I'm trying to understand some papers by Mark van der Laan. He's a theoretical statistician at Berkeley working on problems overlap significantly with machine learning. One problem for me (besides the deep math) is that he often ends up describing familiar machine learning approaches using a completely different terminology. One of his main concepts is "Targeted Maximum Likelihood Expectation".
TMLE is used to analyze censored observational data from a non-controlled experiment in a way that allows effect estimation even in the presence of confounding factors. I strongly suspect that the many of the same concepts exist under other names in other fields, but I don't yet understand it well enough to match it directly to anything.
An attempt to bridge the gap to "Computational Data Analysis" is here:
And an introduction for statisticians is here:
From the second:
In this article, we develop a particular targeted maximum likelihood estimator of causal effects of multiple time point interventions. This involves the use of loss-based super-learning to obtain an initial estimate of the unknown factors of the G-computation formula, and subsequently, applying a target-parameter specific optimal fluctuation function (least favorable parametric submodel) to each estimated factor, estimating the fluctuation parameter(s) with maximum likelihood estimation, and iterating this updating step of the initial factor till convergence. This iterative targeted maximum likelihood updating step makes the resulting estimator of the causal effect double robust in the sense that it is consistent if either the initial estimator is consistent, or the estimator of the optimal fluctuation function is consistent. The optimal fluctuation function is correctly specified if the conditional distributions of the nodes in the causal graph one intervenes upon are correctly specified.
In his terminology, "super learning" is ensemble learning with a a theoretically sound non-negative weighting scheme. But what does he mean by "applying a target-parameter specific optimal fluctuation function (least favorable parametric submodel) to each estimated factor".
Or breaking it into three distinct questions, does TMLE have a parallel in machine learning, what is a "least favorable parametric submodel", and what is a "fluctuation function" in other fields?