Parameter estimation via expectation maximization - Expectation consistent algorithm

In the context of the expectation-maximization (EM) algorithm, which often faces challenges due to intractable posterior distributions, this study explores an innovative approach by integrating the EM algorithm with expectation consistent (EC) approximate inference. Our method involves the incorporation of the EC algorithm into the M-step of the EM algorithm, resulting in the EM-EC algorithm. We demonstrate that the fixed points of the proposed EM-EC algorithm correspond to stationary points of a specific constrained auxiliary function, thereby providing a variational interpretation of the algorithm. Through simulations, we showcase the effectiveness and robustness of this novel approach, highlighting its potential for advancing the field of Bayesian network estimation.