There are many fine how-to articles describing how to implement TMLE but they avoid the details of the underlying theory. I'm currently working my way through Targeted Learning: Causal Inference for Observational and Experimental Data by Mark J. van der Laan and Sherri Rose. The math isn't terribly complicated but the notation and terminology is a bit confusing.

I understand TMLE's aim of finding an unbiased estimate of the Average Treatment Effect by using machine learning, and am familiar with the theory behind causal inference, the Super Learner algorithm, and doubly robust models, but I hit a brick wall when it comes to calculating the efficient influence curve, the "clever covariate", and guaranteeing the final ATE estimate's unbiasedness with the Central Limit Theorem.

My understanding is that TMLE uses the delta method (1st order Taylor series) to approximate the ATE and then converges to an estimate of the ATE via gradient descent(?). Am I too far off?

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  • $\begingroup$ @kjetilbhalvorsen I did read those questions but unfortunately they weren't helpful. Possibly targeted learning is still such a young field that aside from Mark J. van der Laan and Sherri Rose there aren't a lot of statisticians who do completely understand TMLE theory? $\endgroup$ – RobertF Dec 29 '19 at 14:55
  • $\begingroup$ I should also add that I haven't been able to find a copy of Frank R. Hampel's 1974 paper on influence curves, "The Influence Curve and its Role in Robust Estimation" that isn't stuck behind a paywall. $\endgroup$ – RobertF Dec 29 '19 at 15:06
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    $\begingroup$ Found an article that does a good job explaining the theory behind using influence functions to estimate ATEs: arxiv.org/pdf/1810.03260.pdf $\endgroup$ – RobertF Jan 1 '20 at 22:58
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    $\begingroup$ David Benkeser and Antoine Chambaz wrote a useful explanation of TMLE theory here: achambaz.github.io/tlride $\endgroup$ – RobertF Feb 5 at 20:52

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