Estimating the probabilities of causation via deep monotonic twin networks

There has been much recent work using machine learning to answer causal queries. Most focus on interventional queries, such as the conditional average treatment effect. However, as noted by Pearl, interventional queries only form part of a larger hierarchy of causal queries, with counterfactuals sitting at the top. Despite this, our community has not fully succeeded in adapting machine learning tools to answer counterfactual queries. This work addresses this challenge by showing how to implement twin network counterfactual inference -- an alternative to abduction, action, & prediction counterfactual inference -- with deep learning to estimate counterfactual queries. We show how the graphical nature of twin networks makes them particularly amenable to deep learning, yielding simple neural network architectures that, when trained, are capable of counterfactual inference. Importantly, we show how to enforce known identifiability constraints during training, ensuring the answer to each counterfactual query is uniquely determined. We demonstrate our approach by using it to accurately estimate the probabilities of causation -- important counterfactual queries that quantify the degree to which one event was a necessary or sufficient cause of another -- on both synthetic and real data.