Optimal Transport Theory Offers Fresh Foundation for Inferring Causation from Observational Data

Researchers have documented a deep, often overlooked connection between optimal transport theory and causal inference with observational data. Rather than introducing an entirely new toolkit, the work shows that optimal transport principles have been embedded within foundational causal models for decades—only without being explicitly recognized as such.

The Hidden Connection#

The intersection of optimal transport and causal inference is intuitive in hindsight. Optimal transport provides an elegant framework for comparing probability distributions by analyzing their underlying state spaces. Causal inference, by contrast, centers on understanding and quantifying counterfactual scenarios—what would have happened under different conditions. Both endeavors share a common goal: making meaningful comparisons across different probability structures. Yet explicit research linking these two fields has only recently begun to emerge.

A Unifying Review#

The new primer aims to unify terminology and notation across statistics, mathematics, and econometrics by mapping out these existing connections. Rather than present optimal transport as merely another tool in the causal inference toolkit, the work demonstrates that optimal transport principles actually form the mathematical bedrock upon which key causal identification assumptions rest. This reframing has implications for how researchers understand their own methods and potentially how they develop new ones.

Future Directions#

By making these connections explicit, the research opens avenues for novel problems and applications in both optimal transport and causal inference. The unified perspective may help researchers spot patterns across disciplines and develop techniques that leverage insights from both areas more deliberately than previous methods have done.