Estimating how a treatment affects different individuals, known as heterogeneous treatment effect estimation, is an important problem in empirical sciences. In the last few years, there has been a considerable interest in adapting machine learning algorithms to the problem of estimating heterogeneous effects from observational and experimental data. However, these algorithms often make strong assumptions about the observed features in the data and ignore the structure of the underlying causal model, which can lead to biased estimation. At the same time, the underlying causal mechanism is rarely known in real-world datasets, making it hard to take it into consideration. In this work, we provide a survey of state-of-the-art data-driven methods for heterogeneous treatment effect estimation using machine learning, broadly categorizing them as methods that focus on counterfactual prediction and methods that directly estimate the causal effect. We also provide an overview of a third category of methods which rely on structural causal models and learn the model structure from data. Our empirical evaluation under various underlying structural model mechanisms shows the advantages and deficiencies of existing estimators and of the metrics for measuring their performance.
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