Regularization Paths for Generalized Linear Models via Coordinate Descent
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Cites methods from "Regularization Paths for Generalize..."
..., the logarithm of the density of the Normal prior (up to an additive constant), can be read as a ridge penalty term, and therefore, we perform the optimization using the iteratively reweighted ridge regression algorithm [55], also known as weighted updates [56]....
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28,898 citations
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Cites methods from "Regularization Paths for Generalize..."
..., the logarithm of the density of the Normal prior (up to an additive constant), can be read as a ridge penalty term, and therefore, we perform the optimization using the iteratively reweighted ridge regression algorithm [55], also known as weighted updates [56]....
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8,059 citations
Cites methods from "Regularization Paths for Generalize..."
...The method described in (Friedman et al. 2010) combines coordinate descent with this warmstarting strategy, and computes the full regularization path for any 1 regularized GLM....
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References
40,785 citations
"Regularization Paths for Generalize..." refers methods in this paper
...This idea has been broadly applied, for example to generalized linear models (Tibshirani 1996) and Cox’s proportional hazard models for survival data (Tibshirani 1997)....
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...Keywords: lasso, elastic net, logistic regression, ` 1 penalty, regularization path, coordinatedescent....
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...The lasso (Tibshirani 1996) is a popular method for regression that uses an ` 1 penalty to achieve a sparse solution....
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16,538 citations
Additional excerpts
...For simplicity we assume the x ij are standardized: P N i=1 x ij = 0, 1 N P N i=1 x2 ij = 1, for j = 1, . . . , p....
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...Keywords: lasso, elastic net, logistic regression, ` 1 penalty, regularization path, coordinatedescent....
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12,530 citations
"Regularization Paths for Generalize..." refers background or methods in this paper
...More generally, the entire family P ↵ creates a useful compromise between ridge and lasso....
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...The dataset is from (Golub et al. 1999), consisting of 72 observations on 3571 genes measured with DNA microarrays....
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...Here we compare glmnet with BMR (Genkin et al. 2007), a multinomial version of BBR. Leukemia (Golub et al. 1999): gene-expression data with a binary response indicating type of leukemia—AML vs ALL....
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9,950 citations
"Regularization Paths for Generalize..." refers background in this paper
...In the signal processing literature, the lasso is also known as basis pursuit (Chen et al. 1998)....
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...Keywords: lasso, elastic net, logistic regression, ` 1 penalty, regularization path, coordinatedescent....
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8,314 citations
"Regularization Paths for Generalize..." refers methods in this paper
...Methods using non-concave penalties, such as SCAD (Fan and Li 2005) and Friedman’s generalized elastic net (Friedman 2008), enforce more severe variable selection than the lasso....
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