Multifactorial Dimensionality Reduction for Disordered Trait

Alexander Rakitko


We develop our recent works concerning the identification of the factors associated with a certain complex disease. The case of disordered discrete trait is studied. We build two models (3D and 2D) for the range of response variable indicating the state of the health of a patient. In this work we consider the problem of optimal forecast for response variable depending on a finite collection of factors with values in arbitrary finite set. The quality of prediction is described by the error function involving a penalty function. The estimation of the error requires some cross-validation procedure. The developed approach provides the basis to identify the set of significant factors. Such problem arises naturally, e.g., in the genome-wide association study. Using simulated data we illustrate the efficiency of our method.


  1. Adams, H. P., Bendixen, B. H., Kappelle, L. J., Biller, J., Love, B. B., Gordon, D. L., and Marsh (1993). Classification of subtype of acute ischemic stroke. Definitions for use in a multicenter clinical trial. TOAST. Trial of Org 10172 in Acute Stroke Treatment. Stroke, 24(1):35-41.
  2. Arlot, S. and Celisse, A. (2010). A survey of crossvalidation procedures for model selection. Statistics Surveys, 4:40-79.
  3. Bulinski, A. (2014). On foundation of the dimensionality reduction method for explanatory variables. Journal of Mathematical Sciences, 199(2):113-122.
  4. Bulinski, A. and Rakitko, A. (2014). Estimation of nonbinary random response. Doklady Mathematics, 89(2):225-229.
  5. Hastie, T., Tibshirani, R., and Friedman, J. (2001). The Elements of Statistical Learning. Springer Series in Statistics. Springer New York Inc., New York, NY, USA.
  6. Iman, R. L. and Conover, W. J. (1982). A distribution-free approach to inducing rank correlation among input variables. Communications in Statistics - Simulation and Computation, 11(3):311-334.
  7. Lee, S., Epstein, M. P., Duncan, R., and Lin, X. (2012). Sparse principal component analysis for identifying ancestry-informative markers in genome-wide association studies. Genetic Epidemiology, 36(4):293-302.
  8. Ritchie, M. D., Hahn, L. W., Roodi, N., Bailey, L. R., Dupont, W. D., Parl, F. F., and Moore, J. H. (2001). Multifactor-dimensionality reduction reveals high-order interactions among estrogen-metabolism genes in sporadic breast cancer. The American Journal of Human Genetics, 69(1):138 - 147.
  9. Ruczinski, I., Kooperberg, C., and LeBlanc, M. (2003). Logic regression. Journal of Computational and Graphical Statistics, 12(3):475-511.
  10. Sikorska, K., Lesaffre, E., Groenen, P. F. J., and Eilers, P. H. C. (2013). Gwas on your notebook: fast semiparallel linear and logistic regression for genomewide association studies. BMC Bioinformatics, pages 166-166.
  11. Tibshirani, R. J. and Taylor, J. (2012). Degrees of freedom in lasso problems. The Annals of Statistics, 40(2):1198-1232.
  12. Velez, D. R., White, B. C., Motsinger, A. A., Bush, W. S., Ritchie, M. D., Williams, S. M., and Moore, J. H. (2007). A balanced accuracy function for epistasis modeling in imbalanced datasets using multifactor dimensionality reduction. Genetic Epidemiology, 31(4):306-315.

Paper Citation

in Harvard Style

Rakitko A. (2015). Multifactorial Dimensionality Reduction for Disordered Trait . In Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms - Volume 1: BIOINFORMATICS, (BIOSTEC 2015) ISBN 978-989-758-070-3, pages 232-236. DOI: 10.5220/0005285302320236

in Bibtex Style

author={Alexander Rakitko},
title={Multifactorial Dimensionality Reduction for Disordered Trait},
booktitle={Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms - Volume 1: BIOINFORMATICS, (BIOSTEC 2015)},

in EndNote Style

JO - Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms - Volume 1: BIOINFORMATICS, (BIOSTEC 2015)
TI - Multifactorial Dimensionality Reduction for Disordered Trait
SN - 978-989-758-070-3
AU - Rakitko A.
PY - 2015
SP - 232
EP - 236
DO - 10.5220/0005285302320236