A probability propagation in hypertrees

Author(s):  
Chun-Hung Tzeng
Author(s):  
M. JULIA FLORES ◽  
JOSE A. GÁMEZ ◽  
KRISTIAN G. OLESEN

When a Bayesian network (BN) is modified, for example adding or deleting a node, or changing the probability distributions, we usually will need a total recompilation of the model, despite feeling that a partial (re)compilation could have been enough. Especially when considering dynamic models, in which variables are added and removed very frequently, these recompilations are quite resource consuming. But even further, for the task of building a model, which is in many occasions an iterative process, there is a clear lack of flexibility. When we use the term Incremental Compilation or IC we refer to the possibility of modifying a network and avoiding a complete recompilation to obtain the new (and different) join tree (JT). The main point we intend to study in this work is JT-based inference in Bayesian networks. Apart from undertaking the triangulation problem itself, we have achieved a great improvement for the compilation in BNs. We do not develop a new architecture for BNs inference, but taking some already existing framework JT-based for probability propagation such as Hugin or Shenoy and Shafer, we have designed a method that can be successfully applied to get better performance, as the experimental evaluation will show.


2000 ◽  
Vol 12 (1) ◽  
pp. 1-41 ◽  
Author(s):  
Yair Weiss

Graphical models, such as Bayesian networks and Markov networks, represent joint distributions over a set of variables by means of a graph. When the graph is singly connected, local propagation rules of the sort proposed by Pearl (1988) are guaranteed to converge to the correct posterior probabilities. Recently a number of researchers have empirically demonstrated good performance of these same local propagation schemes on graphs with loops, but a theoretical understanding of this performance has yet to be achieved. For graphical models with a single loop, we derive an analytical relationship between the probabilities computed using local propagation and the correct marginals. Using this relationship we show a category of graphical models with loops for which local propagation gives rise to provably optimal maximum a posteriori assignments (although the computed marginals will be incorrect). We also show how nodes can use local information in the messages they receive in order to correct their computed marginals. We discuss how these results can be extended to graphical models with multiple loops and show simulation results suggesting that some properties of propagation on single-loop graphs may hold for a larger class of graphs. Specifically we discuss the implication of our results for understanding a class of recently proposed error-correcting codes known as turbo codes.


Sign in / Sign up

Export Citation Format

Share Document