Causal and nonparametric estimands in economics and biostatistics can often be viewed as the mean of a linear functional applied to an unknown outcome regression function. Naively learning the regression function and taking a sample mean of the target functional results in biased estimators, and a rich debiasing literature has developed where one additionally learns the so-called Riesz representer (RR) of the target estimand (targeted learning, double ML, automatic debiasing etc.). Learning the RR via its derived functional form can be challenging, e.g. due to extreme inverse probability weights or the need to learn conditional density functions. Such challenges have motivated recent advances in automatic debiasing (AD), where the RR is learned directly via minimization of a bespoke loss. We propose moment-constrained learning as a new RR learning approach that addresses some shortcomings in AD, constraining the predicted moments and improving the robustness of RR estimates to optimization hyperparamters. Though our approach is not tied to a particular class of learner, we illustrate it using neural networks, and evaluate on the problems of average treatment/derivative effect estimation using semi-synthetic data. Our numerical experiments show improved performance versus state of the art benchmarks.

翻译：经济学和生物统计学中的因果与非参数估计量，通常可视为对未知结果回归函数施加线性泛函后的均值。若直接学习回归函数并对目标泛函取样本均值，将导致有偏估计量，因此催生了丰富的去偏文献——其中还需学习目标估计量的所谓Riesz表示元（目标学习、双重机器学习、自动去偏等）。通过推导泛函形式学习Riesz表示元可能面临挑战，例如极端逆概率权重或需要学习条件密度函数。这些挑战推动了自动去偏领域的最新进展，即通过定制化损失函数的最小化直接学习Riesz表示元。我们提出矩约束学习作为新的Riesz表示元学习方法，以解决自动去偏中的某些缺陷：通过约束预测矩来提升Riesz表示元估计对优化超参数的鲁棒性。虽然该方法不依赖于特定学习器类别，但我们以神经网络为例进行说明，并基于半合成数据在平均处理效应/导数效应估计问题上进行评估。数值实验表明，相较于现有先进基准方法，本方法具有更优性能。