Causal Discovery in High-Dimensional Point Process Networks with Hidden Nodes

TL;DR

This paper introduces a deconfounding method for causal discovery in high-dimensional point process networks with hidden nodes, enabling accurate inference despite unobserved processes and complex connections.

Contribution

It proposes a novel deconfounding procedure that handles unobserved nodes and unknown network size, improving causal inference in multivariate point processes.

Findings

Method effectively identifies causal interactions among observed processes.

Theoretical analysis confirms consistency and robustness.

Numerical studies demonstrate superior performance over naive approaches.

Abstract

Thanks to technological advances leading to near-continuous time observations, emerging multivariate point process data offer new opportunities for causal discovery. However, a key obstacle in achieving this goal is that many relevant processes may not be observed in practice. Naive estimation approaches that ignore these hidden variables can generate misleading results because of the unadjusted confounding. To plug this gap, we propose a deconfounding procedure to estimate high-dimensional point process networks with only a subset of the nodes being observed. Our method allows flexible connections between the observed and unobserved processes. It also allows the number of unobserved processes to be unknown and potentially larger than the number of observed nodes. Theoretical analyses and numerical studies highlight the advantages of the proposed method in identifying causal interactions among the observed processes.