Relaxing the local independence assumption for quantitative learning in acyclic directed graphical models through hierarchical partition models.
Daniela Golinelli, David Madigan, Guido Consonni · 1999
The simplest method proposed by Spiegelhalter and Lauritzen (1990) to perform quantitative learning in ADG presents a potential weakness: the local independence assumption. We propose to alleviate this problem through the use of Hierarchical Partition Models. Our approach is compared with the previous one from an interpretative and predictive point of view. 1 INTRODUCTION Spiegelhalter and Lauritzen (1990) (S-L) proposed a Bayesian model for Acyclic Directed Graphical Models (ADG) (also known as Bayesian Networks) that has become somewhat standard in the burgeoning literature on learning discrete graphical models. The basic idea is to treat the conditional probabilities of the random variables at each vertex in the graph as unknowns and associate a prior distribution on each one (the conditioning in each case is on the random variables associated with the parent vertices in the graph). The simplest approach of S-L introduces strong assumptions on the unknown conditional probabilities ...