Random weighting in LASSO regression

We establish statistical properties of random-weighting methods in LASSO regression under different regularization parameters ?n and suitable regularity conditions. The view concern repeated optimization a randomized objective function, motivated by the need for computationally efficient uncertainty quantification contemporary estimation settings. In context regression, we repeatedly assign analyst-drawn random weights to terms optimize obtain sample estimators. show that existing approaches have conditional model selection consistency asymptotic normality at growth rates as n??. propose an extension available resulting samples attain sparse growing-dimension setting. illustrate proposed methodology using synthetic benchmark data sets, discuss relationship results approximate nonparametric Bayesian analysis perturbation bootstrap methods.