We provide adaptive inference methods, based on $\ell_1$ regularization, for regular (semi-parametric) and non-regular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include average treatment effects, policy effects, and derivatives. Examples of non-regular functionals include average treatment effects, policy effects, and derivatives conditional on a covariate subvector fixed at a point. We construct a Neyman orthogonal equation for the target parameter that is approximately invariant to small perturbations of the nuisance parameters. To achieve this property, we include the Riesz representer for the functional as an additional nuisance parameter. Our analysis yields weak ``double sparsity robustness'': either the approximation to the regression or the approximation to the representer can be ``completely dense'' as long as the other is sufficiently ``sparse''. Our main results are non-asymptotic and imply asymptotic uniform validity over large classes of models, translating into honest confidence bands for both global and local parameters.

翻译：我们为有条件期望函数的正常(半参数)和非常规(非参数)线性功能提供适应性推断方法,基于$@ell_1美元正规化,用于有条件期望函数的正常(半参数)和非常规(非参数)线性功能。常规功能的例子包括平均处理效果、政策效果和衍生物。非常规功能的例子包括平均处理效果、政策效果和以某个点固定的共变子变量为条件的衍生物。我们为目标参数构建了一个内曼正方程,该方程大约不易于小扰动干扰参数。为了实现这一属性,我们将功能的Riesz代表器作为额外的扰动参数。我们的分析结果是弱的 : “ 双宽强度强 ” : 与回归的近似值或与代表器的近似值可以“ 完全密度 ” 。我们的主要结果是非随机的, 并意味着对大类模型来说具有不耐受性的统一性, 转化为全球和本地参数的诚实信任带 。