Federated Instrumental Variable Analysis via Federated Generalized Method of Moments

2025-05-27

AI Summary

Instrumental variable (IV) analysis for high-dimensional causal inference in privacy-sensitive, federated, and non-i.i.d. settings—common in healthcare and consumer economics—remains largely unaddressed. Method: This paper introduces Federated Generalized Method of Moments (FedGMM), the first framework to formulate IV estimation as a federated zero-sum game and solve it via a distributed gradient descent-ascent (FedGDA) algorithm. FedGMM leverages deep neural networks to model nonlinear moment conditions and establishes theoretical guarantees on local equilibrium existence and estimation consistency. Contribution/Results: We prove that FedGMM consistently estimates local moment conditions across clients. Experiments demonstrate its superiority over existing federated and centralized baselines on heterogeneous multi-source data, achieving higher causal effect estimation accuracy while preserving strong privacy protection.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

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.

Problem

• Federated learning for instrumental variable analysis.
• Solving non-i.i.d. data challenges in decentralized settings.
• Theoretical characterization of federated local optimality.

Innovation

• Federated GMM for IV analysis
• Federated zero-sum game optimization
• Federated gradient descent ascent algorithm