Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
The complexity of linear problems in fields
Journal of Symbolic Computation
A logic for reasoning about probabilities
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
Axioms and algorithms for inferences involving probabilistic independence
Information and Computation
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Algorithmic algebra
On the undecidability of implications between embedded multivalued database dependencies
Information and Computation
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Equivalence and synthesis of causal models
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Graphical models and exponential families
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
Strong completeness and faithfulness in Bayesian networks
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
On the testable implications of causal models with hidden variables
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Conditional independences in gaussian vectors and rings of polynomials
WCII'02 Proceedings of the 2002 international conference on Conditionals, Information, and Inference
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Recent improvements on Tarski's procedure for quantifier elimination in the first order theory of real numbers makes it feasible to solve small instances of the following problems completely automatically: 1. listing all equality and inequality constraints implied by a graphical model with hidden variables. 2. Comparing graphical models with hidden variables (i.e., model equivalence, inclusion, and overlap). 3. Answering questions about the identification of a model or portion of a model, and about bounds on quantities derived from a model. 4. Determining whether an independence assertion is implied from a given set of independence assertions. We discuss the foundations of quantifier elimination and demonstrate its application to these problems.