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## Features of Big Data and sparsest solution in high confidence set

Citations: | 2 - 2 self |

### Citations

13234 | The Nature of Statistical Learning Theory
- Vapnik
- 1995
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Citation Context ...L(θ, y) = b(θ) − θy under the canonical link where b(θ) is a modeldependent convex function, robust regression with L(θ, y) = |y− θ|, the hinge loss L(θ, y) = (1 − θy)+ in the support vector machine (=-=Vapnik, 1999-=-) and exponential loss L(θ, y) = exp(−θy) in AdaBoost (Freund and Schapire, 1997; Breiman, 1998) in classification in which y takes values ±1, among others. Let Ln(β) = 1 n n∑ i=1 L(X>i β, Yi) be the ... |

4212 | Regression shrinkage and selection via the lasso,”
- Tibshirani
- 1996
(Show Context)
Citation Context ...inference. In response to these challenges, many new statistical tools have been developed. These include boosting algorithms (Freund and Schapire, 1997; Bickel et al., 2006), regularization methods (=-=Tibshirani, 1996-=-; Chen et al., 1998; Fan and Li, 2001; Candès and Tao, 2007; Fan and Lv, 2011; Negahban et al., 2012), and screening methods (Fan and Lv, 2008; Hall et al., 2009; Li et al., 2012). According to Bicke... |

3499 | A Decision-theoretic Generalization of On-line Learning and an Application to Boosting. in
- Freund, Schapire
- 1995
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Citation Context ... high-confident set as a viable solution to high-dimensional statistical inference. In response to these challenges, many new statistical tools have been developed. These include boosting algorithms (=-=Freund and Schapire, 1997-=-; Bickel et al., 2006), regularization methods (Tibshirani, 1996; Chen et al., 1998; Fan and Li, 2001; Candès and Tao, 2007; Fan and Lv, 2011; Negahban et al., 2012), and screening methods (Fan and L... |

3480 | The elements of statistical learning, - Hastie, Tibshirani, et al. - 2009 |

3178 |
Generalized Linear Models.
- McCullagh, Nelder
- 1989
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Citation Context ...or β0 ∈ Rp such that it minimizes L(β) = E{L(X>β, Y )}, in which the loss function is assumed convex in the first argument so that L(β) is convex. The setup encompasses the generalized linear models (=-=McCullagh and Nelder, 1989-=-) with L(θ, y) = b(θ) − θy under the canonical link where b(θ) is a modeldependent convex function, robust regression with L(θ, y) = |y− θ|, the hinge loss L(θ, y) = (1 − θy)+ in the support vector ma... |

2728 | Atomic decomposition by basis pursuit,
- Chen, Donoho, et al.
- 1998
(Show Context)
Citation Context ...onse to these challenges, many new statistical tools have been developed. These include boosting algorithms (Freund and Schapire, 1997; Bickel et al., 2006), regularization methods (Tibshirani, 1996; =-=Chen et al., 1998-=-; Fan and Li, 2001; Candès and Tao, 2007; Fan and Lv, 2011; Negahban et al., 2012), and screening methods (Fan and Lv, 2008; Hall et al., 2009; Li et al., 2012). According to Bickel (2008), the main ... |

948 | Variable selection via nonconcave penalized likelihood and its oracle properties’,
- Fan, Li
- 2001
(Show Context)
Citation Context ...enges, many new statistical tools have been developed. These include boosting algorithms (Freund and Schapire, 1997; Bickel et al., 2006), regularization methods (Tibshirani, 1996; Chen et al., 1998; =-=Fan and Li, 2001-=-; Candès and Tao, 2007; Fan and Lv, 2011; Negahban et al., 2012), and screening methods (Fan and Lv, 2008; Hall et al., 2009; Li et al., 2012). According to Bickel (2008), the main goals of high-dime... |

879 | The Dantzig Selector: Statistical Estimation When p is Much Larger than n,” - Candes, Tao - 2007 |

283 | Sure independence screening for ultrahigh dimensional feature space.
- Fan, Lv
- 2008
(Show Context)
Citation Context ...ire, 1997; Bickel et al., 2006), regularization methods (Tibshirani, 1996; Chen et al., 1998; Fan and Li, 2001; Candès and Tao, 2007; Fan and Lv, 2011; Negahban et al., 2012), and screening methods (=-=Fan and Lv, 2008-=-; Hall et al., 2009; Li et al., 2012). According to Bickel (2008), the main goals of high-dimensional inference are to construct as effective a method as possible to predict future observations, to ga... |

218 | A unified framework for high-dimensional analysis of m-estimators with decomposable regularizers.
- Negahban, Yu, et al.
- 2009
(Show Context)
Citation Context ...e include boosting algorithms (Freund and Schapire, 1997; Bickel et al., 2006), regularization methods (Tibshirani, 1996; Chen et al., 1998; Fan and Li, 2001; Candès and Tao, 2007; Fan and Lv, 2011; =-=Negahban et al., 2012-=-), and screening methods (Fan and Lv, 2008; Hall et al., 2009; Li et al., 2012). According to Bickel (2008), the main goals of high-dimensional inference are to construct as effective a method as poss... |

86 | Geometric representation of high dimension low sample size data, submitted to - Hall, Marron, et al. - 2004 |

80 | High-dimensional classification using features annealed independence rules. Ann Statist.
- Fan, Fan
- 2008
(Show Context)
Citation Context ...ss and selected the best m features from the p-dimensional space, according to the absolute values of the components of µ1; this is an infeasible procedure, but can be well estimated when m is small (=-=Fan and Fan, 2008-=-). We then projected the m-dimensional data on their first two principal components. Figure 43.5 presents their projections for various values of m. Clearly, when m = 2, these two projections have hig... |

58 |
Arcing classifier. The annals of statistics.
- Breiman
- 1998
(Show Context)
Citation Context ...obust regression with L(θ, y) = |y− θ|, the hinge loss L(θ, y) = (1 − θy)+ in the support vector machine (Vapnik, 1999) and exponential loss L(θ, y) = exp(−θy) in AdaBoost (Freund and Schapire, 1997; =-=Breiman, 1998-=-) in classification in which y takes values ±1, among others. Let Ln(β) = 1 n n∑ i=1 L(X>i β, Yi) be the empirical loss and L′n(β) be its gradient. Given that L ′(β0) = 0, a natural confidence set is ... |

55 | Properties of non-concave penalized likelihood with NP-
- Fan, Lv
- 2010
(Show Context)
Citation Context ...en developed. These include boosting algorithms (Freund and Schapire, 1997; Bickel et al., 2006), regularization methods (Tibshirani, 1996; Chen et al., 1998; Fan and Li, 2001; Candès and Tao, 2007; =-=Fan and Lv, 2011-=-; Negahban et al., 2012), and screening methods (Fan and Lv, 2008; Hall et al., 2009; Li et al., 2012). According to Bickel (2008), the main goals of high-dimensional inference are to construct as eff... |

50 | Ultrahigh dimensional feature selection: beyond the linear model, - Fan, Samworth, et al. - 2009 |

38 | A constrained `1 minimization approach to sparse precision matrix estimation,” - Cai, Liu, et al. - 2011 |

31 | Variance estimation using refitted cross-validation in ultrahigh dimensional regression. Arxiv preprint arXiv:1004.5178. - Fan, Guo, et al. - 2010 |

22 | Feature Screening via Distance Correlation Learning.
- Li, Zhong, et al.
- 2012
(Show Context)
Citation Context ...larization methods (Tibshirani, 1996; Chen et al., 1998; Fan and Li, 2001; Candès and Tao, 2007; Fan and Lv, 2011; Negahban et al., 2012), and screening methods (Fan and Lv, 2008; Hall et al., 2009; =-=Li et al., 2012-=-). According to Bickel (2008), the main goals of high-dimensional inference are to construct as effective a method as possible to predict future observations, to gain insight into the relationship bet... |

19 | Some theory for generalized boosting algorithms
- Bickel, Ritov, et al.
(Show Context)
Citation Context ...able solution to high-dimensional statistical inference. In response to these challenges, many new statistical tools have been developed. These include boosting algorithms (Freund and Schapire, 1997; =-=Bickel et al., 2006-=-), regularization methods (Tibshirani, 1996; Chen et al., 1998; Fan and Li, 2001; Candès and Tao, 2007; Fan and Lv, 2011; Negahban et al., 2012), and screening methods (Fan and Lv, 2008; Hall et al.,... |

19 | Phase transition in limiting distributions of coherence of highdimensional random matrices. - Cai, Jiang - 2012 |

19 | 2007), “Variable selection in finite mixtures of regression models - Khalili, Chen |

16 |
Tilting methods for assessing the influence of components in a classifier
- Hall, Titterington, et al.
- 2009
(Show Context)
Citation Context ...et al., 2006), regularization methods (Tibshirani, 1996; Chen et al., 1998; Fan and Li, 2001; Candès and Tao, 2007; Fan and Lv, 2011; Negahban et al., 2012), and screening methods (Fan and Lv, 2008; =-=Hall et al., 2009-=-; Li et al., 2012). According to Bickel (2008), the main goals of high-dimensional inference are to construct as effective a method as possible to predict future observations, to gain insight into the... |

6 | Population genomics of human gene expression. Nature Genetics 39 - Stranger, Nica, et al. - 2007 |

4 | l1-penalization for mixture regression models (with discussion - Städler, Bühlmann, et al. - 2010 |

3 | Discussion on the paper “Sure independence screening for ultrahigh dimensional feature space” by Fan and Lv - Bickel - 2008 |

1 | 522 Features of Big Data - Bühlmann, Geer - 2011 |

1 | Endogeneity in ultrahigh dimension. Available at SSRN - Fan, Liao - 2012 |