Assumptionless consistency of the Lasso
By Sourav Chatterjee. 2013
52 citations recorded by the source corpus.
The Lasso is a popular statistical tool invented by Robert Tibshirani for linear regression when the number of covariates is greater than or comparable to the number of observations. The purpose of this note is to highlight the simple fact (noted in a number of earlier papers in various guises) that for the loss function considered in Tibshirani's original paper, the Lasso is consistent under almost no assumptions at all.
Subfields: Artificial Intelligence, Statistics and Probability
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Whitney K. Newey
- Victor Chernozhukov
- Jafar Jafarov
- Rahul Singh
- Sourav Chatterjee
- D. Chetverikov
- Kengo Kato
- Alexandre Belloni
In Statistics and Probability
- Victor Chernozhukov
- Rahul Singh
- Whitney K. Newey
- Stefan Wager
- D. Chetverikov
- Susan Athey
- Jafar Jafarov
- Guido W. Imbens
Citations in the corpus
- Double/De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers (2018, methodology): “This result tightens the result in Chatterjee (2013) who established a “slow rate” bound (in the context of Lasso) that applies under no assumptions on G.”
- Prediction error of cross-validated Lasso (2015, methodology): “…on the smallest nonzero singular value of the design matrix looks a bit restrictive, especially since it has been observed in several recent papers that risk consistency in Lasso (with deterministic value of the tuning parameter) holds without any conditions on the design matrix [1, 3, 6, 27].”