A Variational Inference Approach to Learning Multivariate Wold Processes
Jalal Etesami, William Trouleau, Negar Kiyavash, Matthias Grossglauser, Patrick Thiran
Abstract
Temporal point-processes are often used for mathematical modeling of sequences of discrete events with asynchronous timestamps. We focus on a class of temporal point-process models called multivariate Wold processes (MWP). These processes are well suited to model real-world communication dynamics. Statistical inference on such processes often requires learning their corresponding parameters using a set of observed timestamps. In this work, we relax some of the restrictive modeling assumptions made in the state-of-the-art and introduce a Bayesian approach for inferring the parameters of MWP. We develop a computationally efficient variational inference algorithm that allows scaling up the approach to high-dimensional processes and long sequences of observations. Our experimental results on both synthetic and real-world datasets show that our proposed algorithm outperforms existing methods.
BibTeX
@InProceedings{pmlr-v130-etesami21a,
title = { A Variational Inference Approach to Learning Multivariate Wold Processes },
author = {Etesami, Jalal and Trouleau, William and Kiyavash, Negar and Grossglauser, Matthias and Thiran, Patrick},
booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics},
pages = {2044--2052},
year = {2021},
editor = {Banerjee, Arindam and Fukumizu, Kenji},
volume = {130},
series = {Proceedings of Machine Learning Research},
month = {13--15 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v130/etesami21a/etesami21a.pdf},
url = {https://proceedings.mlr.press/v130/etesami21a.html},
abstract = { Temporal point-processes are often used for mathematical modeling of sequences of discrete events with asynchronous timestamps. We focus on a class of temporal point-process models called multivariate Wold processes (MWP). These processes are well suited to model real-world communication dynamics. Statistical inference on such processes often requires learning their corresponding parameters using a set of observed timestamps. In this work, we relax some of the restrictive modeling assumptions made in the state-of-the-art and introduce a Bayesian approach for inferring the parameters of MWP. We develop a computationally efficient variational inference algorithm that allows scaling up the approach to high-dimensional processes and long sequences of observations. Our experimental results on both synthetic and real-world datasets show that our proposed algorithm outperforms existing methods. }
}