# Representation Learning for Sample-Efficient CATE Estimation by Leveraging Multiple Outcomes

arXiv: https://arxiv.org/abs/2609.06294 · HTML: https://mlsanity.com/paper/2609.06294/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 65 references that are in the map.
- First posted on arXiv 5 Sep 2026.

## Builds on (most cited first, 30 of 34)

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- [Big Transfer (BiT): General Visual Representation Learning](https://mlsanity.com/paper/1912.11370/) (2019)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Causal Inference in Natural Language Processing: Estimation, Prediction, Interpretation and Beyond](https://mlsanity.com/paper/2109.00725/) (2021)
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- [External Validity: From Do-Calculus to Transportability Across Populations](https://mlsanity.com/paper/1503.01603/) (2015)
- [CausalML: Python Package for Causal Machine Learning](https://mlsanity.com/paper/2002.11631/) (2020)
- [Treatment effect estimation with disentangled latent factors](https://mlsanity.com/paper/2001.10652/) (2020)
- [On the role of surrogates in the efficient estimation of treatment effects with limited outcome data](https://mlsanity.com/paper/2003.12408/) (2020)
- [Long-term Causal Inference Under Persistent Confounding via Data Combination](https://mlsanity.com/paper/2202.07234/) (2022)
- [Transfer Learning on Heterogeneous Feature Spaces for Treatment Effects Estimation](https://mlsanity.com/paper/2210.06183/) (2022)
- [Zero-shot causal learning](https://mlsanity.com/paper/2301.12292/) (2023)
- [Transfer Learning for Estimating Causal Effects using Neural Networks](https://mlsanity.com/paper/1808.07804/) (2018)
- [Long-term Causal Effects Estimation via Latent Surrogates Representation Learning](https://mlsanity.com/paper/2208.04589/) (2022)
- [Data fusion methods for the heterogeneity of treatment effect and confounding function](https://mlsanity.com/paper/2007.12922/) (2020)
- [On the Actionability of Outcome Prediction](https://mlsanity.com/paper/2309.04470/) (2023)
- [Machine Learning Who to Nudge: Causal vs Predictive Targeting in a Field Experiment on Student Financial Aid Renewal](https://mlsanity.com/paper/2310.08672/) (2023)

## Abstract (arXiv)

Estimating conditional average treatment effects (CATE) enables efficient targeting of interventions, but many applications have limited experimental samples, making it difficult to estimate heterogeneous effects from high-dimensional covariates. In such settings, policymakers and medical practitioners often succumb to the curse of dimensionality or apply off-the-shelf dimension reduction methods that may not preserve treatment heterogeneity. Yet these domains often come with large historical datasets measuring a wide range of outcomes -- a source of supervision that is rarely exploited in practice. Following causal representation learning, we hypothesize that such domains with high-dimensional covariates have lower-dimensional underlying dynamics. We can thus leverage the diverse outcomes measured in historical data to learn a lower-dimensional representation of the covariates. Theoretically, we prove that when the auxiliary outcomes satisfy a set of surrogacy conditions and the representation retains relevant covariate information, the original CATE is identified when the high-dimensional covariates are replaced by the learned representation. Combined with existing dimension-dependent rates for CATE estimation, the result implies greater sample-efficiency on the same experimental sample. Additionally, we characterize the bias-variance tradeoff when the assumptions do not hold perfectly, and show that the representation-based estimator can still achieve lower error when the reduction in estimator variance outweighs the bias due to compression. Empirically, we evaluate the method on synthetic data and semi-synthetic medical data.