# Counterfactual Temporal Point Processes

arXiv: https://arxiv.org/abs/2111.07603 · HTML: https://mlsanity.com/paper/2111.07603/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 64 references that are in the map.
- First posted on arXiv 15 Nov 2021.

## Builds on (most cited first, 21 of 21)

- [A* Sampling](https://mlsanity.com/paper/1411.0030/) (2014)
- [Counterfactual Off-Policy Evaluation with Gumbel-Max Structural Causal Models](https://mlsanity.com/paper/1905.05824/) (2019)
- [Neural Temporal Point Processes: A Review](https://mlsanity.com/paper/2104.03528/) (2021)
- [Counterfactual Data Augmentation using Locally Factored Dynamics](https://mlsanity.com/paper/2007.02863/) (2020)
- [Woulda, Coulda, Shoulda: Counterfactually-Guided Policy Search](https://mlsanity.com/paper/1811.06272/) (2018)
- [A Review of the Gumbel-max Trick and its Extensions for Discrete Stochasticity in Machine Learning](https://mlsanity.com/paper/2110.01515/) (2021)
- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [Uncovering Causality from Multivariate Hawkes Integrated Cumulants](https://mlsanity.com/paper/1607.06333/) (2016)
- [COEVOLVE: A Joint Point Process Model for Information Diffusion and Network Co-evolution](https://mlsanity.com/paper/1507.02293/) (2015)
- [Counterfactual Explanations in Sequential Decision Making Under Uncertainty](https://mlsanity.com/paper/2107.02776/) (2021)
- [CAUSE: Learning Granger Causality from Event Sequences using Attribution Methods](https://mlsanity.com/paper/2002.07906/) (2020)
- [Deep Reinforcement Learning of Marked Temporal Point Processes](https://mlsanity.com/paper/1805.09360/) (2018)
- [Discovering Latent Network Structure in Point Process Data](https://mlsanity.com/paper/1402.0914/) (2014)
- [Teaching Multiple Concepts to a Forgetful Learner](https://mlsanity.com/paper/1805.08322/) (2018)
- [Stochastic Optimal Control of Epidemic Processes in Networks](https://mlsanity.com/paper/1810.13043/) (2018)
- [Quantifying the Effects of Contact Tracing, Testing, and Containment Measures in the Presence of Infection Hotspots](https://mlsanity.com/paper/2004.07641/) (2020)
- [Steering Social Activity: A Stochastic Optimal Control Point Of View](https://mlsanity.com/paper/1802.07244/) (2018)
- [Distilling Information Reliability and Source Trustworthiness from Digital Traces](https://mlsanity.com/paper/1610.07472/) (2016)
- [Causal Inference in Disease Spread across a Heterogeneous Social System](https://mlsanity.com/paper/1801.08133/) (2018)
- [Fast Estimation of Causal Interactions using Wold Processes](https://mlsanity.com/paper/1807.04595/) (2018)
- [Time-dependent mediators in survival analysis: Modelling direct and indirect effects with the additive hazards model](https://mlsanity.com/paper/2011.13415/) (2020)

## Built on by (most cited first, 20 of 20)

- [Counterfactual Neural Temporal Point Process for Estimating Causal Influence of Misinformation on Social Media](https://mlsanity.com/paper/2210.07518/) (2022)
- [Counterfactual Inference of Second Opinions](https://mlsanity.com/paper/2203.08653/) (2022)
- [Counterfactual Token Generation in Large Language Models](https://mlsanity.com/paper/2409.17027/) (2024)
- [Finding Counterfactually Optimal Action Sequences in Continuous State Spaces](https://mlsanity.com/paper/2306.03929/) (2023)
- [ODE Discovery for Longitudinal Heterogeneous Treatment Effects Inference](https://mlsanity.com/paper/2403.10766/) (2024)
- [Evaluation of Large Language Models via Coupled Token Generation](https://mlsanity.com/paper/2502.01754/) (2025)
- [Granger Causal Chain Discovery for Sepsis-Associated Derangements via Continuous-Time Hawkes Processes](https://mlsanity.com/paper/2209.04480/) (2022)
- [Counterfactual Influence in Markov Decision Processes](https://mlsanity.com/paper/2402.08514/) (2024)
- [Neural Spatiotemporal Point Processes: Trends and Challenges](https://mlsanity.com/paper/2502.09341/) (2025)
- [Causal Modeling of Policy Interventions From Sequences of Treatments and Outcomes](https://mlsanity.com/paper/2209.04142/) (2022)
- [Causal Graph Discovery from Self and Mutually Exciting Time Series](https://mlsanity.com/paper/2301.11197/) (2023)
- [Temporal Causal Mediation through a Point Process: Direct and Indirect Effects of Healthcare Interventions](https://mlsanity.com/paper/2306.09656/) (2023)
- [When Counterfactual Reasoning Fails: Chaos and Real-World Complexity](https://mlsanity.com/paper/2503.23820/) (2025)
- [Explainable History Distillation by Marked Temporal Point Process](https://mlsanity.com/paper/2311.07797/) (2023)
- [Uncovering Causal Relation Shifts in Event Sequences under Out-of-Domain Interventions](https://mlsanity.com/paper/2507.10809/) (2025)
- [Learning Marked Temporal Point Process Explanations based on Counterfactual and Factual Reasoning](https://mlsanity.com/paper/2508.11943/) (2025)
- [MOCHA: Discovering Multi-Order Dynamic Causality in Temporal Point Processes](https://mlsanity.com/paper/2508.18873/) (2025)
- [Generating Causal Temporal Interaction Graphs for Counterfactual Validation of Temporal Link Prediction](https://mlsanity.com/paper/2602.02161/) (2026)
- [Certifying What Helps Customer-Return Timing: A Screen-and-Confirm Test for Conditioning Signals, and Why Decay Is Nearly Enough](https://mlsanity.com/paper/2608.11555/) (2026)
- [Design-Ignoring versus Design-Respecting World Models for Epidemiology](https://mlsanity.com/paper/2609.30679/) (2026)

## Abstract (arXiv)

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.