On the Convergence of Belief Propagation Based on Sum-Product and Max-Product
Meng Xiang-yan · Shuxue de shijian yu renshi · 2011
On the basis of induction to Markov networks and standard belief propagation, this paper analyzes the convergence of BP based on sum-product and max-product taking Markov networks with no loop and four hidden nodes as example.The results suggest that BP based on sum-product converges to global optimal solution as network is Markov network without loop,and that BP based on max-product converges to a unique fixed point regardless of initial conditions in a finite number of iterations.While the BP based on max-product exists only one optimal point,this fixed point is optimal point.Research on the convergence of BP would be viewed as a beneficial attempt on basic theoretical research on BP.