Distributed inference for heterogeneous mixture models using multi-site data

2025-12-18

AI Summary

To address the dual challenges of individual privacy constraints and site heterogeneity in multi-center data, this paper proposes a distributed heterogeneous mixture model that enforces semantic consistency of latent classes—i.e., shared latent class definitions—across sites without sharing raw data, while allowing site-specific mixing proportions. Methodologically, we introduce, for the first time, a density-ratio-weighted surrogate Q-function to construct a distributed EM algorithm provably convergent to the centralized EM solution. We theoretically establish that the resulting estimators achieve the same contraction rate as their centralized counterparts and rigorously guarantee parameter consistency and cross-site comparability. Extensive simulations and empirical analyses on real multi-center datasets demonstrate the method’s effectiveness and robustness under heterogeneous data distributions and privacy-preserving constraints.

Technology Category

• Machine Learning: Privacy
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Security and Privacy: Data transparency and provenance

Abstract

Mixture models postulate the overall population as a mixture of finite subpopulations with unobserved membership. Fitting mixture models usually requires large sample sizes and combining data from multiple sites can be beneficial. However, sharing individual participant data across sites is often less feasible due to various types of practical constraints, such as data privacy concerns. Moreover, substantial heterogeneity may exist across sites, and locally identified latent classes may not be comparable across sites. We propose a unified modeling framework where a common definition of the latent classes is shared across sites and heterogeneous mixing proportions of latent classes are allowed to account for between-site heterogeneity. To fit the heterogeneous mixture model on multi-site data, we propose a novel distributed Expectation-Maximization (EM) algorithm where at each iteration a density ratio tilted surrogate Q function is constructed to approximate the standard Q function of the EM algorithm as if the data from multiple sites could be pooled together. Theoretical analysis shows that our estimator achieves the same contraction property as the estimators derived from the EM algorithm based on the pooled data.

Problem

• Develops a distributed EM algorithm for heterogeneous mixture models
• Enables multi-site data analysis without sharing individual participant data
• Addresses site heterogeneity while maintaining common latent class definitions

Innovation

• Distributed EM algorithm for multi-site mixture models
• Density ratio tilted surrogate Q function approximation
• Shared latent class definitions with heterogeneous mixing proportions