On Model Selection Consistency of Lasso

ZhaoPeng; Yubin Yubin

doi:10.5555/1248547.1248637

December 1, 2006Journal of Machine Learning Research

On Model Selection Consistency of Lasso

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Key Points

To establish the general mathematical conditions under which the Lasso estimator consistently selects the true sparse set of predictors in linear regression models.
Analyzed asymptotic and finite-sample properties of the Lasso penalty in high-dimensional linear regression.
Formulated the Irrepresentable Condition on the predictor covariance matrix to evaluate exact variable recovery.
Demonstrated that the Irrepresentable Condition is almost necessary and sufficient for Lasso to achieve model selection consistency.
Showed that consistent model selection holds even when the total number of predictors grows exponentially relative to sample size under sparsity constraints.

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Implication

Theoretical analysis establishes necessary and sufficient conditions for Lasso model selection consistency, highlighting the role of the Irrepresentable Condition.

Abstract

Sparsity or parsimony of statistical models is crucial for their proper interpretations, as in sciences and social sciences. Model selection is a commonly used method to find such models, but usual...

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ZhaoPeng et al. (2006) studied this question.

synapsesocial.com/papers/6a1298f74891eb3ecca3f318 https://doi.org/10.5555/1248547.1248637

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On Model Selection Consistency of Lasso

Key Points

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Implication

Abstract

Discussion

Cite This Study

On Model Selection Consistency of Lasso

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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