Pragmatic DML with AI-Learned Representations

Abstract

Text, images, and other rich covariates are increasingly compressed into AI-learned representations and then used as controls in causal analysis. We study when this approach is valid and develop a practical framework for causal inference with learned representations. For a broad class of estimands, an imperfect representation distorts the target causal parameter by the product of two representation errors: one in the outcome regression and one in the balancing weight (or Riesz representer). This yields three constructive results. First, cross-fitted double machine learning (DML) provides valid Wald inference for the representation-dependent target. When representation errors are small, the same interval covers the causal parameter, and it can even attain the semiparametric efficiency bound. Second, fold-wise representation learning (or fine-tuning) is compatible with DML inference for the causal parameter. To this end, we develop convex- and star-aggregation pipelines for learning and combining representations. Third, when representation errors are substantial, we can provide interpretable sensitivity regions and root-n inference for their endpoints. In a multi-modal demand application, seven representation-specific estimates and their star aggregate all imply a negative near-unit elasticity for rank-based price response, and the result remains robust over the reported sensitivity grid.

When Reconstruction Is Not Enough: Doubly Robust Counterfactual and Interventional Mediation Analysis with Learned Multimodal Representations
Cong Cao
arXiv21 Oct 2026PreprintCC BY 4.0Full textStatisticsarXiv
Learning Transfers: Kan Extensions of Topological Invariants of Learned Representations
Luciano Melodia
arXiv9 Oct 2026PreprintCC BY 4.0Full textAlgebra & number theory Geometry & topologyarXiv
Constraint Learning by Optimizing over Trained Neural Networks: A Pragmatic Tutorial
Jiaxiao Fang, Thiago Serra
arXiv26 Oct 2026PreprintarXiv licenceFull textOptimisation & controlarXiv
Adaptive control of pool-type research nuclear reactors: theory limits, pragmatic actuation constraints, and realized performance and adaptation
Dimitrios Pylorof, Linyu Lin
arXiv5 Oct 2026PreprintCC BY-NC-ND 4.0Full textOptimisation & controlarXiv
A Mathematical Theory of Pragmatic Information
Kai Niu, Ping Zhang
arXiv30 Sep 2026PreprintarXiv licenceFull textGeneral mathematicsarXiv

Cite

BibTeX RIS

BibTeX

@misc{fernandez2026pragmatic,
  title = {{Pragmatic DML with AI-Learned Representations}},
  author = {Andres Aradillas Fernandez and Victor Chernozhukov and Carlos Cinelli and Sven Klaassen and Whitney Newey and Martin Spindler and Jan Teichert-Kluge and Suhas Vijaykumar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01935},
  eprint = {2610.01935},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01935},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Pragmatic DML with AI-Learned Representations
AU  - Andres Aradillas Fernandez
AU  - Victor Chernozhukov
AU  - Carlos Cinelli
AU  - Sven Klaassen
AU  - Whitney Newey
AU  - Martin Spindler
AU  - Jan Teichert-Kluge
AU  - Suhas Vijaykumar
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.01935
UR  - https://arxiv.org/abs/2610.01935
AB  - Text, images, and other rich covariates are increasingly compressed into AI-learned representations and then used as controls in causal analysis. We study when this approach is valid and develop a practical framework for causal inference with learned representations. For a broad class of estimands, an imperfect representation distorts the target causal parameter by the product of two representation errors: one in the outcome regression and one in the balancing weight (or Riesz representer). This yields three constructive results. First, cross-fitted double machine learning (DML) provides valid Wald inference for the representation-dependent target. When representation errors are small, the same interval covers the causal parameter, and it can even attain the semiparametric efficiency bound. Second, fold-wise representation learning (or fine-tuning) is compatible with DML inference for the causal parameter. To this end, we develop convex- and star-aggregation pipelines for learning and combining representations. Third, when representation errors are substantial, we can provide interpretable sensitivity regions and root-n inference for their endpoints. In a multi-modal demand application, seven representation-specific estimates and their star aggregate all imply a negative near-unit elasticity for rank-based price response, and the result remains robust over the reported sensitivity grid.
ER  -

Abstract

Related

Cite