  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.
