Causal inference studies whether the presence of a variable influences an
observed outcome. As measured by quantities such as the "average treatment
effect," this paradigm is employed across numerous biological fields, from
vaccine and drug development to policy interventions. Unfortunately, the
majority of these methods are often limited to univariate outcomes. Our work
generalizes causal estimands to outcomes with any number of dimensions or any
measurable space, and formulates traditional causal estimands for nominal
variables as causal discrepancy tests. We propose a simple technique for
adjusting universally consistent conditional independence tests and prove that
these tests are universally consistent causal discrepancy tests. Numerical
experiments illustrate that our method, Causal CDcorr, leads to improvements in
both finite sample validity and power when compared to existing strategies. Our
methods are all open source and available at github.com/ebridge2/cdcorr
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