Counterfactual Temporal Point Processes

TL;DR

This paper introduces a causal model for temporal point processes that enables counterfactual reasoning, allowing for simulation of alternative event scenarios to improve targeted interventions.

Contribution

It develops a novel causal thinning model based on the Gumbel-Max framework and a sampling algorithm for counterfactual simulation of temporal point processes.

Findings

Counterfactual realizations provide valuable insights for interventions.

Model satisfies counterfactual monotonicity, ensuring valid causal inference.

Algorithm performs well on synthetic and epidemiological data.

Abstract

Machine learning models based on temporal point processes are the state of the art in a wide variety of applications involving discrete events in continuous time. However, these models lack the ability to answer counterfactual questions, which are increasingly relevant as these models are being used to inform targeted interventions. In this work, our goal is to fill this gap. To this end, we first develop a causal model of thinning for temporal point processes that builds upon the Gumbel-Max structural causal model. This model satisfies a desirable counterfactual monotonicity condition, which is sufficient to identify counterfactual dynamics in the process of thinning. Then, given an observed realization of a temporal point process with a given intensity function, we develop a sampling algorithm that uses the above causal model of thinning and the superposition theorem to simulate counterfactual realizations of the temporal point process under a given alternative intensity function. Simulation experiments using synthetic and real epidemiological data show that the counterfactual realizations provided by our algorithm may give valuable insights to enhance targeted interventions.