These lecture notes consist of three chapters. In the first chapter we
present oracle inequalities for the prediction error of the Lasso and
square-root Lasso and briefly describe the scaled Lasso. In the second chapter
we establish asymptotic linearity of a de-sparsified Lasso. This implies
asymptotic normality under certain conditions and therefore can be used to
construct confidence intervals for parameters of interest. A similar line of
reasoning can be invoked to derive bounds in sup-norm for the Lasso and
asymptotic linearity of de-sparsified estimators of a precision matrix. In the
third chapter we consider chaining and the more general generic chaining method
developed by Talagrand. This allows one to bound suprema of random processes.
Concentration inequalities are refined probability inequalities, mostly again
for suprema of random processes. We combine the two. We prove a deviation
inequality directly using (generic) chaining.

这篇论文讨论了 Lasso 和去稀疏化 Lasso 的预测误差、渐进线性性及其应用：构建感兴趣参数的置信区间和精度矩阵的去稀疏化估计器，同时考虑经典的 chaining 和通用的 generic chaining 方法，并结合浓度不等式来证明偏差不等式。