  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 family of algorithms based on kernel ridge regression for learning
nonparametric treatment effects with negative controls. Examples include dose
response curves, dose response curves with distribution shift, and
heterogeneous treatment effects. Data may be discrete or continuous, and low,
high, or infinite dimensional. I prove uniform consistency and provide finite
sample rates of convergence. I estimate the dose response curve of cigarette
smoking on infant birth weight adjusting for unobserved confounding due to
household income, using a data set of singleton births in the state of
Pennsylvania between 1989 and 1991.
