Federated Instrumental Variable Analysis via Federated Generalized Method of Moments

TL;DR

This paper introduces FedIV, a federated approach for instrumental variables analysis using GMM and deep neural networks, enabling privacy-preserving estimation in decentralized high-dimensional data settings.

Contribution

It develops FedGMM, a novel federated GMM algorithm for IV analysis, formulated as a federated minimax problem solved by FedGDA, with theoretical guarantees and empirical validation.

Findings

FedGMM effectively estimates local moment conditions.

The algorithm converges to local equilibria in federated settings.

Experimental results demonstrate superior performance over baselines.

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.