TNPAR: Topological Neural Poisson Auto-Regressive Model for Learning Granger Causal Structure from Event Sequences

TL;DR

A unified topological neural Poisson auto-regressive model with two processes, which encapsulate these two processes within a unified likelihood function, providing an end-to-end framework for this task.

Abstract

Learning Granger causality from event sequences is a challenging but essential task across various applications. Most existing methods rely on the assumption that event sequences are independent and identically distributed (i.i.d.). However, this i.i.d. assumption is often violated due to the inherent dependencies among the event sequences. Fortunately, in practice, we find these dependencies can be modeled by a topological network, suggesting a potential solution to the non-i.i.d. problem by introducing the prior topological network into Granger causal discovery. This observation prompts us to tackle two ensuing challenges: 1) how to model the event sequences while incorporating both the prior topological network and the latent Granger causal structure, and 2) how to learn the Granger causal structure. To this end, we devise a unified topological neural Poisson auto-regressive model with two processes. In the generation process, we employ a variant of the neural Poisson process to model the event sequences, considering influences from both the topological network and the Granger causal structure. In the inference process, we formulate an amortized inference algorithm to infer the latent Granger causal structure. We encapsulate these two processes within a unified likelihood function, providing an end-to-end framework for this task. Experiments on simulated and real-world data demonstrate the effectiveness of our approach.

Figures (8)

• Figure 1: An example of the topological event sequences generated by a mobile network in an operation and maintenance scenario. In this context, $\{n_1, n_2, n_3\}$ represent the network elements, and $\{v_1,v_2,v_3\}$ denote the event types of the alarms. The term $\mathrm{P}_{v_1}(t_1)$ stands for the distribution of $v_1$ alarm at $t_1$ timestamp, and so on. Black arrows represent the correct causal edges, whereas the red arrow represents an incorrect edge. (a) Generation process of topological event sequences. The event distribution varies with time and is influenced by both a topological network (connected by the solid lines) and a Granger causal structure (depicted in part (b)). (b) Ground truth of the Granger causal structure. (c) Granger causal structure learned under i.i.d. assumption.
• Figure 2: An illustration of the generation and inference processes for TNPAR. In this figure, $\mathbf{A}_{0:K}$ represents the causal matrices of $\mathcal{G}_V$, and $\mathbf{B}_{0:K}$ represents the topological matrices of $\mathcal{G}_N$. Solid lines signify the generation process for the data $O_{t}^{v,n}$, and dashed lines correspond to the inference process for the causal matrices $\mathbf{A}_{0:K}$. Observed variables are denoted by the solid circles, with the latent variables represented by the dashed circles.
• Figure 3: Results on the simulated data
• Figure D.4: F1 scores on the simulated data
• Figure D.5: Precision on the simulated data

Theorems & Definitions (6)

• Definition 1: Granger causal discovery from topological event sequences
• Definition 2: Granger non-causality of multi-type event sequences
• Definition 3: Granger non-causality of topological event sequences
• Proposition 1
• Proposition 2
• proof