Title: Should We Model X in High-Dimensional Inference?

Abstract: For answering questions about the relationship between a response
variable Y and a set of explanatory variables X, most statistical methods
focus their assumptions on the conditional distribution of Y given X (or Y | X for short).

I will describe some benefits of shifting those assumptions from the conditional
distribution Y | X to the joint distribution of X, especially for high-dimensional
data. First, modeling X can lead to assumptions that are more realistic and verifiable.

Second, there are substantial methodological payoffs in terms of much greater flexibility
in the tools an analyst can bring to bear on their data while also being guaranteed exact
(non-asymptotic) inference. I will briefly mention some of my recent and ongoing work on
methods for high-dimensional inference that model X instead of Y, as well as some
challenges and interesting directions for the future.