Learning network of multivariate hawkes processes: A time series approach

Jalal Etesami, Negar Kiyavash, Kun Zhang, Kushagra Singhal

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Learning the influence structure of multiple time series data is of great interest to many disciplines. This paper studies the problem of recovering the causal structure in network of multivariate linear Hawkes processes. In such processes, the occurrence of an event in one process affects the probability of occurrence of new events in some other processes. Thus, a natural notion of causality exists between such processes captured by the support of the excitation matrix. We show that the resulting causal influence network is equivalent to the Directed Information graph (DIG) of the processes, which encodes the causal factorization of the joint distribution of the processes. Furthermore, we present an algorithm for learning the support of excitation matrix of a class of multivariate Hawkes processes with exponential exciting functions (or equivalently the DIG). The performance of the algorithm is evaluated on synthesized multivariate Hawkes networks as well as a stock market and MemeTracker real-world dataset.

Original languageEnglish (US)
Title of host publication32nd Conference on Uncertainty in Artificial Intelligence 2016, UAI 2016
EditorsDominik Janzing, Alexander Ihler
PublisherAssociation For Uncertainty in Artificial Intelligence (AUAI)
Pages162-171
Number of pages10
ISBN (Electronic)9781510827806
StatePublished - Jan 1 2016
Event32nd Conference on Uncertainty in Artificial Intelligence 2016, UAI 2016 - Jersey City, United States
Duration: Jun 25 2016Jun 29 2016

Publication series

Name32nd Conference on Uncertainty in Artificial Intelligence 2016, UAI 2016

Other

Other32nd Conference on Uncertainty in Artificial Intelligence 2016, UAI 2016
CountryUnited States
CityJersey City
Period6/25/166/29/16

ASJC Scopus subject areas

  • Artificial Intelligence

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  • Cite this

    Etesami, J., Kiyavash, N., Zhang, K., & Singhal, K. (2016). Learning network of multivariate hawkes processes: A time series approach. In D. Janzing, & A. Ihler (Eds.), 32nd Conference on Uncertainty in Artificial Intelligence 2016, UAI 2016 (pp. 162-171). (32nd Conference on Uncertainty in Artificial Intelligence 2016, UAI 2016). Association For Uncertainty in Artificial Intelligence (AUAI).