An Asymmetric Independence Model for Causal Discovery on Path Spaces

Georg Manten, Cecilia Casolo, Søren Wengel Mogensen, Niki Kilbertus

Keywords: causal discovery, stochastic processes, path space, E-separation, graphical models, conditional independence, independence model

TL;DR: This paper establishes a framework using DMGs and E-separation to model conditional independencies in SDEs, supporting causal analysis in complex systems.

Abstract: In this paper, we develop the theory linking directed mixed graphs (DMGs) with the graphical ’E-separation’-criterion to form asymmetric independence models that are closed under marginalization and which graphically describe the conditional independence relations among coordinate processes in stochastic differential equations (SDEs) when testing ”which variables enter the governing equations of which other variables.” Besides a global Markov property for cyclic SDEs, which naturally extends to latent, cyclic SDEs, we also characterize graphs, which encode the same set of independence relations and show that in the fully observed case, modelled by directed graphs, each class of graphs under this equivalence relation has a maximal element that is graphi- cally characterizable, analogous to the famous ‘same skeleton and V-structure’ result for Directed Acyclic Graphs (DAGs) and in addition is recoverable from data. Moreover, we conjecture that same holds true in the partially observed case and verify this empirically for graphs up to 4 nodes.

Submission Number: 68