Fast Estimation of Causal Interactions using Wold Processes
This work addresses the computational bottleneck in causal inference for large-scale multivariate point processes, enabling training on full datasets where prior methods fail.
The paper tackles the problem of learning Granger causality matrices for multivariate point processes by introducing the first use of Wold processes, resulting in a learning algorithm with O(N(log(N) + log(K))) cost per iteration, which is significantly faster than state-of-the-art methods, and achieves three times higher accuracy in Precision@10 on Memetracker datasets.
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 $O(N^3\,K^2)$ or $O(K^3)$ 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.