Learning the Distribution Map in Reverse Causal Performative Prediction

TL;DR

The paper addresses performativity in predictive systems in which the model alters the data-generating distribution through agents' responses. It introduces a reverse-causal framework in which the distribution shift is generated only by a finite set of agent actions, formalized via a distribution-shift map $\Psi: \mathcal{A} \to \mathcal{P}(\mathcal{Z})$ that maps agent actions to a new data distribution. A microfoundation model for agent actions is developed, enabling statistically justified learning of the shift map from data, and training objectives are adjusted to minimize the performative risk under the learned $\Psi$ (e.g., $R_{\text{perf}}(f,\Psi)$). The paper demonstrates the effectiveness of learning the shift map within this framework to reduce performative risk in environments where agents react to predictions.

Abstract

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 systems. Such shifts in distribution are particularly prevalent in the realm of 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 learn the distribution shift. Our method is predicated on a 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 be effective in minimizing the performative prediction risk.