An analysis of penalized interaction models

Preprint, Other literature type English OPEN
Zhao, Junlong; Leng, Chenlei;
  • Publisher: Bernoulli Society for Mathematical Statistics and Probability
  • Journal: issn: 1350-7265
  • Related identifiers: doi: 10.3150/15-BEJ715
  • Subject: restricted eigenvalue condition | Mathematics - Statistics Theory | interaction models | Lasso | hierarchical variable selection | high-dimensionality | convergence rate

An important consideration for variable selection in interaction models is to design an appropriate penalty that respects hierarchy of the importance of the variables. A common theme is to include an interaction term only after the corresponding main effects are present... View more
  • References (33)
    33 references, page 1 of 4

    [1] Bach, F., Jenatton, R., Mairal, J. and Obozinski, G. (2012). Structured sparsity through convex optimization. Statist. Sci. 27 450-468. MR3025128

    [2] Bickel, P.J., Ritov, Y. and Tsybakov, A.B. (2009). Simultaneous analysis of lasso and Dantzig selector. Ann. Statist. 37 1705-1732. MR2533469

    [3] Bickel, P.J., Ritov, Y. and Tsybakov, A.B. (2010). Hierarchical selection of variables in sparse high-dimensional regression. In Borrowing Strength: Theory Powering Applications-a Festschrift for Lawrence D. Brown. Inst. Math. Stat. Collect. 6 56-69. Beachwood, OH: IMS. MR2798511

    [4] Bien, J., Taylor, J. and Tibshirani, R. (2013). A LASSO for hierarchical interactions. Ann. Statist. 41 1111-1141. MR3113805

    [5] Candes, E. and Tao, T. (2007). The Dantzig selector: Statistical estimation when p is much larger than n. Ann. Statist. 35 2313-2351. MR2382644

    [6] Choi, N.H., Li, W. and Zhu, J. (2010). Variable selection with the strong heredity constraint and its oracle property. J. Amer. Statist. Assoc. 105 354-364. MR2656056

    [7] Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc. 96 1348-1360. MR1946581

    [8] Fang, Y.G., Loparo, K.A. and Feng, X. (1994). Inequalities for the trace of matrix product. IEEE Trans. Automat. Control 39 2489-2490. MR1337578

    [9] Hall, P. and Xue, J.-H. (2014). On selecting interacting features from high-dimensional data. Comput. Statist. Data Anal. 71 694-708. MR3132000

    [10] Hao, N. and Zhang, H.H. (2012). Interaction selection under marginality principle in high dimensional regression. Manuscript.

  • Related Research Results (1)
  • Metrics
    No metrics available
Share - Bookmark