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.
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...