A Completed Information Projection Interpretation of Expectation Propagation

Expectation propagation (EP), a family of methods for iterative approximate statistical inference closely related to belief propagation, is linked to a hybrid between Dykstra’s algorithm with cyclic Bregman projections and the method of alternating Bregman projections from convex analysis via the use of the information geometry of exponential families. Doing so justifies extrinsic information extraction within the context of projections on convex sets, without the need for an iteration varying convex set which was required in previous information geometric descriptions of EP. It is suggested that new convergence results for EP might be developed through this connection by adapting the convergence proofs for alternating projections and Dykstra’s algorithm with cyclic Bregman projections.