Causality: models, reasoning, and inference
Causality: models, reasoning, and inference
Learning Bayesian Networks
Information Sciences: an International Journal
VC dimension and inner product space induced by Bayesian networks
International Journal of Approximate Reasoning
On the incompatibility of faithfulness and monotone DAG faithfulness
Artificial Intelligence
On the testable implications of causal models with hidden variables
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
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Bayesian networks are a probabilistic representation for uncertain relationships, which has proven to be useful for modeling real world problems. Causal Independence and stochastic Independence are two important notations to characterize the flow of information on Bayesian network. They correspond to unidirectional separation and directional separation in Bayesian network structure respectively. In this paper, we focus on the relationship between directional separation and unidirectional separation. By using the layer sorting structure of Bayesian networks, the condition demanded to be satisfied to ensure d-separation and ud-separation hold is given. At the same time, we show that it is easy to find d-separation and ud-separation sets to identify direct causal effect quickly.