# Spectral Representation for Causal Estimation with Hidden Confounders

arXiv: https://arxiv.org/abs/2407.10448 · HTML: https://mlsanity.com/paper/2407.10448/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 53 references that are in the map.
- First posted on arXiv 15 Jul 2024.

## Builds on (most cited first, 24 of 24)

- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Reinforcement Learning in Feature Space: Matrix Bandit, Kernels, and Regret Bound](https://mlsanity.com/paper/1905.10389/) (2019)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [Deep Generalized Method of Moments for Instrumental Variable Analysis](https://mlsanity.com/paper/1905.12495/) (2019)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [Learning Deep Features in Instrumental Variable Regression](https://mlsanity.com/paper/2010.07154/) (2020)
- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
- [Making Linear MDPs Practical via Contrastive Representation Learning](https://mlsanity.com/paper/2207.07150/) (2022)
- [Optimal Rates for Regularized Conditional Mean Embedding Learning](https://mlsanity.com/paper/2208.01711/) (2022)
- [Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluation](https://mlsanity.com/paper/2106.03907/) (2021)
- [Spectral Decomposition Representation for Reinforcement Learning](https://mlsanity.com/paper/2208.09515/) (2022)
- [Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach](https://mlsanity.com/paper/2007.01290/) (2020)
- [Optimal Sup-norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regression](https://mlsanity.com/paper/1508.03365/) (2015)
- [Contrastive UCB: Provably Efficient Contrastive Self-Supervised Learning in Online Reinforcement Learning](https://mlsanity.com/paper/2207.14800/) (2022)
- [Latent Variable Representation for Reinforcement Learning](https://mlsanity.com/paper/2212.08765/) (2022)
- [Instrumental Variable Regression via Kernel Maximum Moment Loss](https://mlsanity.com/paper/2010.07684/) (2020)
- [Deep Learning Methods for Proximal Inference via Maximum Moment Restriction](https://mlsanity.com/paper/2205.09824/) (2022)
- [Minimax Instrumental Variable Regression and L2 Convergence Guarantees without Identification or Closedness](https://mlsanity.com/paper/2302.05404/) (2023)
- [Inference on Strongly Identified Functionals of Weakly Identified Functions](https://mlsanity.com/paper/2208.08291/) (2022)
- [Spectral Representation Learning for Conditional Moment Models](https://mlsanity.com/paper/2210.16525/) (2022)
- [Source Condition Double Robust Inference on Functionals of Inverse Problems](https://mlsanity.com/paper/2307.13793/) (2023)
- [Regularized DeepIV with Model Selection](https://mlsanity.com/paper/2403.04236/) (2024)

## Built on by (most cited first, 12 of 12)

- [Nonparametric Instrumental Regression via Kernel Methods is Minimax Optimal](https://mlsanity.com/paper/2411.19653/) (2024)
- [Self-Supervised Evolution Operator Learning for High-Dimensional Dynamical Systems](https://mlsanity.com/paper/2505.18671/) (2025)
- [Representation Learning via Non-Contrastive Mutual Information](https://mlsanity.com/paper/2504.16667/) (2025)
- [Demystifying Spectral Feature Learning for Instrumental Variable Regression](https://mlsanity.com/paper/2506.10899/) (2025)
- [Optimality and Adaptivity of Deep Neural Features for Instrumental Variable Regression](https://mlsanity.com/paper/2501.04898/) (2025)
- [An Analysis of Causal Effect Estimation using Outcome Invariant Data Augmentation](https://mlsanity.com/paper/2510.25128/) (2025)
- [Outcome-Aware Spectral Feature Learning for Instrumental Variable Regression](https://mlsanity.com/paper/2512.00919/) (2025)
- [ActiveCQ: Active Estimation of Causal Quantities](https://mlsanity.com/paper/2509.24293/) (2025)
- [Toward Scalable and Valid Conditional Independence Testing with Spectral Representations](https://mlsanity.com/paper/2512.19510/) (2025)
- [Canonical correlation regression with noisy data](https://mlsanity.com/paper/2512.22697/) (2025)
- [Spectral Ghost in Representation Learning: from Component Analysis to Self-Supervised Learning](https://mlsanity.com/paper/2601.20154/) (2026)
- [Learning Conditional Expectation Operators via Functional Newton Updates](https://mlsanity.com/paper/2609.35598/) (2026)

## Abstract (arXiv)

We address the problem of causal effect estimation where hidden confounders are present, with a focus on two settings: instrumental variable regression with additional observed confounders, and proxy causal learning. Our approach uses a singular value decomposition of a conditional expectation operator, followed by a saddle-point optimization problem, which, in the context of IV regression, can be thought of as a neural net generalization of the seminal approach due to Darolles et al. [2011]. Saddle-point formulations have gathered considerable attention recently, as they can avoid double sampling bias and are amenable to modern function approximation methods. We provide experimental validation in various settings, and show that our approach outperforms existing methods on common benchmarks.