Using Generalized Correlation to Effect Variable Selection in Very High Dimensional Problems

By Peter Hall, Hugh Miller. 2009

212 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b59687421f231999130709cf81f9ee90c37d9725

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Citations in the corpus

Using the bootstrap to quantify the authority of an empirical ranking (2009, methodology): “Hall and Miller (2009) used generalized correlation between the observed Y and each set of gene expressions Xj to rank the genes, and then applied the standard, synchronous bootstrap to give indicative prediction intervals for these rankings.”
A Selective Overview of Variable Selection in High Dimensional Feature Space (2009, methodology): “…Shaﬀer and Boldrick (2003); Storey and Tibshirani (2003); Fan and Ren (2006); Efron (2007)), feature ranking using a generalized correlation (Hall and Miller (2009a)), non-parametric learning under sparse additive models (Ravikumar et al. (2009)), and the method in Huang, Horowitz and Ma…”
Nonparametric Independence Screening in Sparse Ultra-High Dimensional Additive Models (2009, background): “Hall and Miller (2009) proposed a generalized correlation ranking, which allows nonlinear regression.”
Feature Screening via Distance Correlation Learning (2012, methodology): “The cardiomyopathy microarray dataset was once analyzed by Segal, Dahlquist, and Conklin (2003) and Hall and Miller (2009).”
Robust rank correlation based screening (2010, methodology): “suggested by Hall and Miller (2009) and Huang, Horowitz and Ma (2008), independence screening could be conducted with other criteria. For correlation relationships, there are several measurements in the literature, and the Kendall τ [Kendall (1938)] is a very commonly used one that is a correlation ”
Challenges of Big Data Analysis (2013, unknown): “For an overview, see [72] and [73].”
Quantile-adaptive model-free variable screening for high-dimensional heterogeneous data (2013, methodology): “The problem of nonlinear features screening was addressed in Hall and Miller (2009) using generalized correlation ranking and more systematically in Fan, Feng and Song (2011) using nonparametric marginal ranking, which extended the scope of applications of sure independence screening.”
Sequential sufficient dimension reduction for large p, small n problems (2015, background): “See also Huang et al. (2008), Fan et al. (2009), Fan and Song (2010) and Hall and Miller (2009).”
High dimensional ordinary least squares projection for screening variables (2015, methodology): “A number of papers have proposed alternative ways to improve the marginal correlation aspect of screening, see, for example, Hall, et al. (2009); Wang (2009, 2012); Cho and Fryzlewicz (2012).”
Rates of convergence of the Adaptive LASSO estimators to the Oracle distribution and higher order refinements by the bootstrap (2013, methodology): “The data, available from a microarray experiment was collected from Hall and Miller (2009) and originally used in Segal, Dahlquist and Conklin (2003). The data consisted of observations from n= 30 specimens on the Ro1 expression level (y), and genetic expression levels x= (x1, .”
Non-Concave Penalized Likelihood with NP-Dimensionality (2009, background): “Then the exponential bounds in (19) and (21) can be expressed as”
Sure independence screening in generalized linear models with NP-dimensionality (2009, background): “Hall and Miller (2009) proposed a generalized correlation ranking, which allows nonlinear regression.”