A primer on optimal transport for causal inference with observational data

• URL: http://arxiv.org/abs/2503.07811v2
• Date: Wed, 12 Mar 2025 18:18:00 GMT
• Title: A primer on optimal transport for causal inference with observational data
• Authors: Florian F Gunsilius,
• Abstract summary: The goal of this review is to offer an introduction to the surprisingly deep existing connections between optimal transport and the identification of causal effects with observational data.<n>As a result, this review is intended to unify the language and notation between different areas of statistics, mathematics, and econometrics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The theory of optimal transportation has developed into a powerful and elegant framework for comparing probability distributions, with wide-ranging applications in all areas of science. The fundamental idea of analyzing probabilities by comparing their underlying state space naturally aligns with the core idea of causal inference, where understanding and quantifying counterfactual states is paramount. Despite this intuitive connection, explicit research at the intersection of optimal transport and causal inference is only beginning to develop. Yet, many foundational models in causal inference have implicitly relied on optimal transport principles for decades, without recognizing the underlying connection. Therefore, the goal of this review is to offer an introduction to the surprisingly deep existing connections between optimal transport and the identification of causal effects with observational data -- where optimal transport is not just a set of potential tools, but actually builds the foundation of model assumptions. As a result, this review is intended to unify the language and notation between different areas of statistics, mathematics, and econometrics, by pointing out these existing connections, and to explore novel problems and directions for future work in both areas derived from this realization.

Related papers

• Towards Understanding Extrapolation: a Causal Lens [53.15488984371969]
  We provide a theoretical understanding of when extrapolation is possible and offer principled methods to achieve it. Under this formulation, we cast the extrapolation problem into a latent-variable identification problem. Our theory reveals the intricate interplay between the underlying manifold's smoothness and the shift properties.
  arXiv  Detail & Related papers  (2025-01-15T21:29:29Z)
• Deriving Causal Order from Single-Variable Interventions: Guarantees & Algorithm [14.980926991441345]
  We show that datasets containing interventional data can be effectively extracted under realistic assumptions about the data distribution. We introduce interventional faithfulness, which relies on comparisons between the marginal distributions of each variable across observational and interventional settings. We also introduce Intersort, an algorithm designed to infer the causal order from datasets containing large numbers of single-variable interventions.
  arXiv  Detail & Related papers  (2024-05-28T16:07:17Z)
• Optimal Transport for Structure Learning Under Missing Data [31.240965564055138]
  We propose a score-based algorithm for learning causal structures from missing data based on optimal transport. Our framework is shown to recover the true causal structure more effectively than competing methods in most simulations and real-data settings.
  arXiv  Detail & Related papers  (2024-02-23T10:49:04Z)
• Conditional Optimal Transport on Function Spaces [53.9025059364831]
  We develop a theory of constrained optimal transport problems that describe block-triangular Monge maps. This generalizes the theory of optimal triangular transport to separable infinite-dimensional function spaces with general cost functions. We present numerical experiments that demonstrate the computational applicability of our theoretical results for amortized and likelihood-free inference of functional parameters.
  arXiv  Detail & Related papers  (2023-11-09T18:44:42Z)
• Advancing Counterfactual Inference through Nonlinear Quantile Regression [77.28323341329461]
  We propose a framework for efficient and effective counterfactual inference implemented with neural networks. The proposed approach enhances the capacity to generalize estimated counterfactual outcomes to unseen data. Empirical results conducted on multiple datasets offer compelling support for our theoretical assertions.
  arXiv  Detail & Related papers  (2023-06-09T08:30:51Z)
• Inherent Inconsistencies of Feature Importance [6.02357145653815]
  Feature importance is a method that assigns scores to the contribution of individual features on prediction outcomes. This paper presents an axiomatic framework designed to establish coherent relationships among the different contexts of feature importance scores.
  arXiv  Detail & Related papers  (2022-06-16T14:21:51Z)
• Congestion-aware Multi-agent Trajectory Prediction for Collision Avoidance [110.63037190641414]
  We propose to learn congestion patterns explicitly and devise a novel "Sense--Learn--Reason--Predict" framework. By decomposing the learning phases into two stages, a "student" can learn contextual cues from a "teacher" while generating collision-free trajectories. In experiments, we demonstrate that the proposed model is able to generate collision-free trajectory predictions in a synthetic dataset.
  arXiv  Detail & Related papers  (2021-03-26T02:42:33Z)
• Localisation in quasiperiodic chains: a theory based on convergence of local propagators [68.8204255655161]
  We present a theory of localisation in quasiperiodic chains with nearest-neighbour hoppings, based on the convergence of local propagators. Analysing the convergence of these continued fractions, localisation or its absence can be determined, yielding in turn the critical points and mobility edges. Results are exemplified by analysing the theory for three quasiperiodic models covering a range of behaviour.
  arXiv  Detail & Related papers  (2021-02-18T16:19:52Z)
• A contribution to Optimal Transport on incomparable spaces [4.873362301533825]
  This thesis proposes to study the complex scenario in which the different data belong to incomparable spaces. This thesis proposes a set of Optimal Transport tools for these different cases.
  arXiv  Detail & Related papers  (2020-11-09T14:13:52Z)
• Generalization Properties of Optimal Transport GANs with Latent Distribution Learning [52.25145141639159]
  We study how the interplay between the latent distribution and the complexity of the pushforward map affects performance. Motivated by our analysis, we advocate learning the latent distribution as well as the pushforward map within the GAN paradigm.
  arXiv  Detail & Related papers  (2020-07-29T07:31:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.