Correlation Adjusted Debiasing (CAD): Debiasing the Lasso with Inaccurate Covariate Model
summary
Proposes a correlation-adjusted debiasing estimator that recovers a single coefficient beta consistently even when the covariate model gamma and outcome theta are not estimated consistently; works in a semi-supervised setup with extra unlabeled samples enough for unbiased OLS on gamma but not consistent estimation. Assumes Gaussian design, bounded covariance singular values and sparsity of theta (allowing proportional sparsity), uses correlation-adjusted debiasing (CAD) and analysis via joint exact asymptotics / AMP, and simulations show the CAD correction removes the Lasso bias across signal strengths.
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chapters (8)
- 0:00Intro
- 1:04Linear model
- 2:22The Lasso is biased
- 2:37The Lasso is not consistent under proportional asymptotics
- 3:38Successfully debiasing the Lasso with accurate covariate model
- 4:57What if we don't knowy?
- 6:56Correlation adjusted debiasing (CAD)
- 8:44Exact asymptotics for simultaneous regression Simultaneous estimation
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