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Structural causal models (SCMs) are widely used in various disciplines to represent causal relationships among variables in complex systems. Unfortunately, the true underlying directed acyclic graph (DAG) structure is often unknown, and determining it from observational or interventional data remains a challenging task. However, in many situations, the end goal is to identify changes (shifts) in causal mechanisms between related SCMs rather than recovering the entire underlying DAG structure. Examples include analyzing gene regulatory network structure changes between healthy and cancerous individuals or understanding variations in biological pathways under different cellular contexts. This paper focuses on identifying functional mechanism shifts in two or more related SCMs over the same set of variables -- without estimating the entire DAG structure of each SCM. Prior work under this setting assumed linear models with Gaussian noises; instead, in this work we assume that each SCM belongs to the more general class of nonlinear additive noise models (ANMs). A key contribution of this work is to show that the Jacobian of the score function for the mixture distribution allows for identification of shifts in general non-parametric functional mechanisms. Once the shifted variables are identified, we leverage recent work to estimate the structural differences, if any, for the shifted variables. Experiments on synthetic and real-world data are provided to showcase the applicability of this approach.
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Causal Inference Despite Limited Global Confounding via Mixture Models
A Bayesian Network is a directed acyclic graph (DAG) on a set of n random variables (the vertices); a Bayesian Network Distribution (BND) is a probability distribution on the random variables that is Markovian on the graph. A finite k-mixture of such models is graphically represented by a larger graph which has an additional “hidden” (or “latent”) random variable U, ranging in {1,...,k}, and a directed edge from U to every other vertex. Models of this type are fundamental to causal inference, where U models an unobserved confounding effect of multiple populations, obscuring the causal relationships in the observable DAG. By solving the mixture problem and recovering the joint probability distribution with U, traditionally unidentifiable causal relationships become identifiable. Using a reduction to the more well-studied “product” case on empty graphs, we give the first algorithm to learn mixtures of non-empty DAGs.
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- Award ID(s):
- 1909972
- PAR ID:
- 10475956
- Editor(s):
- van der Schaar, M.; Zhang, C.; Janzing, D.
- Publisher / Repository:
- PMLR
- Date Published:
- Journal Name:
- Proceedings of Machine Learning Research
- Volume:
- 213
- ISSN:
- 2640-3498
- Page Range / eLocation ID:
- 574-601
- Format(s):
- Medium: X
- Location:
- Tubingen, Germany
- Sponsoring Org:
- National Science Foundation
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