# Federated Instrumental Variable Analysis via Federated Generalized Method of Moments

arXiv: https://arxiv.org/abs/2505.21012 · HTML: https://mlsanity.com/paper/2505.21012/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 70 references that are in the map.
- First posted on arXiv 27 May 2025.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Federated Learning with Matched Averaging](https://mlsanity.com/paper/2002.06440/) (2020)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [The Marginal Value of Adaptive Gradient Methods in Machine Learning](https://mlsanity.com/paper/1705.08292/) (2017)
- [Loss landscapes and optimization in over-parameterized non-linear systems and neural networks](https://mlsanity.com/paper/2003.00307/) (2020)
- [Training GANs with Optimism](https://mlsanity.com/paper/1711.00141/) (2017)
- [Federated Learning for Smart Healthcare: A Survey](https://mlsanity.com/paper/2111.08834/) (2021)
- [Heterogeneous Federated Learning: State-of-the-art and Research Challenges](https://mlsanity.com/paper/2307.10616/) (2023)
- [Federated Learning for Open Banking](https://mlsanity.com/paper/2108.10749/) (2021)
- [Stability and Generalization of Learning Algorithms that Converge to Global Optima](https://mlsanity.com/paper/1710.08402/) (2017)
- [Deep Generalized Method of Moments for Instrumental Variable Analysis](https://mlsanity.com/paper/1905.12495/) (2019)
- [Differentially Private Federated Learning on Heterogeneous Data](https://mlsanity.com/paper/2111.09278/) (2021)
- [Treatment effect estimation with disentangled latent factors](https://mlsanity.com/paper/2001.10652/) (2020)
- [Differentially Private Secure Multi-Party Computation for Federated Learning in Financial Applications](https://mlsanity.com/paper/2010.05867/) (2020)
- [DeepMatch: Balancing Deep Covariate Representations for Causal Inference Using Adversarial Training](https://mlsanity.com/paper/1802.05664/) (2018)
- [Local Stochastic Gradient Descent Ascent: Convergence Analysis and Communication Efficiency](https://mlsanity.com/paper/2102.13152/) (2021)
- [Generalized Optimal Matching Methods for Causal Inference](https://mlsanity.com/paper/1612.08321/) (2016)
- [Federated Minimax Optimization: Improved Convergence Analyses and Algorithms](https://mlsanity.com/paper/2203.04850/) (2022)
- [Personalized Federated Learning under Mixture of Distributions](https://mlsanity.com/paper/2305.01068/) (2023)
- [Adversarial Generalized Method of Moments](https://mlsanity.com/paper/1803.07164/) (2018)
- [Federated Causal Inference in Heterogeneous Observational Data](https://mlsanity.com/paper/2107.11732/) (2021)
- [Industry-Scale Orchestrated Federated Learning for Drug Discovery](https://mlsanity.com/paper/2210.08871/) (2022)
- [An Adaptive Kernel Approach to Federated Learning of Heterogeneous Causal Effects](https://mlsanity.com/paper/2301.00346/) (2023)

## Built on by (most cited first, 1 of 1)

- [A Survey on Federated Causal Discovery and Inference](https://mlsanity.com/paper/2606.23741/) (2026)

## Abstract (arXiv)

Instrumental variables (IV) analysis is an important applied tool for areas such as healthcare and consumer economics. For IV analysis in high-dimensional settings, the Generalized Method of Moments (GMM) using deep neural networks offers an efficient approach. With non-i.i.d. data sourced from scattered decentralized clients, federated learning is a popular paradigm for training the models while promising data privacy. However, to our knowledge, no federated algorithm for either GMM or IV analysis exists to date. In this work, we introduce federated instrumental variables analysis (FedIV) via federated generalized method of moments (FedGMM). We formulate FedGMM as a federated zero-sum game defined by a federated non-convex non-concave minimax optimization problem, which is solved using federated gradient descent ascent (FedGDA) algorithm. One key challenge arises in theoretically characterizing the federated local optimality. To address this, we present properties and existence results of clients' local equilibria via FedGDA limit points. Thereby, we show that the federated solution consistently estimates the local moment conditions of every participating client. The proposed algorithm is backed by extensive experiments to demonstrate the efficacy of our approach.