Log In Sign Up

Learning Network of Multivariate Hawkes Processes: A Time Series Approach

by   Jalal Etesami, et al.

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 (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.


page 1

page 2

page 3

page 4


Normalized multivariate time series causality analysis and causal graph reconstruction

Causality analysis is an important problem lying at the heart of science...

Causal Discovery in Hawkes Processes by Minimum Description Length

Hawkes processes are a special class of temporal point processes which e...

Fast Estimation of Causal Interactions using Wold Processes

We here focus on the task of learning Granger causality matrices for mul...

Measuring Sample Path Causal Influences with Relative Entropy

We present a sample path dependent measure of causal influence between t...

Robust Online Detection in Serially Correlated Directed Network

As the complexity of production processes increases, the diversity of da...

A Sample Path Measure of Causal Influence

We present a sample path dependent measure of causal influence between t...