Cardinality-Regularized Hawkes-Granger Model

Tsuyoshi Ide, Georgios Kollias, Dzung T. Phan, Naoki Abe

Keywords: point process, Hawkes process, minorization-maximization, cardinality, Granger causality, temporal events

TL;DR: The first point-process-based causal learning model with mathematically guaranteed sparsity.

Abstract: We propose a new sparse Granger-causal learning framework for temporal event data. We focus on a specific class of point processes called the Hawkes process. We begin by pointing out that most of the existing sparse causal learning algorithms for the Hawkes process suffer from a singularity in maximum likelihood estimation. As a result, their sparse solutions can appear only as numerical artifacts. In this paper, we propose a mathematically well-defined sparse causal learning framework based on a cardinality-regularized Hawkes process, which remedies the pathological issues of existing approaches. We leverage the proposed algorithm for the task of instance-wise causal event analysis, where sparsity plays a critical role. We validate the proposed framework with two real use-cases, one from the power grid and the other from the cloud data center management domain.

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Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:2208.10671/code)