Uncovering Causality from Multivariate Hawkes Integrated Cumulants

Abstract

We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each nodes of the process, but also disentangles the causality relationships between them. Our approach is the first that leads to an estimation of this matrix without any parametric modeling and estimation of the kernels themselves. A consequence is that it can give an estimation of causality relationships between nodes (or users), based on their activity timestamps (on a social network for instance), without knowing or estimating the shape of the activities lifetime. For that purpose, we introduce a moment matching method that fits the third-order integrated cumulants of the process. We show on numerical experiments that our approach is indeed very robust to the shape of the kernels, and gives appealing results on the MemeTracker database.

References in corpus (10)

• TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems
• Robust dynamic classes revealed by measuring the response function of a social system
• The Loss Surfaces of Multilayer Networks
• The DARPA Twitter Bot Challenge
• Learning Granger Causality for Hawkes Processes
• Branching ratio approximation for the self-exciting Hawkes process
• COEVOLVE: A Joint Point Process Model for Information Diffusion and Network Co-evolution
• Estimation of slowly decreasing Hawkes kernels: Application to high frequency order book modelling
• Nonparametric Markovian Learning of Triggering Kernels for Mutually Exciting and Mutually Inhibiting Multivariate Hawkes Processes
• Rethinking LDA: moment matching for discrete ICA

Cited by in corpus (6)

• Visual Causality Analysis of Event Sequence Data
• Nonparametric Conditional Local Independence Testing
• Predicting Smoking Events with a Time-Varying Semi-Parametric Hawkes Process Model
• Superposition-Assisted Stochastic Optimization for Hawkes Processes
• Analysis of order book flows using a nonparametric estimation of the branching ratio matrix
• A Metric Space for Point Process Excitations