Sure independence screening for ultrahigh dimensional feature space Discussion

By Peter J. Bickel, Peter Buhlmann, Qiwei Yao, Richard J. Samworth, Peter Hall, D. M. Titterington, Jing-Hao Xue, C. Anagnostopoulos, Dk Tasoullis, Wenyang Zhang and 31 more. 2008

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Citations in the corpus

On asymptotically optimal confidence regions and tests for high-dimensional models (2013, background): “The vast majority of work has been pursued for point estimation such as consistency for prediction [21, 7], oracle inequalities and estimation of a high-dimensional parameter [12, 11, 50, 45, 33, 6, 34, 24] or variable selection [30, 53, 17, 48].”
Challenges of Big Data Analysis (2013, unknown): “An effective variable screening technique based on marginal screening has been proposed by the authors of [11].”
Model-Free Feature Screening for Ultrahigh Dimensional Data (2011, methodology): “Similarly to the iterative SIS procedures, we also propose an iterative version of our new screening method.”
Ultrahigh dimensional feature selection: beyond the linear model (2009, methodology): “Under certain regularity conditions, Fan & Lv (2008) show surprisingly that this fast feature selection method has a ‘sure screening property’; that is, with probability very close to 1, the in-dependence screening technique retains all of the important features in the model.”
A Selective Overview of Variable Selection in High Dimensional Feature Space (2009, methodology): “…can be estimated by | ˆ α j | / ˆ σ j , where the latter is in fact n/ ( n 1 n 2 ) T j | , in which the pooled sample variance is used. p This is indeed the same as ranking the feature by using the correlation between the j th variable with the class response ± 1 when n 1 = n 2 (Fan and Lv (2008)).”
Large Covariance Estimation by Thresholding Principal Orthogonal Complements (2011, unknown): “6See Fan, Liao and Mincheva (2011), working paper, arxiv.org/pdf/1201.0175.pdf Assumption 3.4.”
High-Dimensional Sparse Additive Hazards Regression (2012, methodology): “In the contexts of (generalized) linear models, this class of penalty functions has been studied by Lv and Fan (2009) and Fan and Lv (2011). Of particular interest are the following examples.”
Semiparametric Ultra-High Dimensional Model Averaging of Nonlinear Dynamic Time Series (2018, unknown): “To further the comparison, we also employ the iterative sure independence screening (ISIS) method proposed in Fan and Lv (2008), the penalized method for highdimensional generalized additive models (penGAM) proposed in Meier, van de Geer, and Bühlmann (2009), and the oracle additive modeling with…”
Quantile-adaptive model-free variable screening for high-dimensional heterogeneous data (2013, methodology): “Fan and Lv (2008) proposed the sure independence screening (SIS) methodology for linear regression which screens variables by ranking their marginal correlations with the response variable.”
NONCONCAVE PENALIZED M-ESTIMATION WITH A DIVERGING NUMBER OF PARAMETERS (2011, methodology): “It also addresses the gap between the SIS (Fan and Lv (2008)) and nonconcave penalized methods.”
Feature Screening via Distance Correlation Learning (2012, methodology): “Compared with the model-based screening procedures (Fan and Lv 2008; Fan, Samworth, and Wu 2009; Wang 2009; Fan and Song 2010; Fan, Feng, and Song 2011), the DCSIS is a model-free screening procedure.”
The Dantzig Selector in Cox's Proportional Hazards Model (2009, unknown): “…data set and one way to reach an upper bound on p that achieves this is to extend and use a concept similar to that of sure screening proposed recently by Fan & Lv (2008) in the linear regression setting to reduce high dimensionality to a relatively smaller scale, possibly below the sample size.”
Strong rules for discarding predictors in lasso-type problems (2010, background): “Also, Fan and Lv (2008) studied the screening of variables based on their inner products in the lasso and related problems, but not from an optimization point of view; their screening rules may again set coefficients to 0 that are non-zero in the solution; however, they argued that under certain sit”
Tuning Parameter Selection for the Adaptive Lasso Using ERIC (2015, methodology): “To overcome this problem, we adapt the two-stage approach of Zou (2006) and Wang and Zhu (2011), and apply SIS (Fan and Lv 2008; Fan et al. 2010b) at a first stage to reduce the dimensionality of the problem from p to dn = O(nκ ) where κ ∈ (0, 1).”
Confidence intervals for low dimensional parameters in high dimensional linear models (2011, methodology): “…methods (Frank and Friedman, 1993; Fan and Li, 2001; Fan and Peng, 2004; Kim et al., 2008; Zhang, 2010; Zhang and Zhang, 2012), greedy methods (Zhang, 2011a), adaptive methods (Zou, 2006; Huang et al., 2008; Zhang, 2011b; Zhang and Zhang, 2012), screening methods (Fan and Lv, 2008), and more.”
Independent screening for single‐index hazard rate models with ultrahigh dimensional features (2011, methodology): “Following Fan and Lv (2008) and Fan et al. (2009), we would typically choose γ n such that | M n pre | is of order n / log n .”
Fast Computing for Distance Covariance (2014, methodology): “Both the SIS and the SIRS have little chance to identify the important predictors X1 and X2 in models (1.b) and (1.c), and X22 in model (1.d).”
A variational Bayes approach to variable selection (2017, background): “This might be mitigated to a certain extent but the use of screening procedures such as sure independence screening (Fan and Lv, 2008) which can be seen as searching for a correct model with high probability.”