Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Connectionist learning of belief networks
Artificial Intelligence
A Tighter Bound for Graphical Models
Neural Computation
Parallel linear programming in fixed dimension almost surely in constant time
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Mean field theory for sigmoid belief networks
Journal of Artificial Intelligence Research
Variational probabilistic inference and the QMR-DT network
Journal of Artificial Intelligence Research
Loopy belief propagation for approximate inference: an empirical study
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
A new class of upper bounds on the log partition function
IEEE Transactions on Information Theory
Approximate inference by Markov chains on union spaces
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
An anytime scheme for bounding posterior beliefs
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Active tuples-based scheme for bounding posterior beliefs
Journal of Artificial Intelligence Research
Bounding the probability of error for high precision optical character recognition
The Journal of Machine Learning Research
The Journal of Machine Learning Research
Hi-index | 0.01 |
In this article we present an algorithm to compute bounds on the marginals of a graphical model. For several small clusters of nodes upper and lower bounds on the marginal values are computed independently of the rest of the network. The range of allowed probability distributions over the surrounding nodes is restricted using earlier computed bounds. As we will show, this can be considered as a set of constraints in a linear programming problem of which the objective function is the marginal probability of the center nodes. In this way knowledge about the maginals of neighbouring clusters is passed to other clusters thereby tightening the bounds on their marginals. We show that sharp bounds can be obtained for undirected and directed graphs that are used for practical applications, but for which exact computations are infeasible.