Geometric Causal Models
2026-07-06 • Machine Learning
Machine Learning
AI summaryⓘ
The authors introduce geometric causal models (GCMs) to analyze data where samples are connected or dependent, like spatial maps or networks. They use mathematical symmetries related to the structure of the data (such as translations in space or node rearrangements in graphs) to help find cause-and-effect relationships. By applying group theory and ergodic theory, they develop methods to identify and estimate causal effects even when data isn’t independently distributed. They apply their approach to genetic data, creating causal models that respect DNA’s symmetries and improve understanding of genetic variation effects. Their work extends standard causal inference methods to more complex, structured data types.
causal inferencegeometric causal modelsdependent datasymmetrygroup theoryergodic theorygeometric deep learningBayesian inferencedo-calculusgenomic data
Authors
Eli N. Weinstein, David M. Blei
Abstract
Scientists often seek to draw causal inferences from structured data that is not independently and identically distributed, such as spatial data, network data, or molecular data. We develop geometric causal models (GCMs), a framework for causal inference from dependent data that exploits underlying symmetries of the data generating process. For example, in spatial data, we consider processes that are symmetric under translations, or in graph data, symmetric under permutations of the nodes. We show how symmetries, formalized with group theory, can enable causal identification and estimation. We deploy ergodic theory for amenable groups to establish identification, and combine geometric deep learning with scalable Bayesian inference for estimation. We recover i.i.d. causal models and do-calculus when the data is a sequence and the symmetry is permutation equivariance, and find novel types of causal models when we use alternate structures and symmetries. As an example, we construct a causal model that satisfies the symmetries of DNA. This GCM enables new estimators for the effects of genetic variation, combining deep functional genomics models to describe outcomes and DNA language models to describe propensities. We illustrate on semisynthetic data.