We propose strategies to estimate and make inference on key features of heterogeneous effects in randomized experiments. These key features include best linear predictors of the effects using machine learning proxies, average effects sorted by impact groups, and average characteristics of most and least impacted units. The approach is valid in high dimensional settings, where the effects are proxied (but not necessarily consistently estimated) by predictive and causal machine learning methods. We post-process these proxies into estimates of the key features. Our approach is generic, it can be used in conjunction with penalized methods, neural networks, random forests, boosted trees, and ensemble methods, both predictive and causal. Estimation and inference are based on repeated data splitting to avoid overfitting and achieve validity. We use quantile aggregation of the results across many potential splits, in particular taking medians of p-values and medians and other quantiles of confidence intervals. We show that quantile aggregation lowers estimation risks over a single split procedure, and establish its principal inferential properties. Finally, our analysis reveals ways to build provably better machine learning proxies through causal learning: we can use the objective functions that we develop to construct the best linear predictors of the effects, to obtain better machine learning proxies in the initial step. We illustrate the use of both inferential tools and causal learners with a randomized field experiment that evaluates a combination of nudges to stimulate demand for immunization in India.

翻译：本文提出在随机实验中估计异质性效应关键特征并进行推断的策略。这些关键特征包括：使用机器学习代理变量的效应最佳线性预测、按影响组别排序的平均效应、以及受影响最大和最小单元的平均特征。该方法适用于高维场景，其中效应可由预测性和因果性机器学习方法代理（但无需一致估计）。我们将这些代理变量后处理为关键特征的估计值。该方法具有通用性，可与惩罚方法、神经网络、随机森林、提升树及集成方法（包括预测性与因果性）结合使用。估计与推断基于重复数据分割以避免过拟合并确保有效性。我们采用跨多次潜在分割的分位数聚合结果，特别是取p值的中位数以及置信区间的中位数与其他分位数。研究表明，分位数聚合相较于单次分割程序可降低估计风险，并建立了其主要推断性质。最后，分析揭示了通过因果学习构建可证明更优的机器学习代理变量的途径：可利用我们开发的目标函数构建效应的最佳线性预测器，从而在初始步骤获得更优的机器学习代理变量。我们通过一项评估多种助推组合以刺激印度免疫接种需求的随机实地实验，展示了推断工具与因果学习器的实际应用。