# Identifying Unique Spatial-Temporal Bayesian Network without Markov Equivalence

arXiv: https://arxiv.org/abs/2211.10085 · HTML: https://mlsanity.com/paper/2211.10085/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 34 references that are in the map.
- First posted on arXiv 18 Nov 2022.

## Builds on (most cited first, 9 of 9)

- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Learning Temporally Causal Latent Processes from General Temporal Data](https://mlsanity.com/paper/2110.05428/) (2021)
- [Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systems](https://mlsanity.com/paper/2206.06169/) (2022)
- [Rhino: Deep Causal Temporal Relationship Learning With History-dependent Noise](https://mlsanity.com/paper/2210.14706/) (2022)
- [Directed Cyclic Graphical Representations of Feedback Models](https://mlsanity.com/paper/1302.4982/) (2013)
- [A Constraint-Based Algorithm for the Structural Learning of Continuous-Time Bayesian Networks](https://mlsanity.com/paper/2007.03248/) (2020)
- [Integrating Markov processes with structural causal modeling enables counterfactual inference in complex systems](https://mlsanity.com/paper/1911.02175/) (2019)

## Built on by (most cited first, 1 of 1)

- [Spatio-Temporal Graphical Counterfactuals: An Overview](https://mlsanity.com/paper/2407.01875/) (2024)

## Abstract (arXiv)

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 Xrightarrow Z rightarrow Y and Xleftarrow 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 O(n3τmax), where n is the number of variables and τmax 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.