Advertisement

Graphical Multi-way Models

  • Ilkka Huopaniemi
  • Tommi Suvitaival
  • Matej Orešič
  • Samuel Kaski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6321)

Abstract

Multivariate multi-way ANOVA-type models are the default tools for analyzing experimental data with multiple independent covariates. However, formulating standard multi-way models is not possible when the data comes from different sources or in cases where some covariates have (partly) unknown structure, such as time with unknown alignment. The “small n, large p”, large dimensionality p with small number of samples n, settings bring further problems to the standard multivariate methods. We extend our recent graphical multi-way model to three general setups, with timely applications in biomedicine: (i) multi-view learning with paired samples, (ii) one covariate is time with unknown alignment, and (iii) multi-view learning without paired samples.

Keywords

ANOVA Bayesian latent variable modeling data integration multi-view learning multi-way learning 

References

  1. 1.
    Bach, F.R., Jordan, M.I.: A probabilistic interpretation of canonical correlation analysis. Tech. Rep. 688, Department of Statistics, University of California, Berkeley (2005)Google Scholar
  2. 2.
    Bishop, C.M.: Bayesian PCA. In: Kearns, M.S., Solla, S., Cohn, D. (eds.) Advances in Neural Information Processing Systems, vol. 11, pp. 382–388. MIT Press, Cambridge (1999)Google Scholar
  3. 3.
    Costa, I.G., Schonhuth, A., Hafemeister, C., Schliep, A.: Constrained mixture estimation for analysis and robust classification of clinical time series. Bioinformatics 25(12), i6–i14 (2009)CrossRefGoogle Scholar
  4. 4.
    Fisher, R.: The correlation between relatives on the supposition of mendelian inheritance. Royal Society of Edinburgh from Transactions of the Society 52, 399–433 (1918)Google Scholar
  5. 5.
    Huopaniemi, I., Suvitaival, T., Nikkilä, J., Orešič, M., Kaski, S.: Multivariate multi-way analysis of multi-source data. Bioinformatics 26, i391–i398 (2010)CrossRefGoogle Scholar
  6. 6.
    Huopaniemi, I., Suvitaival, T., Nikkilä, J., Orešič, M., Kaski, S.: Two-way analysis of high-dimensional collinear data. Data Mining and Knowledge Discovery 19(2), 261–276 (2009)CrossRefGoogle Scholar
  7. 7.
    Klami, A., Kaski, S.: Local dependent components. In: Ghahramani, Z. (ed.) Proceedings of ICML 2007, the 24th International Conference on Machine Learning, pp. 425–432. Omni Press (2007)Google Scholar
  8. 8.
    Langsrud, O.: 50-50 multivariate analysis of variance for collinear responses. Journal of the Royal Statistical Society Series D-the Statistician 51, 305–317 (2002)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Lu, Y., Huggins, P., Bar-Joseph, Z.: Cross species analysis of microarray expression data. Bioinformatics 25(12), 1476–1483 (2009)CrossRefGoogle Scholar
  10. 10.
    Lucas, J., Carvalho, C., West, M.: A bayesian analysis strategy for cross-study translation of gene expression biomarkers. Statistical Applications in Genetics and Molecular Biology 8(1), 11 (2009)CrossRefGoogle Scholar
  11. 11.
    Nikkilä, J., Sysi-Aho, M., Ermolov, A., Seppänen-Laakso, T., Simell, O., Kaski, S., Orešič, M.: Gender dependent progression of systemic metabolic states in early childhood. Molecular Systems Biology 4, 197 (2008)CrossRefGoogle Scholar
  12. 12.
    Orešič, M., et al.: Dysregulation of lipid and amino acid metabolism precedes islet autoimmunity in children who later progress to type 1 diabetes. Journal of Experimental Medicine 205(13), 2975–2984 (2008)CrossRefGoogle Scholar
  13. 13.
    Tripathi, A., Klami, A., Kaski, S.: Using dependencies to pair samples for multi-view learning. In: Proceedings of ICASSP 2009, the International Conference on Acoustics, Speech, and Signal Processing, pp. 1561–1564 (2009)Google Scholar
  14. 14.
    West, M.: Bayesian factor regression models in the large p, small n paradigm. Bayesian Statistics 7, 723–732 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Ilkka Huopaniemi
    • 1
  • Tommi Suvitaival
    • 1
  • Matej Orešič
    • 2
  • Samuel Kaski
    • 1
  1. 1.Department of Information and Computer Science, Helsinki Institute for, Information Technology HIITAalto University School of Science and TechnologyAaltoFinland
  2. 2.VTT Technical Research Centre of FinlandVTT, EspooFinland

Personalised recommendations