Understand
Many modern applications seek to understand the relationship between an outcome variable $Y$ and a covariate $X$ in the presence of a (possibly high-dimensional) confounding variable $Z$.
- Although much attention has been paid to testing \emph{whether} $Y$ depends on $X$ given $Z$, in this paper we seek to go beyond testing by inferring the \emph{strength} of that dependence.
- We first define our estimand, the minimum mean squared error (mMSE) gap, which quantifies the conditional relationship between $Y$ and $X$ in a way that is deterministic, model-free, interpretable, and sensitive to nonlinearities and interactions.
- We then propose a new inferential approach called \emph{floodgate} that can leverage any working regression function chosen by the user (allowing, e.g., it to be fitted by a state-of-the-art machine learning algorithm or be derived from qualitative domain knowledge) to construct asymptotic confidence bounds, and we apply it to the mMSE gap.