A Variational Inference Approach to Learning Multivariate Wold Processes

Jalal Etesami, William Trouleau, Negar Kiyavash, Matthias Grossglauser, Patrick Thiran
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:2044-2052, 2021.

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.

Cite this Paper

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. } }
Endnote
%0 Conference Paper %T A Variational Inference Approach to Learning Multivariate Wold Processes %A Jalal Etesami %A William Trouleau %A Negar Kiyavash %A Matthias Grossglauser %A Patrick Thiran %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-etesami21a %I PMLR %P 2044--2052 %U https://proceedings.mlr.press/v130/etesami21a.html %V 130 %X 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.
APA
Etesami, J., Trouleau, W., Kiyavash, N., Grossglauser, M. & Thiran, P.. (2021). A Variational Inference Approach to Learning Multivariate Wold Processes . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:2044-2052 Available from https://proceedings.mlr.press/v130/etesami21a.html.

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