Penalized Composite Quasi-Likelihood for Ultrahigh-Dimensional Variable Selection
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Cites methods from "Penalized Composite Quasi-Likelihoo..."
...Fan et al. (2014), Bradic et al. (2011) introduced the penalized quantile regression with the weighted L1-penalty for robust regularization....
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Additional excerpts
...Fan and Li (2001), Zou and Li (2008), Bradic et al. (2011), and Fan and Lv (2011) propose methods for analyzing models defined by quasi-likelihood....
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Cites background or methods from "Penalized Composite Quasi-Likelihoo..."
...Knots are denoted by λ1 ≥ λ2 ≥ · · · ≥ λm ≥ 0, where m = min(n − 1, p) is the length of the solution path (Efron et al., 2004). Recent developments in high-dimensional regression focus on hypothesis testing for variable selection. Impressive progress has been made in Zhang & Zhang (2014), Van De Geer et al....
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...Bradic et al. (2011) studied the same samples for eQTL mapping but only focused on cis-eQTLs....
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...Table 4 reports the locations on the solution path of the variables identified in Bradic et al. (2011)....
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...Bradic et al. (2011) studied the same samples for eQTL mapping but only focused on cis-eQTLs. Therefore, the numbers of SNPs included in their analysis are much smaller with p = 1955, 1978, 2146 for the three populations, respectively. More SNP variables are identified in Bradic et al. (2011) for each population due to larger ratio of sample size to dimension....
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...Knots are denoted by λ1 ≥ λ2 ≥ · · · ≥ λm ≥ 0, where m = min(n − 1, p) is the length of the solution path (Efron et al., 2004). Recent developments in high-dimensional regression focus on hypothesis testing for variable selection. Impressive progress has been made in Zhang & Zhang (2014), Van De Geer et al. (2014), Lockhart et al. (2014), Barber & Candès (2015), Bogdan et al....
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References
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"Penalized Composite Quasi-Likelihoo..." refers background or methods in this paper
...…(16) can be recast as a penalized weighted least square regression argmin β n∑ i=1 w1∣∣∣Yi −XTi β̂ (0) ∣∣∣ + w2 ( Yi −XTi β )2 + n p∑ j=1 γλ(|β(0)j |)|βj | which can be efficiently solved by pathwise coordinate optimization (Friedman et al., 2008) or least angle regression (Efron et al., 2004)....
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...) are all nonnegative. This class of problems can be solved with fast and efficient computational algorithms such as pathwise coordinate optimization (Friedman et al., 2008) and least angle regression (Efron et al., 2004). One particular example is the combination of L 1 and L 2 regressions, in which K= 2, ρ 1(t) = |t−b 0|andρ 2(t) = t2. Here b 0 denotes themedian of error distributionε. Iftheerror distribution is sym...
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...i=1 w 1 Yi −XT i βˆ (0) +w 2 Yi −XT i β 2 +n Xp j=1 γλ(|β (0) j |)|βj| which can be efficiently solved by pathwise coordinate optimization (Friedman et al., 2008) or least angle regression (Efron et al., 2004). If b 0 6= 0, the penalized least-squares problem ( 16) is somewhat different from (5) since we have an additional parameter b 0. Using the same arguments, and treating b 0 as an additional parameter ...
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...This class of problems can be solved with fast and efficient computational algorithms such as pathwise coordinate optimization (Friedman et al., 2008) and least angle regression (Efron et al., 2004)....
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