The Annals of Applied Statistics

Structured, sparse regression with application to HIV drug resistance

Daniel Percival, Kathryn Roeder, Roni Rosenfeld, and Larry Wasserman

Full-text: Open access

Abstract

We introduce a new version of forward stepwise regression. Our modification finds solutions to regression problems where the selected predictors appear in a structured pattern, with respect to a predefined distance measure over the candidate predictors. Our method is motivated by the problem of predicting HIV-1 drug resistance from protein sequences. We find that our method improves the interpretability of drug resistance while producing comparable predictive accuracy to standard methods. We also demonstrate our method in a simulation study and present some theoretical results and connections.

Article information

Source
Ann. Appl. Stat. Volume 5, Number 2A (2011), 628-644.

Dates
First available in Project Euclid: 13 July 2011

Permanent link to this document
http://projecteuclid.org/euclid.aoas/1310562198

Digital Object Identifier
doi:10.1214/10-AOAS428

Mathematical Reviews number (MathSciNet)
MR2840168

Zentralblatt MATH identifier
1223.62164

Citation

Percival, Daniel; Roeder, Kathryn; Rosenfeld, Roni; Wasserman, Larry. Structured, sparse regression with application to HIV drug resistance. Ann. Appl. Stat. 5 (2011), no. 2A, 628--644. doi:10.1214/10-AOAS428. http://projecteuclid.org/euclid.aoas/1310562198.


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References

  • Barron, A. R., Cohen, A., Dahmen, W. and DeVore, R. A. (2008). Approximation and learning by greedy algorithms. Ann. Statist. 36 64–94.
  • Beerenwinkel, N., Daumer, M., Oette, M., Korn, K., Hoffmann, D., Kaiser, R., Lengauer, T., Selbig, J. and Walter, H. (2003). Geno2pheno: Estimating phenotypic drug resistance from HIV-1 genotypes. Nucleic Acids Res. 31 3850–3855.
  • Bunea, F., Tsybakov, A. and Wegkamp, M. (2007). Sparsity oracle inequalities for the lasso. Electron. J. Statist. 1 169–194.
  • Friedman, J., Hastie, T. and Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. J. Statist. Software 33 1–13.
  • Greenshtein, E. and Ritov, Y. (2004). Persistency in high dimensional linear predictor-selection and the virtue of over-parametrization. Bernoulli 10 971–988.
  • Huang, J., Zhang, T. and Metaxas, D. (2009). Learning with structured sparsity. In ICML’09: Proceedings of the 26th Annual International Conference on Machine Learning 417–424. ACM, New York.
  • Jacob, L., Obozinski, G. and Vert, J.-P. (2009). Group lasso with overlap and graph lasso. In ICML’09: Proceedings of the 26th Annual International Conference on Machine Learning 433–440. ACM, New York.
  • Liu, D., Lin, X. and Ghosh, D. (2007). Semiparametric regression for multi-dimensional genomic pathway data: Least square kernel machines and linear mixed models. Biometrics 63 1079–1088.
  • Petropoulos, C. J., Parkin, N. T., Limoli, K. L., Lie, Y. S., Wrin, T., Huang, W., Tian, H., Smith, D., Winslow, G. A., Capon, D. J. and Whitcomb, J. M. (2000). A novel phenotypic drug susceptibility assay for human immunodeficiency virus type 1. Antimicrobial Agents and Chemotherapy 44 920–928.
  • Rhee, S.-Y., Gonzales, M. J., Kantor, R., Betts, B. J., Ravela, J. and Shafer, R. W. (2003). Human immunodeficiency virus reverse transcriptase and protease sequence database. Nucleic Acids Res. 31 298–303.
  • Rhee, S.-Y., Taylor, J., Wadhera, G., Ben-Hur, A., Brutlag, D. L. and Shafer, R. W. (2006). Genotypic predictors of human immunodeficiency virus type 1 drug resistance. Proc. Natl. Acad. Sci. USA 103 17355–17360.
  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 58 267–288.
  • Tibshirani, R., Saunders, M., Rosset, S., Zhu, J. and Knight, K. (2005). Sparsity and smoothness via the fused lasso. J. Roy. Statist. Soc. Ser. B 67 91–108.
  • Wainwright, M. J. (2007). Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting. Available at arXiv:math/0702301v2.
  • Yuan, M. and Lin, Y. (2006). Model selection and estimation in regression with grouped variables. J. Roy. Statist. Soc. Ser. B 68 49–67.
  • Zhang, T. (2009). On the consistency of feature selection using greedy least squares regression. J. Mach. Learn. Res. 10 555–568.
  • Zhang, J., Rhee, S.-Y., Taylor, J. and Shafer, R. W. (2005). Comparison of the precision and sensitivity of the antivirogram and PhenoSense HIV drug susceptibility assays. Journal of Aquired Immune Deficiency Syndrones 38 439–444.