Reproduce “Adaptive Lasso, Transfer Lasso, and Beyond: An Asymptotic Perspective” on OpenResearch

About this paper

Masaaki Takada, Hironori Fujisawa

A theoretical analysis systematically compares the asymptotic properties of Adaptive Lasso and Transfer Lasso, revealing their distinct advantages in high-dimensional regression with initial estimators. The research introduces the Adaptive Transfer Lasso, which uniquely achieves both oot{m}-consistency and consistent variable selection, effectively leveraging large source datasets for improved performance.

Key insights

• Adaptive Lasso achieves the oracle property ( oot{n}-consistency and consistent active variable selection) but does not leverage a larger source data size ($m ext{ » } n$) for faster convergence rates.
• Transfer Lasso can achieve a faster oot{m}-consistency rate when source data is much larger ($m ext{ » } n$), but generally struggles with consistent active variable selection, primarily showing consistent invariant variable selection.
• The Adaptive Transfer Lasso uniquely achieves both oot{m}-consistency and consistent active variable selection simultaneously in a specific hyperparameter region, combining the strengths of its predecessors.

Summary by alphaXiv.