  This paper is about the feasibility and means of root-n consistently
estimating linear, mean-square continuous functionals of a high dimensional,
approximately sparse regression. Such objects include a wide variety of
interesting parameters such as regression coefficients, average derivatives,
and the average treatment effect. We give lower bounds on the convergence rate
of estimators of a regression slope and an average derivative and find that
these bounds are substantially larger than in a low dimensional, semiparametric
setting. We also give debiased machine learners that are root-n consistent
under either a minimal approximate sparsity condition or rate double
robustness. These estimators improve on existing estimators in being root-n
consistent under more general conditions that previously known.
