H. Jr. (1963). Hierarchical grouping to optimize an objective function. J. Amer. Statist. Assoc. 58 236–244.
  • Wässle, H. (2004). Parallel processing in the mammalian retina. Nat. Rev. Neurosci. 5 747–757.
  • Winkler, G. (2003). Image Analysis, Random Fields and Markov Chain Monte Carlo Methods. A Mathematical Introduction, 2nd ed. Applications of Mathematics (New York) 27. Springer, Berlin.
  • Yeung, K. Y., Fraley, C., Murua, A., Raftery, A. E. and Ruzzo, W. L. (2001). Model-based clustering and data transformations for gene expression data. Bioinformatics 17 977–987.
  • Zhang, J. (2010). A Bayesian model for biclustering with applications. J. R. Stat. Soc. Ser. C. Appl. Stat. 59 635–656.

Supplemental materials

  • Supplement to “The Gibbs-plaid biclustering model”. A high-resolution version of the image shown in Figure 6, as well as the complete biclustering results associated with the RD data have been provided as supplementary material. A proof of the convergence of the stochastic algorithm of Section 3 and further details on Lin’s similarity (Section 2.2) are also included.