Learning the Distribution Map in Reverse Causal Performative Prediction

In numerous predictive scenarios, the predictive model affects the sampling distribution; for example, job applicants often meticulously craft their resumes to navigate through a screening system. Such shifts in distribution are particularly prevalent in social computing, yet, the strategies to learn these shifts from data remain remarkably limited. Inspired by a microeconomic model that adeptly characterizes agents' behavior within labor markets, we introduce a novel approach to learning the distribution shift. Our method is predicated on a \emph{reverse causal model}, wherein the predictive model instigates a distribution shift exclusively through a finite set of agents' actions. Within this framework, we employ a microfoundation model for the agents' actions and develop a statistically justified methodology to learn the distribution shift map, which we demonstrate to effectively minimize the performative prediction risk.