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Cumulants of Hawkes Processes are Robust to Observation Noise
William Trouleau · Jalal Etesami · Matthias Grossglauser · Negar Kiyavash · Patrick Thiran

Wed Jul 21 06:45 PM -- 06:50 PM (PDT) @

Multivariate Hawkes processes (MHPs) are widely used in a variety of fields to model the occurrence of causally related discrete events in continuous time. Most state-of-the-art approaches address the problem of learning MHPs from perfect traces without noise. In practice, the process through which events are collected might introduce noise in the timestamps. In this work, we address the problem of learning the causal structure of MHPs when the observed timestamps of events are subject to random and unknown shifts, also known as random translations. We prove that the cumulants of MHPs are invariant to random translations, and therefore can be used to learn their underlying causal structure. Furthermore, we empirically characterize the effect of random translations on state-of-the-art learning methods. We show that maximum likelihood-based estimators are brittle, while cumulant-based estimators remain stable even in the presence of significant time shifts.

Author Information

William Trouleau (EPFL)
Jalal Etesami (Bosch Research Center for AI, Germany)
Matthias Grossglauser (EPFL)

Matthias Grossglauser is Associate Professor in the School of Computer and Communication Sciences at EPFL. His current research interests are in machine learning for large social systems, stochastic models and algorithms for graph and mobility mining, and recommender systems. He is also the current director of the Doctoral School in Computer and Communication Sciences. From 2007-2010, he was with the Nokia Research Center (NRC) in Helsinki, Finland, serving as head of the Internet Laboratory, and later as head of a tech-transfer program focused on data mining, analytics, and machine learning. In addition, he served on Nokia's CEO Technology Council, a technology advisory group reporting to the CEO. Prior to this, he was Assistant Professor at EPFL, and a Research Scientist in the Networking and Distributed Systems Laboratory at AT&T Research in New Jersey. He received the 1998 Cor Baayen Award from the European Research Consortium for Informatics and Mathematics (ERCIM), the 2006 CoNEXT/SIGCOMM Rising Star Award, and two best paper awards. He served on the editorial board of IEEE/ACM Transactions on Networking, and on numerous Technical Program Committees.

Negar Kiyavash (École Polytechnique Fédérale de Lausanne)
Patrick Thiran (EPFL)

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