AI 中文总结
研究半参数估计中黑箱学习器的最优使用，提出新估计器及TAME方法，新估计器有特定误差率且建立了匹配下界，TAME可与初始估计结合，在干扰不平衡时改进DML保证，还讨论了其优势。
AI 中文摘要
考虑结构不可知情况下的部分线性模型\(Y = \mu_0(X) + \beta_0 \cdot T + \varepsilon\)和\(T = \pi_0(X) + u\)，在此结构中对\(\mu_0\)和\(\pi_0\)结构未知，通过黑箱假设类估计干扰项。该类的可学习性由无模型误设时的估计误差\(\delta_s\)及其对\(\mu_0\)和\(\pi_0\)的\(L_2\)误设误差\(\delta_{a, \mu}\)和\(\delta_{a, \pi}\)表征。我们提出了目标线性系数\(\theta_0 = \beta_0\)的一种新估计器，其误差率为\(\frac{1}{\sqrt{n}} + \delta_{a, \mu} \cdot \delta_{a, \pi} + [\delta_s]^2\)，还建立了匹配的下界，表明该速率不可改进。与双机器学习（DML）产生的乘积速率相比，我们的估计器无需额外成本或假设即可去除次优项\(\max(\delta_{a, \mu}, \delta_{a, \pi})\cdot \delta_s\)。基于这些基本见解，我们提出了转导对抗矩校准编辑（TAME），它通过对抗条件矩校准在推理样本上局部编辑由黑箱回归估计引起的去偏权重。TAME可与任何初始黑箱估计相结合，当干扰困难不平衡时能严格改进DML保证。我们还讨论了如何充分利用TAME带来的优势，包括使用两个学习器的收益、模型选择的欠平滑原则以及对其他线性泛函估计问题的扩展。
英文摘要
Consider the partial linear model $Y = μ_0(X) + β_0 \cdot T + \varepsilon$ and $T = π_0(X) + u$ in the structure-agnostic setting, where we are blind to the structure $μ_0$ and $π_0$ and estimate the nuisances by a black-box hypothesis class. The learnability of the class is characterized by the estimation error $δ_s$ in the absence of model misspecification and its $L_2$ mis-specification error $δ_{a, μ}$ and $δ_{a, π}$ for $μ_0$ and $π_0$, respectively. We propose a novel estimator of the target linear coefficient $θ_0 = β_0$ with error rate \[ \frac{1}{\sqrt{n}} + δ_{a, μ} \cdot δ_{a, π} + [δ_s]^2. \] A matching lower bound is also established, implying that this rate is unimprovable. Compared with the product rate yielded by double machine learning (DML), our estimator removes the suboptimal term $\max(δ_{a, μ}, δ_{a, π})\cdot δ_s$ at no extra cost or assumption. Building on the underlying insights, which are neither tailored to the one-learner setting nor the partial linear model, we propose Transductive Adversarial Moment-calibrated Editing (TAME), which locally edits debiasing weights induced by black-box regression estimates on the inference sample through adversarial conditional moment calibration. TAME can be combined with any initial black-box estimates and can strictly improve on DML guarantees when the nuisance difficulties are imbalanced. We discuss how to fully exploit the advantages introduced by TAME, including the gains from using two learners, the resulting under-smoothing principle for model selection, and extensions to other linear functional estimation problems.
Comments30 pages
