Applying a causal graph structure in the challenging environment of a no-holds-barred nonparametric machine learning algorithm such as a neural net or its ilk.

TBD.

Léon Bottou, From Causal Graphs to Causal Invariance

For many problems, it’s difficult to even attempt drawing a causal graph. While structural causal models provide a complete framework for causal inference, it is often hard to encode known physical laws (such as Newton’s gravitation, or the ideal gas law) as causal graphs. In familiar machine learning territory, how does one model the causal relationships between individual pixels and a target prediction? This is one of the motivating questions behind the paper Invariant Risk Minimization (IRM). In place of structured graphs, the authors elevate invariance to the defining feature of causality.

Nisha Muktewar and Chris Wallace, Causality for Machine Learning is the book Bottou recommends on this theme.

Künzel et al. (2019) (HT Mike McKenna) looks interesting:

… We describe a number of metaalgorithms that can take advantage of any supervised learning or regression method in machine learning and statistics to estimate the conditional average treatment effect (CATE) function. Metaalgorithms build on base algorithms—such as random forests (RFs), Bayesian additive regression trees (BARTs), or neural networks—to estimate the CATE, a function that the base algorithms are not designed to estimate directly. We introduce a metaalgorithm, the X-learner, that is provably efficient when the number of units in one treatment group is much larger than in the other and can exploit structural properties of the CATE function. For example, if the CATE function is linear and the response functions in treatment and control are Lipschitz-continuous, the X-learner can still achieve the parametric rate under regularity conditions. We then introduce versions of the X-learner that use RF and BART as base learners. In extensive simulation studies, the X-learner performs favorably, although none of the metalearners is uniformly the best. In two persuasion field experiments from political science, we demonstrate how our X-learner can be used to target treatment regimes and to shed light on underlying mechanisms.

## References

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*Advances In Neural Information Processing Systems*. http://arxiv.org/abs/1911.07420.

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*Proceedings of the IEEE*109 (5): 612–34. https://doi.org/10.1109/JPROC.2021.3058954.

*Advances in Neural Information Processing Systems*. Vol. 33. https://arxiv.org/abs/2002.03278.

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