# Fast Estimation of Causal Interactions using Wold Processes

arXiv: https://arxiv.org/abs/1807.04595 · HTML: https://mlsanity.com/paper/1807.04595/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2018.

## Built on by (most cited first, 4 of 4)

- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Counterfactual Temporal Point Processes](https://mlsanity.com/paper/2111.07603/) (2021)
- [Surfacing Estimation Uncertainty in the Decay Parameters of Hawkes Processes with Exponential Kernels](https://mlsanity.com/paper/2104.01029/) (2021)
- [Resilient Concurrent Causal Discovery for Topological Event Sequences](https://mlsanity.com/paper/2608.21815/) (2026)

## Abstract (arXiv)

We here focus on the task of learning Granger causality matrices for multivariate point processes. In order to accomplish this task, our work is the first to explore the use of Wold processes. By doing so, we are able to develop asymptotically fast MCMC learning algorithms. With N being the total number of events and K the number of processes, our learning algorithm has a O(N(,log(N),+,log(K))) cost per iteration. This is much faster than the O(N3,K2) or O(K3) for the state of the art. Our approach, called GrangerBusca, is validated on nine datasets. This is an advance in relation to most prior efforts which focus mostly on subsets of the Memetracker data. Regarding accuracy, GrangerBusca is three times more accurate (in Precision@10) than the state of the art for the commonly explored subsets Memetracker. Due to GrangerBusca's much lower training complexity, our approach is the only one able to train models for larger, full, sets of data.