Regression Shrinkage and Selection via the Lasso.¶
Tibshirani, R. (1996). Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1), 267-288.
Cited by¶
4 citations across 4 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Convexity
- Statistics and machine learning. Log-likelihoods of exponential families are concave, so maximum-likelihood is a convex problem; convex relaxations (LP relaxation of integer programs, nuclear-norm for rank, the Lasso for sparsity) make hard tasks tractable, and convex surrogate losses replace the non-convex 0–1 loss.
This sourceThe Lasso — an L1-constrained (convex) reformulation that yields sparse, interpretable models — exemplifying convex relaxation/surrogate machinery in statistics and machine learning.
- Statistics and machine learning. Log-likelihoods of exponential families are concave, so maximum-likelihood is a convex problem; convex relaxations (LP relaxation of integer programs, nuclear-norm for rank, the Lasso for sparsity) make hard tasks tractable, and convex surrogate losses replace the non-convex 0–1 loss.
- Overfitting
- Listed in the references but not attached to a specific claim.
- Parsimony (Occam's Razor)
- Regularization
- The frame's prior-penalty duality is exact here — ridge is precisely MAP estimation under a Gaussian prior on \(\beta\), so the penalty is a prior — and the choice-of-norm inference is visible by swapping the L2 norm for L1, which yields the lasso and induces sparsity rather than uniform shrinkage.
This sourceIntroduces the lasso (L1 penalty) inducing sparsity; equivalently MAP estimation under a Laplace prior.
- The frame's prior-penalty duality is exact here — ridge is precisely MAP estimation under a Gaussian prior on \(\beta\), so the penalty is a prior — and the choice-of-norm inference is visible by swapping the L2 norm for L1, which yields the lasso and induces sparsity rather than uniform shrinkage.
Verification¶
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