Skip to content

Files

Latest commit

d6ba44b · Sep 12, 2024

History

History
55 lines (55 loc) · 2.26 KB

2024-09-12-hochsprung24a.md

File metadata and controls

55 lines (55 loc) · 2.26 KB
title abstract openreview section layout series publisher issn id month tex_title firstpage lastpage page order cycles bibtex_author author date address container-title volume genre issued pdf extras
A Global Markov Property for Solutions of Stochastic Difference Equations and the corresponding Full Time Graphs
Structural Causal Models (SCMs) are an important tool in causal inference. They induce a graph and if the graph is acyclic, a unique observational distribution. A standard result states that in this acyclic case, the induced observational distribution satisfies a d-separation global Markov property relative to the induced graph. Time series can also be modelled like SCMs: One just interprets the stochastic difference equations that a time series solves as structural equations. However, technical problems arise when time series "start" at minus infinity. In particular, a d-separation global Markov property for time series and the corresponding infinite graphs, the so-called full time graphs, has thus far only been shown for stable vector autoregressive processes with independent finite-second-moment noise. In this paper, we prove a much more general version of this Markov property. We discuss our assumptions and study violations of them. Doing so hints at several pitfalls at the intersection of time series analysis and causal inference. Moreover, we introduce a new projection procedure for these infinite graphs which might be of independent interest.
o5pOj2IDYB
Papers
inproceedings
Proceedings of Machine Learning Research
PMLR
2640-3498
hochsprung24a
0
A Global Markov Property for Solutions of Stochastic Difference Equations and the corresponding Full Time Graphs
1698
1726
1698-1726
1698
false
Hochsprung, Tom and Runge, Jakob and Gerhardus, Andreas
given family
Tom
Hochsprung
given family
Jakob
Runge
given family
Andreas
Gerhardus
2024-09-12
Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence
244
inproceedings
date-parts
2024
9
12