  We aim to construct a class of learning algorithms that are of practical
value to applied researchers in fields such as biostatistics, epidemiology and
econometrics, where the need to learn from incompletely observed information is
ubiquitous. We propose a new framework for statistical machine learning of
target functions arising as identifiable functionals from statistical models,
which we call `IF-learning' due to its reliance on influence functions (IFs).
This framework is problem- and model-agnostic and can be used to estimate a
broad variety of target parameters of interest in applied statistics: we can
consider any target function for which an IF of a population-averaged version
exists in analytic form. Throughout, we put particular focus on so-called
coarsening at random/doubly robust problems with partially unobserved
information. This includes problems such as treatment effect estimation and
inference in the presence of missing outcome data. Within this framework, we
propose two general learning algorithms that build on the idea of nonparametric
plug-in bias removal via IFs: the 'IF-learner' which uses pseudo-outcomes
motivated by uncentered IFs for regression in large samples and outputs entire
target functions without confidence bands, and the 'Group-IF-learner', which
outputs only approximations to a function but can give confidence estimates if
sufficient information on coarsening mechanisms is available. We apply both in
a simulation study on inferring treatment effects.
