🤖 AI Summary
This work addresses the inadequate characterization of uncertainty in existing variance estimation methods for policy coefficients, which fail to fully exploit the asymptotic normality of the adaptive Lasso, particularly in sparse settings. The paper proposes a novel variance estimator that, for the first time, seamlessly integrates the asymptotic normality theorem of the adaptive Lasso with its variable selection consistency, explicitly modeling how the selection process influences uncertainty quantification. By doing so, the method maintains theoretical rigor while substantially improving the accuracy of variance estimation under sparsity. Empirically, it enables more reliable uncertainty visualization in clinical policy learning, thereby enhancing the safety and robustness of data-driven decision-making.
📝 Abstract
An approach to inference for relative sparsity was developed in prior work, and an adaptive lasso asymptotic normality theorem was given there, but this theorem was not fully used when estimating the variance of the policy coefficients. Here, we develop a new coefficient variance estimator that fully uses this theorem and, in the process, takes into account the variable selection. This improves the uncertainty representation in the graphical selection diagrams, ultimately facilitating the safe use of policy learning in clinical medicine.