 
Summary: Generalized Loopy 2U: A New Algorithm for Approximate
Inference in Credal Networks
Alessandro Antonucci, Marco Zaffalon, Yi Sun, Cassio P. de Campos
Istituto Dalle Molle di Studi sull'Intelligenza Artificiale (IDSIA)
Lugano, Switzerland
Abstract
Credal nets generalize Bayesian nets by relaxing the requirement of precision of proba
bilities. Credal nets are considerably more expressive than Bayesian nets, but this makes
belief updating NPhard even on polytrees. We develop a new efficient algorithm for
approximate belief updating in credal nets. The algorithm is based on an important rep
resentation result we prove for general credal nets: that any credal net can be equivalently
reformulated as a credal net with binary variables; moreover, the transformation, which is
considerably more complex than in the Bayesian case, can be implemented in polynomial
time. The equivalent binary credal net is updated by L2U, a loopy approximate algorithm
for binary credal nets. Thus, we generalize L2U to nonbinary credal nets, obtaining an
accurate and scalable algorithm for the general case, which is approximate only because
of its loopy nature. The accuracy of the inferences is evaluated by empirical tests.
1 Introduction
Bayesian nets (Sect. 2.1) are probabilistic
graphical models based on precise assessments
