Expectation Consistent Approximate Inference: Generalizations and Convergence
This is an incremental improvement for researchers in approximate inference methods, offering a more general framework.
The paper tackles the problem of probabilistic inference by generalizing the expectation consistent (EC) method to create Generalized Expectation Consistency (GEC), which applies to MAP and MMSE estimation, and analyzes its fixed points, convergence, and performance relative to replica predictions.
Approximations of loopy belief propagation, including expectation propagation and approximate message passing, have attracted considerable attention for probabilistic inference problems. This paper proposes and analyzes a generalization of Opper and Winther's expectation consistent (EC) approximate inference method. The proposed method, called Generalized Expectation Consistency (GEC), can be applied to both maximum a posteriori (MAP) and minimum mean squared error (MMSE) estimation. Here we characterize its fixed points, convergence, and performance relative to the replica prediction of optimality.