# MOCHA: Discovering Multi-Order Dynamic Causality in Temporal Point Processes

arXiv: https://arxiv.org/abs/2508.18873 · HTML: https://mlsanity.com/paper/2508.18873/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 39 references that are in the map.
- First posted on arXiv 26 Aug 2025.

## Builds on (most cited first, 15 of 15)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [EasyTPP: Towards Open Benchmarking Temporal Point Processes](https://mlsanity.com/paper/2307.08097/) (2023)
- [HYPRO: A Hybridly Normalized Probabilistic Model for Long-Horizon Prediction of Event Sequences](https://mlsanity.com/paper/2210.01753/) (2022)
- [SNAP: A General Purpose Network Analysis and Graph Mining Library](https://mlsanity.com/paper/1606.07550/) (2016)
- [CAUSE: Learning Granger Causality from Event Sequences using Attribution Methods](https://mlsanity.com/paper/2002.07906/) (2020)
- [Counterfactual Temporal Point Processes](https://mlsanity.com/paper/2111.07603/) (2021)
- [Counterfactual Neural Temporal Point Process for Estimating Causal Influence of Misinformation on Social Media](https://mlsanity.com/paper/2210.07518/) (2022)
- [Structural Hawkes Processes for Learning Causal Structure from Discrete-Time Event Sequences](https://mlsanity.com/paper/2305.05986/) (2023)
- [Causal Discovery in Hawkes Processes by Minimum Description Length](https://mlsanity.com/paper/2206.06124/) (2022)
- [Interpretable Transformer Hawkes Processes: Unveiling Complex Interactions in Social Networks](https://mlsanity.com/paper/2405.16059/) (2024)
- [A Variational Autoencoder for Neural Temporal Point Processes with Dynamic Latent Graphs](https://mlsanity.com/paper/2312.16083/) (2023)
- [Dynamic Representation Learning with Temporal Point Processes for Higher-Order Interaction Forecasting](https://mlsanity.com/paper/2112.10154/) (2021)

## Abstract (arXiv)

Discovering complex causal dependencies in temporal point processes (TPPs) is critical for modeling real-world event sequences. Existing methods typically rely on static or first-order causal structures, overlooking the multi-order and time-varying nature of causal relationships. In this paper, we propose MOCHA, a novel framework for discovering multi-order dynamic causality in TPPs. MOCHA characterizes multi-order influences as multi-hop causal paths over a latent time-evolving graph. To model such dynamics, we introduce a time-varying directed acyclic graph (DAG) with learnable structural weights, where acyclicity and sparsity constraints are enforced to ensure structural validity. We design an end-to-end differentiable framework that jointly models causal discovery and TPP dynamics, enabling accurate event prediction and revealing interpretable structures. Extensive experiments on real-world datasets demonstrate that MOCHA not only achieves state-of-the-art performance in event prediction, but also reveals meaningful and interpretable causal structures.