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Jian Huang

  1. A Selective Review of Group Selection in High Dimensional Models.

    Tue, 05/01/2012 - 15:01 — SomNambul
    Authors: Shuangge Ma, Jian Huang, Patrick Breheny
    Subjects: Statistics
    Abstract

    Grouping structures arise naturally in many statistical modeling problems.
    Several methods have been proposed for variable selection that respect grouping
    structure in variables. Examples include the group LASSO and several concave
    group selection methods. In this article, we give a selective review of group
    selection concerning methodological developments, theoretical properties, and
    computational algorithms. We pay particular attention to group selection
    methods involving concave penalties. We address both group selection and
    bi-level selection methods.

  2. The sparse Laplacian shrinkage estimator for high-dimensional regression.

    Fri, 12/16/2011 - 15:01 — SomNambul
    Authors: Cun-Hui Zhang, Shuangge Ma, Jian Huang, Hongzhe Li
    Subjects: Statistics
    Abstract

    We propose a new penalized method for variable selection and estimation that
    explicitly incorporates the correlation patterns among predictors. This method
    is based on a combination of the minimax concave penalty and Laplacian
    quadratic associated with a graph as the penalty function. We call it the
    sparse Laplacian shrinkage (SLS) method. The SLS uses the minimax concave
    penalty for encouraging sparsity and Laplacian quadratic penalty for promoting
    smoothness among coefficients associated with the correlated predictors.

  3. Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection.

    Fri, 04/15/2011 - 15:01 — SomNambul
    Authors: Jian Huang, Patrick Breheny
    Subjects: Applications
    Abstract

    A number of variable selection methods have been proposed involving nonconvex
    penalty functions. These methods, which include the smoothly clipped absolute
    deviation (SCAD) penalty and the minimax concave penalty (MCP), have been
    demonstrated to have attractive theoretical properties, but model fitting is
    not a straightforward task, and the resulting solutions may be unstable.

  4. Consistent group selection in high-dimensional linear regression.

    Tue, 11/30/2010 - 16:01 — SomNambul
    Authors: Jian Huang, Fengrong Wei
    Subjects: Statistics
    Abstract

    In regression problems where covariates can be naturally grouped, the group
    Lasso is an attractive method for variable selection since it respects the
    grouping structure in the data. We study the selection and estimation
    properties of the group Lasso in high-dimensional settings when the number of
    groups exceeds the sample size. We provide sufficient conditions under which
    the group Lasso selects a model whose dimension is comparable with the
    underlying model with high probability and is estimation consistent.

  5. Variable selection in nonparametric additive models.

    Thu, 10/21/2010 - 15:01 — SomNambul
    Authors: Jian Huang, Joel L. Horowitz, Fengrong Wei
    Subjects: Statistics
    Abstract

    We consider a nonparametric additive model of a conditional mean function in
    which the number of variables and additive components may be larger than the
    sample size but the number of nonzero additive components is "small" relative
    to the sample size. The statistical problem is to determine which additive
    components are nonzero. The additive components are approximated by truncated
    series expansions with B-spline bases. With this approximation, the problem of
    component selection becomes that of selecting the groups of coefficients in the
    expansion.

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