  Negative control is a strategy for learning the causal relationship between
treatment and outcome in the presence of unmeasured confounding. The treatment
effect can nonetheless be identified if two auxiliary variables are available:
a negative control treatment (which has no effect on the actual outcome), and a
negative control outcome (which is not affected by the actual treatment). These
auxiliary variables can also be viewed as proxies for a traditional set of
control variables, and they bear resemblance to instrumental variables. I
propose a new family of non-parametric algorithms for learning treatment
effects with negative controls. I consider treatment effects of the population,
of sub-populations, and of alternative populations. I allow for data that may
be discrete or continuous, and low-, high-, or infinite-dimensional. I impose
the additional structure of the reproducing kernel Hilbert space (RKHS), a
popular non-parametric setting in machine learning. I prove uniform consistency
and provide finite sample rates of convergence. I evaluate the estimators in
simulations.
