Identifying Unique Spatial-Temporal Bayesian Network without Markov Equivalence

TL;DR

This paper introduces a novel Spatial-Temporal Bayesian Network (STBN) model that uniquely captures causality in spatio-temporal data, overcoming limitations of existing models and providing an efficient identification algorithm with state-of-the-art accuracy.

Contribution

It proposes the STBN framework for modeling spatial-temporal causality and the HCE algorithm for its unique identification, addressing issues of Markov equivalence and invariance assumptions.

Findings

HCE algorithm achieves state-of-the-art accuracy

STBN uniquely models spatial-temporal causality

Theoretical proof of STBN's uniqueness

Abstract

Identifying vanilla Bayesian network to model spatial-temporal causality can be a critical yet challenging task. Different Markovian-equivalent directed acyclic graphs would be identified if the identifiability is not satisfied. To address this issue, Directed Cyclic Graph is proposed to drop the directed acyclic constraint. But it does not always hold, and cannot model dynamical time-series process. Then, Full Time Graph is proposed with introducing high-order time delay. Full Time Graph has no Markov equivalence class by assuming no instantaneous effects. But, it also assumes that the causality is invariant with varying time, that is not always satisfied in the spatio-temporal scenarios. Thus, in this work, a Spatial-Temporal Bayesian Network (STBN) is proposed to theoretically model the spatial-temporal causality from the perspective of information transfer. STBN explains the disappearance of network structure $X\rightarrow Z \rightarrow Y$ and $X\leftarrow Z \leftarrow Y$ by the principle of information path blocking. And finally, the uniqueness of STBN is proved. Based on this, a High-order Causal Entropy (HCE) algorithm is also proposed to uniquely identify STBN under time complexity $\mathcal{O}(n^3\tau_{max})$, where $n$ is the number of variables and $\tau_{max}$ is the maximum time delay. Numerical experiments are conducted with comparison to other baseline algorithms. The results show that HCE algorithm obtains state-of-the-art identification accuracy. The code is available at https://github.com/KMY-SEU/HCE.