Federated Instrumental Variable Analysis via Federated Generalized Method of Moments
Geetika, Somya Tyagi, Bapi Chatterjee
TL;DR
The paper addresses federated instrumental variables analysis under non-i.i.d. client data by formulating a federated generalized method of moments (FedGMM) and solving it as a federated zero-sum minimax problem. It introduces FedIV and its federated DeepGMM (FedDeepGMM) variant, with a Federated Gradient Descent Ascent (FedGDA) algorithm to learn a global causal function while preserving data privacy. Theoretical results establish the existence of approximate federated equilibria and show that, under mild heterogeneity, the global estimator is consistent for the true local moments, linking server-side optimization to client-side moment conditions. Empirical evaluations on synthetic and image-based datasets demonstrate convergence and competitive performance relative to centralized DeepGMM, validating the framework for privacy-preserving causal inference in federated settings. The work provides a principled, equilibrium-focused approach to federated IV analysis with deep moment networks and offers a foundation for further exploration of mixed-strategy equilibria in federated zero-sum games.
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.