A Variational Inference Approach to Learning Multivariate Wold Processes

Jalal Etesami · William Trouleau · Negar Kiyavash · Matthias Grossglauser · Patrick Thiran

Keywords: [ Models and Methods ] [ Time Series and Sequence Models ]


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.

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