Quadrature Rules in General Continuous Bayesian Networks : Discrete Inference without Discretization
Marvin Lasserre, Régis Lebrun, Pierre-Henri Wuillemin · HAL (Le Centre pour la Communication Scientifique Directe) · 2024
Probabilistic inference in high-dimensional continuous or hybrid domains poses significantchallenges, commonly addressed through discretization, sampling, or reliance on parametricassumptions. The drawbacks of these methods are well-known: inaccuracy, slow computationalspeeds or overly constrained models.This paper introduces a novel general inference algorithm designed for Bayesian networks featuringboth discrete and continuous variables. The algorithm avoids the discretization of continuous densitiesinto histograms by employing quadrature rules to compute continuous integrals and avoids the use of a parametricmodel by using orthogonal polynomials to represent the posterior density. Additionally, itpreserves the computational efficiency of classical sum-product algorithms by using an auxiliary discreteBayesian networks appropriately constructed to make continuous inference.Numerous experiments are conducted using either the conditional linear Gaussian modelas a benchmark, or non-Gaussian models for greater generality. Our algorithm demonstratessignificant improvements both in speed and accuracy when compared with existing methods.