There are several methods dealing with this problem, such as the well known iterative proportional fitting procedure (IPFP), proposed by R. Kruithof in 1937 for situations that are consistent, and the GEMA algorithm (Generalized Expectation Maximization Algorithm) given by Jirka Vomlel 1999 for inconsistent situations. IPFP does not converge in inconsistent situations but alternates among among a set of certain states. For GEMA, it is very data sensitive and its computation involve the whole knowledge base (denoted as joint probability distribution (JPD) here), so it is very expensive.

We proposed a new method SMOOTH to address this problem. The goal is to deal with both consistent and inconsistent constraints. Our basic idea is to do a modification bi-directionally. When IPFP goes into alternation, we modify the constraints according to the entire JPD, so the certain alternating states can be driven to closer. Experiment results verify that SMOOTH works well for both consistent and inconsistent constraints. Moreover, SMOOTH is data insensitive, factorizable and can be accelerated. We describe a use case for belief updating in Bayesian networks via the virtual evidence method. ]]>