Communication-efficient distributed EM algorithm

The Expectation Maximization (EM) algorithm is widely used in latent variable model inference. However, when data are distributed across various locations, directly applying the EM algorithm can often be impractical due to communication expenses and privacy considerations. To address these challenges, a communication-efficient distributed EM algorithm is proposed. Under mild conditions, the proposed estimator achieves the same mean squared error bound as the centralized estimator. Furthermore, the proposed method requires only one extra round of communication compared to the Average estimator. Numerical simulations and a real data example demonstrate that the proposed estimator significantly outperforms the Average estimator in terms of mean squared errors.