# Adversarial Generalized Method of Moments

arXiv: https://arxiv.org/abs/1803.07164 · HTML: https://mlsanity.com/paper/1803.07164/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2018.

## Built on by (most cited first, 30 of 34)

- [Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach](https://mlsanity.com/paper/2103.14029/) (2021)
- [Instrumental Variable Value Iteration for Causal Offline Reinforcement Learning](https://mlsanity.com/paper/2102.09907/) (2021)
- [On Instrumental Variable Regression for Deep Offline Policy Evaluation](https://mlsanity.com/paper/2105.10148/) (2021)
- [DoWhy: Addressing Challenges in Expressing and Validating Causal Assumptions](https://mlsanity.com/paper/2108.13518/) (2021)
- [Auto IV: Counterfactual Prediction via Automatic Instrumental Variable Decomposition](https://mlsanity.com/paper/2107.05884/) (2021)
- [Demystifying Causal Features on Adversarial Examples and Causal Inoculation for Robust Network by Adversarial Instrumental Variable Regression](https://mlsanity.com/paper/2303.01052/) (2023)
- [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)
- [Falsification of Internal and External Validity in Observational Studies via Conditional Moment Restrictions](https://mlsanity.com/paper/2301.13133/) (2023)
- [Source Condition Double Robust Inference on Functionals of Inverse Problems](https://mlsanity.com/paper/2307.13793/) (2023)
- [Functional Generalized Empirical Likelihood Estimation for Conditional Moment Restrictions](https://mlsanity.com/paper/2207.04771/) (2022)
- [Regularized DeepIV with Model Selection](https://mlsanity.com/paper/2403.04236/) (2024)
- [Nonparametric Instrumental Variable Regression through Stochastic Approximate Gradients](https://mlsanity.com/paper/2402.05639/) (2024)
- [Estimation Beyond Data Reweighting: Kernel Method of Moments](https://mlsanity.com/paper/2305.10898/) (2023)
- [A Look into Causal Effects under Entangled Treatment in Graphs: Investigating the Impact of Contact on MRSA Infection](https://mlsanity.com/paper/2307.08237/) (2023)
- [Stochastic Optimization Algorithms for Instrumental Variable Regression with Streaming Data](https://mlsanity.com/paper/2405.19463/) (2024)
- [Targeted Sequential Indirect Experiment Design](https://mlsanity.com/paper/2405.19985/) (2024)
- [Quasi-Bayesian Dual Instrumental Variable Regression](https://mlsanity.com/paper/2106.08750/) (2021)
- [Causal Inference with Complex Treatments: A Survey](https://mlsanity.com/paper/2407.14022/) (2024)
- [Adversarial Machine Learning in Text Analysis and Generation](https://mlsanity.com/paper/2101.08675/) (2021)
- [Instrument Space Selection for Kernel Maximum Moment Restriction](https://mlsanity.com/paper/2106.03340/) (2021)
- [Adversarial Estimators](https://mlsanity.com/paper/2204.10495/) (2022)
- [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)
- [Taking a Moment for Distributional Robustness](https://mlsanity.com/paper/2405.05461/) (2024)
- [Geometry-Aware Instrumental Variable Regression](https://mlsanity.com/paper/2405.11633/) (2024)
- [Detecting clinician implicit biases in diagnoses using proximal causal inference](https://mlsanity.com/paper/2501.16399/) (2025)
- [Federated Instrumental Variable Analysis via Federated Generalized Method of Moments](https://mlsanity.com/paper/2505.21012/) (2025)

## Abstract (arXiv)

We provide an approach for learning deep neural net representations of models described via conditional moment restrictions. Conditional moment restrictions are widely used, as they are the language by which social scientists describe the assumptions they make to enable causal inference. We formulate the problem of estimating the underling model as a zero-sum game between a modeler and an adversary and apply adversarial training. Our approach is similar in nature to Generative Adversarial Networks (GAN), though here the modeler is learning a representation of a function that satisfies a continuum of moment conditions and the adversary is identifying violating moments. We outline ways of constructing effective adversaries in practice, including kernels centered by k-means clustering, and random forests. We examine the practical performance of our approach in the setting of non-parametric instrumental variable regression.