Identifying Causal Changes Between Linear Structural Equation Models

Vineet Malik, Kevin Bello, Asish Ghoshal, Jean Honorio

Keywords: structural equation models, distribution shifts, root cause analysis, intervention target estimation, difference of precision matrices

TL;DR: New identifiability conditions and algorithm for direct learning of causal changes between linear SEMs

Abstract:

Learning the structures of structural equation models (SEMs) as directed acyclic graphs (DAGs) from data is crucial for representing causal relationships in various scientific domains. Instead of estimating individual DAG structures, it is often preferable to directly estimate changes in causal relations between conditions, such as changes in genetic expression between healthy and diseased subjects.
This work studies the problem of directly estimating the difference between two linear SEMs, i.e. *without estimating the individual DAG structures*, given two sets of samples drawn from the individual SEMs. We consider general classes of linear SEMs where the noise distributions are allowed to be Gaussian or non-Gaussian and have different noise variances across the variables in the individual SEMs. We rigorously characterize novel conditions related to the topological layering of the structural difference that lead to the *identifiability* of the difference DAG (DDAG). Moreover, we propose an *efficient* algorithm to identify the DDAG via sequential re-estimation of the difference of precision matrices. A surprising implication of our results is that causal changes can be identifiable even between *non-identifiable* models such as Gaussian SEMs with unequal noise variances. Synthetic experiments are presented to validate our theoretical results and to show the scalability of our method.

List Of Authors: Malik, Vineet and Bello, Kevin and Ghoshal, Asish and Honorio, Jean

Submission Number: 644