Loopy Belief Propagation in Bayesian Networks : origin and possibilistic perspectives
This addresses convergence issues in probabilistic inference algorithms for researchers in AI and machine learning, but it is incremental as it builds on existing methods.
The paper synthesizes work on belief propagation algorithms for Bayesian networks, noting that Loopy Belief Propagation (LBP) can approximate posterior probabilities well when it converges but oscillates in networks like QMR, preventing convergence. The authors propose translating the inference problem to a possibilistic framework to improve LBP's convergence.
In this paper we present a synthesis of the work performed on two inference algorithms: the Pearl's belief propagation (BP) algorithm applied to Bayesian networks without loops (i.e. polytree) and the Loopy belief propagation (LBP) algorithm (inspired from the BP) which is applied to networks containing undirected cycles. It is known that the BP algorithm, applied to Bayesian networks with loops, gives incorrect numerical results i.e. incorrect posterior probabilities. Murphy and al. [7] find that the LBP algorithm converges on several networks and when this occurs, LBP gives a good approximation of the exact posterior probabilities. However this algorithm presents an oscillatory behaviour when it is applied to QMR (Quick Medical Reference) network [15]. This phenomenon prevents the LBP algorithm from converging towards a good approximation of posterior probabilities. We believe that the translation of the inference computation problem from the probabilistic framework to the possibilistic framework will allow performance improvement of LBP algorithm. We hope that an adaptation of this algorithm to a possibilistic causal network will show an improvement of the convergence of LBP.