Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Graphoids: a qualitative framework for probabilistic inference
Graphoids: a qualitative framework for probabilistic inference
Axioms and algorithms for inferences involving probabilistic independence
Information and Computation
Artificial intelligence in perspective
Causal networks: semantics and expressiveness
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
Learning causal trees from dependence information
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 2
| Hi-index | 0.00 |
Testing the validity of probabilistic models containing unmeasured (hidden) variables is shown to be a hard task. We show that the task of testing whether models are structurally incompatible with the data at hand, requires an exponential number of independence evaluations, each of the form: "X is conditionally independent of Y, given Z." In contrast, a linear number of such evaluations is required to test a standard Bayesian network (one per vertex). On the positive side, we show that if a network with hidden variables G has a tree skeleton, checking whether G represents a given probability model P requires the polynomial number of such independence evaluations. Moreover, we provide an algorithm that efficiently constructs a tree-structured Bayesian network (with hidden variables) that represents P if such a network exists, and further recognizes when such a network does not exist.