Counterfactual Temporal Point Processes
This work addresses a gap in temporal point process models for answering counterfactual questions, which is important for applications like targeted interventions, though it appears incremental as it builds on existing causal frameworks.
The paper tackled the inability of temporal point process models to answer counterfactual questions, which are crucial for informing targeted interventions, by developing a causal model of thinning and a sampling algorithm that simulates counterfactual realizations, showing in simulations with synthetic and real epidemiological data that these realizations provide valuable insights.
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.